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

Percentage Accurate: 58.1% → 98.0%

Time: 21.0s

Alternatives: 22

Speedup: 2.8×

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: 58.1% 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: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(t\_1 + z\right)}{t\_0} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t\_0} + \frac{t\_1}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \left(\left(\frac{y}{{x}^{3}} + \frac{3655.1204654076414}{{x}^{2}}\right) - \left(\frac{110.1139242984811}{x} + \frac{130977.50649958357}{{x}^{3}}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))))
   (if (<= (/ (* (- x 2.0) (+ t_1 z)) t_0) 5e+288)
     (* (+ x -2.0) (+ (/ z t_0) (/ t_1 t_0)))
     (*
      x
      (+
       4.16438922228
       (-
        (+ (/ y (pow x 3.0)) (/ 3655.1204654076414 (pow x 2.0)))
        (+ (/ 110.1139242984811 x) (/ 130977.50649958357 (pow x 3.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288) {
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	} else {
		tmp = x * (4.16438922228 + (((y / pow(x, 3.0)) + (3655.1204654076414 / pow(x, 2.0))) - ((110.1139242984811 / x) + (130977.50649958357 / pow(x, 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_1 = x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)
    if ((((x - 2.0d0) * (t_1 + z)) / t_0) <= 5d+288) then
        tmp = (x + (-2.0d0)) * ((z / t_0) + (t_1 / t_0))
    else
        tmp = x * (4.16438922228d0 + (((y / (x ** 3.0d0)) + (3655.1204654076414d0 / (x ** 2.0d0))) - ((110.1139242984811d0 / x) + (130977.50649958357d0 / (x ** 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288) {
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	} else {
		tmp = x * (4.16438922228 + (((y / Math.pow(x, 3.0)) + (3655.1204654076414 / Math.pow(x, 2.0))) - ((110.1139242984811 / x) + (130977.50649958357 / Math.pow(x, 3.0)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)
	tmp = 0
	if (((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288:
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0))
	else:
		tmp = x * (4.16438922228 + (((y / math.pow(x, 3.0)) + (3655.1204654076414 / math.pow(x, 2.0))) - ((110.1139242984811 / x) + (130977.50649958357 / math.pow(x, 3.0)))))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(t_1 + z)) / t_0) <= 5e+288)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z / t_0) + Float64(t_1 / t_0)));
	else
		tmp = Float64(x * Float64(4.16438922228 + Float64(Float64(Float64(y / (x ^ 3.0)) + Float64(3655.1204654076414 / (x ^ 2.0))) - Float64(Float64(110.1139242984811 / x) + Float64(130977.50649958357 / (x ^ 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	tmp = 0.0;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288)
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	else
		tmp = x * (4.16438922228 + (((y / (x ^ 3.0)) + (3655.1204654076414 / (x ^ 2.0))) - ((110.1139242984811 / x) + (130977.50649958357 / (x ^ 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$1 + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+288], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(4.16438922228 + N[(N[(N[(y / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + N[(3655.1204654076414 / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(110.1139242984811 / x), $MachinePrecision] + N[(130977.50649958357 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.0000000000000003e288

   1. Initial program 96.0%

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

      1. associate-/l* 99.6%

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

      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. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 5.0000000000000003e288 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. sub-neg 0.0%

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

      3. metadata-eval 0.0%

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

      4. fma-define 0.0%

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

      5. fma-define 0.0%

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

      6. fma-define 0.0%

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

      7. fma-define 0.0%

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

      8. fma-define 0.0%

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

      9. fma-define 0.0%

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

      10. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x around inf 99.2%

      \[\leadsto \color{blue}{x \cdot \left(\left(4.16438922228 + \left(\frac{3655.1204654076414}{{x}^{2}} + \frac{y}{{x}^{3}}\right)\right) - \left(110.1139242984811 \cdot \frac{1}{x} + 130977.50649958357 \cdot \frac{1}{{x}^{3}}\right)\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 99.2%

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

      2. +-commutative 99.2%

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

      3. associate-*r/ 99.2%

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

      4. metadata-eval 99.2%

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

      5. associate-*r/ 99.2%

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

      6. metadata-eval 99.2%

         \[\leadsto x \cdot \left(4.16438922228 + \left(\left(\frac{y}{{x}^{3}} + \frac{3655.1204654076414}{{x}^{2}}\right) - \left(\frac{110.1139242984811}{x} + \frac{\color{blue}{130977.50649958357}}{{x}^{3}}\right)\right)\right) \]

   7. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} + \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 + \left(\left(\frac{y}{{x}^{3}} + \frac{3655.1204654076414}{{x}^{2}}\right) - \left(\frac{110.1139242984811}{x} + \frac{130977.50649958357}{{x}^{3}}\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x + 43.3400022514\right)\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(t\_0 + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot t\_0\right)\right)}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+288}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ x 43.3400022514)))
        (t_1
         (/
          (*
           (- x 2.0)
           (+
            (*
             x
             (+
              (*
               x
               (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
              y))
            z))
          (+
           (* x (+ (* x (+ t_0 263.505074721)) 313.399215894))
           47.066876606))))
   (if (<= t_1 (- INFINITY))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        z
        (+
         47.066876606
         (* x (+ 313.399215894 (+ (* x 263.505074721) (* x t_0))))))))
     (if (<= t_1 5e+288)
       t_1
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (t_1 <= 5e+288) {
		tmp = t_1;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (t_1 <= 5e+288) {
		tmp = t_1;
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x + 43.3400022514)
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))))
	elif t_1 <= 5e+288:
		tmp = t_1
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x + 43.3400022514))
	t_1 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(t_0 + 263.505074721)) + 313.399215894)) + 47.066876606))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * t_0))))))));
	elseif (t_1 <= 5e+288)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x + 43.3400022514);
	t_1 = ((x - 2.0) * ((x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)) + z)) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	elseif (t_1 <= 5e+288)
		tmp = t_1;
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(t$95$0 + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+288], t$95$1, N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 6.1%

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

      1. associate-/l* 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. fma-define 99.5%

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

      5. fma-define 99.5%

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

      6. fma-define 99.5%

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

      7. fma-define 99.5%

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

      8. fma-define 99.5%

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

      9. fma-define 99.5%

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

      10. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.5%

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

      1. distribute-rgt-in 99.5%

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

      2. *-commutative 99.5%

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

      3. +-commutative 99.5%

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

   7. Applied egg-rr 99.5%

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

   8. Taylor expanded in x around inf 99.7%

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

   if -inf.0 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.0000000000000003e288

   1. Initial program 99.5%

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

   if 5.0000000000000003e288 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. sub-neg 0.0%

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

      3. metadata-eval 0.0%

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

      4. fma-define 0.0%

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

      5. fma-define 0.0%

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

      6. fma-define 0.0%

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

      7. fma-define 0.0%

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

      8. fma-define 0.0%

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

      9. fma-define 0.0%

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

      10. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. unsub-neg 99.2%

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

      5. mul-1-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. mul-1-neg 99.2%

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

      8. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606\\ t_1 := x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)\\ \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(t\_1 + z\right)}{t\_0} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{t\_0} + \frac{t\_1}{t\_0}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (*
           x
           (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
          47.066876606))
        (t_1
         (*
          x
          (+
           (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
           y))))
   (if (<= (/ (* (- x 2.0) (+ t_1 z)) t_0) 5e+288)
     (* (+ x -2.0) (+ (/ z t_0) (/ t_1 t_0)))
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        (-
         (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
         101.7851458539211)
        x))))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288) {
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / 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) :: t_1
    real(8) :: tmp
    t_0 = (x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0
    t_1 = x * ((x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)) + y)
    if ((((x - 2.0d0) * (t_1 + z)) / t_0) <= 5d+288) then
        tmp = (x + (-2.0d0)) * ((z / t_0) + (t_1 / t_0))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	double t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	double tmp;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288) {
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y)
	tmp = 0
	if (((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288:
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0))
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	t_1 = Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y))
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(t_1 + z)) / t_0) <= 5e+288)
		tmp = Float64(Float64(x + -2.0) * Float64(Float64(z / t_0) + Float64(t_1 / t_0)));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606;
	t_1 = x * ((x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)) + y);
	tmp = 0.0;
	if ((((x - 2.0) * (t_1 + z)) / t_0) <= 5e+288)
		tmp = (x + -2.0) * ((z / t_0) + (t_1 / t_0));
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * N[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(t$95$1 + z), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], 5e+288], N[(N[(x + -2.0), $MachinePrecision] * N[(N[(z / t$95$0), $MachinePrecision] + N[(t$95$1 / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64))) < 5.0000000000000003e288

   1. Initial program 96.0%

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

      1. associate-/l* 99.6%

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

      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. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 5.0000000000000003e288 < (/.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x #s(literal 104109730557/25000000000 binary64)) #s(literal 393497462077/5000000000 binary64)) x) #s(literal 4297481763/31250000 binary64)) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x #s(literal 216700011257/5000000000 binary64)) x) #s(literal 263505074721/1000000000 binary64)) x) #s(literal 156699607947/500000000 binary64)) x) #s(literal 23533438303/500000000 binary64)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.0%

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

      2. sub-neg 0.0%

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

      3. metadata-eval 0.0%

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

      4. fma-define 0.0%

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

      5. fma-define 0.0%

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

      6. fma-define 0.0%

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

      7. fma-define 0.0%

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

      8. fma-define 0.0%

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

      9. fma-define 0.0%

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

      10. fma-define 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. unsub-neg 99.2%

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

      5. mul-1-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. mul-1-neg 99.2%

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

      8. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+288}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(\frac{z}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} + \frac{x \cdot \left(x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right) + y\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x + 43.3400022514\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot t\_0\right)\right)}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot \left(t\_0 + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ x 43.3400022514))))
   (if (<= x -2.2e+25)
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        z
        (+
         47.066876606
         (* x (+ 313.399215894 (+ (* x 263.505074721) (* x t_0))))))))
     (if (<= x 1.15e+25)
       (/
        (*
         (- x 2.0)
         (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154)))))))
        (+ (* x (+ (* x (+ t_0 263.505074721)) 313.399215894)) 47.066876606))
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double tmp;
	if (x <= -2.2e+25) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (x <= 1.15e+25) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x + 43.3400022514d0)
    if (x <= (-2.2d+25)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * t_0)))))))
    else if (x <= 1.15d+25) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0))))))) / ((x * ((x * (t_0 + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double tmp;
	if (x <= -2.2e+25) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (x <= 1.15e+25) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x + 43.3400022514)
	tmp = 0
	if x <= -2.2e+25:
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))))
	elif x <= 1.15e+25:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x + 43.3400022514))
	tmp = 0.0
	if (x <= -2.2e+25)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * t_0))))))));
	elseif (x <= 1.15e+25)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))) / Float64(Float64(x * Float64(Float64(x * Float64(t_0 + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x + 43.3400022514);
	tmp = 0.0;
	if (x <= -2.2e+25)
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	elseif (x <= 1.15e+25)
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+25], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+25], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(t$95$0 + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2000000000000001e25

   1. Initial program 3.7%

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

      1. associate-/l* 11.8%

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

      2. sub-neg 11.8%

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

      3. metadata-eval 11.8%

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

      4. fma-define 11.8%

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

      5. fma-define 11.8%

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

      6. fma-define 11.8%

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

      7. fma-define 11.8%

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

      8. fma-define 11.8%

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

      9. fma-define 11.8%

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

      10. fma-define 11.8%

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

   3. Simplified 11.8%

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

   5. Taylor expanded in z around 0 11.8%

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

      1. distribute-rgt-in 11.8%

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

      2. *-commutative 11.8%

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

      3. +-commutative 11.8%

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

   7. Applied egg-rr 11.8%

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

   8. Taylor expanded in x around inf 97.6%

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

   if -2.2000000000000001e25 < x < 1.1499999999999999e25

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. *-commutative 90.6%

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

   5. Simplified 97.3%

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

   if 1.1499999999999999e25 < x

   1. Initial program 15.8%

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

      1. associate-/l* 15.9%

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

      2. sub-neg 15.9%

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

      3. metadata-eval 15.9%

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

      4. fma-define 15.9%

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

      5. fma-define 15.9%

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

      6. fma-define 15.9%

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

      7. fma-define 15.9%

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

      8. fma-define 15.9%

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

      9. fma-define 15.9%

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

      10. fma-define 15.9%

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

   3. Simplified 15.9%

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

   5. Taylor expanded in x around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. unsub-neg 99.2%

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

      5. mul-1-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. mul-1-neg 99.2%

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

      8. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+25}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-32} \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) + x \cdot \left(0.0212463641547976 \cdot \left(y - 275.038832832\right) - y \cdot -0.28294182010212804\right)\right) - z \cdot -0.28294182010212804\right) + z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.2e-32) (not (<= x 5.2e-15)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      z
      (+
       47.066876606
       (*
        x
        (+
         313.399215894
         (+ (* x 263.505074721) (* x (* x (+ x 43.3400022514))))))))))
   (+
    (*
     x
     (-
      (+
       (* 0.0212463641547976 (+ z (* y -2.0)))
       (*
        x
        (-
         (* 0.0212463641547976 (- y 275.038832832))
         (* y -0.28294182010212804))))
      (* z -0.28294182010212804)))
    (* z -0.0424927283095952))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.2e-32) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = (x * (((0.0212463641547976 * (z + (y * -2.0))) + (x * ((0.0212463641547976 * (y - 275.038832832)) - (y * -0.28294182010212804)))) - (z * -0.28294182010212804))) + (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 <= (-3.2d-32)) .or. (.not. (x <= 5.2d-15))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * (x * (x + 43.3400022514d0)))))))))
    else
        tmp = (x * (((0.0212463641547976d0 * (z + (y * (-2.0d0)))) + (x * ((0.0212463641547976d0 * (y - 275.038832832d0)) - (y * (-0.28294182010212804d0))))) - (z * (-0.28294182010212804d0)))) + (z * (-0.0424927283095952d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.2e-32) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = (x * (((0.0212463641547976 * (z + (y * -2.0))) + (x * ((0.0212463641547976 * (y - 275.038832832)) - (y * -0.28294182010212804)))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.2e-32) or not (x <= 5.2e-15):
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))))
	else:
		tmp = (x * (((0.0212463641547976 * (z + (y * -2.0))) + (x * ((0.0212463641547976 * (y - 275.038832832)) - (y * -0.28294182010212804)))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.2e-32) || !(x <= 5.2e-15))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * Float64(x * Float64(x + 43.3400022514))))))))));
	else
		tmp = Float64(Float64(x * Float64(Float64(Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))) + Float64(x * Float64(Float64(0.0212463641547976 * Float64(y - 275.038832832)) - Float64(y * -0.28294182010212804)))) - Float64(z * -0.28294182010212804))) + Float64(z * -0.0424927283095952));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.2e-32) || ~((x <= 5.2e-15)))
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	else
		tmp = (x * (((0.0212463641547976 * (z + (y * -2.0))) + (x * ((0.0212463641547976 * (y - 275.038832832)) - (y * -0.28294182010212804)))) - (z * -0.28294182010212804))) + (z * -0.0424927283095952);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.2e-32], N[Not[LessEqual[x, 5.2e-15]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(0.0212463641547976 * N[(y - 275.038832832), $MachinePrecision]), $MachinePrecision] - N[(y * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * -0.28294182010212804), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * -0.0424927283095952), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.2000000000000002e-32 or 5.20000000000000009e-15 < x

   1. Initial program 21.7%

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

      1. associate-/l* 25.4%

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

      2. sub-neg 25.4%

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

      3. metadata-eval 25.4%

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

      4. fma-define 25.4%

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

      5. fma-define 25.4%

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

      6. fma-define 25.4%

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

      7. fma-define 25.4%

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

      8. fma-define 25.4%

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

      9. fma-define 25.4%

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

      10. fma-define 25.3%

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

   3. Simplified 25.3%

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

   5. Taylor expanded in z around 0 25.4%

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

      1. distribute-rgt-in 25.4%

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

      2. *-commutative 25.4%

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

      3. +-commutative 25.4%

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

   7. Applied egg-rr 25.4%

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

   8. Taylor expanded in x around inf 94.3%

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

   if -3.2000000000000002e-32 < x < 5.20000000000000009e-15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 99.0%

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

   4. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{-0.0424927283095952 \cdot z + x \cdot \left(\left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) + x \cdot \left(0.0212463641547976 \cdot \left(y - 275.038832832\right) - 6.658593866711955 \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)\right)\right) - -0.28294182010212804 \cdot z\right)} \]

   5. Taylor expanded in z around 0 99.4%

      \[\leadsto -0.0424927283095952 \cdot z + x \cdot \left(\left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) + \color{blue}{x \cdot \left(0.0212463641547976 \cdot \left(y - 275.038832832\right) - -0.28294182010212804 \cdot y\right)}\right) - -0.28294182010212804 \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-32} \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(0.0212463641547976 \cdot \left(z + y \cdot -2\right) + x \cdot \left(0.0212463641547976 \cdot \left(y - 275.038832832\right) - y \cdot -0.28294182010212804\right)\right) - z \cdot -0.28294182010212804\right) + z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x + 43.3400022514\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot t\_0\right)\right)}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(t\_0 + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ x 43.3400022514))))
   (if (<= x -2.1e+25)
     (*
      (+ x -2.0)
      (+
       4.16438922228
       (/
        z
        (+
         47.066876606
         (* x (+ 313.399215894 (+ (* x 263.505074721) (* x t_0))))))))
     (if (<= x 1.15e+25)
       (/
        (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
        (+ (* x (+ (* x (+ t_0 263.505074721)) 313.399215894)) 47.066876606))
       (*
        (+ x -2.0)
        (+
         4.16438922228
         (/
          (-
           (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
           101.7851458539211)
          x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double tmp;
	if (x <= -2.1e+25) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (x <= 1.15e+25) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (x + 43.3400022514d0)
    if (x <= (-2.1d+25)) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * t_0)))))))
    else if (x <= 1.15d+25) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * (t_0 + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (x + 43.3400022514);
	double tmp;
	if (x <= -2.1e+25) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	} else if (x <= 1.15e+25) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x + 43.3400022514)
	tmp = 0
	if x <= -2.1e+25:
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))))
	elif x <= 1.15e+25:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x + 43.3400022514))
	tmp = 0.0
	if (x <= -2.1e+25)
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * t_0))))))));
	elseif (x <= 1.15e+25)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(t_0 + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x + 43.3400022514);
	tmp = 0.0;
	if (x <= -2.1e+25)
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * t_0)))))));
	elseif (x <= 1.15e+25)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * (t_0 + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+25], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e+25], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(x * N[(N[(x * N[(t$95$0 + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.0999999999999999e25

   1. Initial program 3.7%

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

      1. associate-/l* 11.8%

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

      2. sub-neg 11.8%

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

      3. metadata-eval 11.8%

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

      4. fma-define 11.8%

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

      5. fma-define 11.8%

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

      6. fma-define 11.8%

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

      7. fma-define 11.8%

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

      8. fma-define 11.8%

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

      9. fma-define 11.8%

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

      10. fma-define 11.8%

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

   3. Simplified 11.8%

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

   5. Taylor expanded in z around 0 11.8%

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

      1. distribute-rgt-in 11.8%

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

      2. *-commutative 11.8%

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

      3. +-commutative 11.8%

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

   7. Applied egg-rr 11.8%

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

   8. Taylor expanded in x around inf 97.6%

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

   if -2.0999999999999999e25 < x < 1.1499999999999999e25

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 97.2%

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

      1. *-commutative 90.7%

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

   5. Simplified 97.2%

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

   if 1.1499999999999999e25 < x

   1. Initial program 15.8%

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

      1. associate-/l* 15.9%

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

      2. sub-neg 15.9%

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

      3. metadata-eval 15.9%

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

      4. fma-define 15.9%

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

      5. fma-define 15.9%

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

      6. fma-define 15.9%

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

      7. fma-define 15.9%

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

      8. fma-define 15.9%

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

      9. fma-define 15.9%

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

      10. fma-define 15.9%

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

   3. Simplified 15.9%

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

   5. Taylor expanded in x around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. unsub-neg 99.2%

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

      5. mul-1-neg 99.2%

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

      6. unsub-neg 99.2%

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

      7. mul-1-neg 99.2%

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

      8. unsub-neg 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+25}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 94.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.075 \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.075) (not (<= x 5.2e-15)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      z
      (+
       47.066876606
       (*
        x
        (+
         313.399215894
         (+ (* x 263.505074721) (* x (* x (+ x 43.3400022514))))))))))
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x (+ 137.519416416 (* x 78.6994924154)))))))
    (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.075) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.075d0)) .or. (.not. (x <= 5.2d-15))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * (x * (x + 43.3400022514d0)))))))))
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * (137.519416416d0 + (x * 78.6994924154d0))))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.075) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.075) or not (x <= 5.2e-15):
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.075) || !(x <= 5.2e-15))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * Float64(x * Float64(x + 43.3400022514))))))))));
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * Float64(137.519416416 + Float64(x * 78.6994924154))))))) / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(x * 263.505074721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.075) || ~((x <= 5.2e-15)))
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * (137.519416416 + (x * 78.6994924154))))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.075], N[Not[LessEqual[x, 5.2e-15]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(z + N[(x * N[(y + N[(x * N[(137.519416416 + N[(x * 78.6994924154), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(47.066876606 + N[(x * N[(313.399215894 + N[(x * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0749999999999999972 or 5.20000000000000009e-15 < x

   1. Initial program 20.0%

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

      1. associate-/l* 23.7%

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

      2. sub-neg 23.7%

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

      3. metadata-eval 23.7%

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

      4. fma-define 23.7%

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

      5. fma-define 23.7%

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

      6. fma-define 23.7%

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

      7. fma-define 23.7%

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

      8. fma-define 23.6%

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

      9. fma-define 23.6%

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

      10. fma-define 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in z around 0 23.7%

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

      1. distribute-rgt-in 23.6%

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

      2. *-commutative 23.6%

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

      3. +-commutative 23.6%

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

   7. Applied egg-rr 23.6%

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

   8. Taylor expanded in x around inf 94.8%

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

   if -0.0749999999999999972 < x < 5.20000000000000009e-15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.075 \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot \left(137.519416416 + x \cdot 78.6994924154\right)\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.072 \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.072) (not (<= x 5.2e-15)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      z
      (+
       47.066876606
       (*
        x
        (+
         313.399215894
         (+ (* x 263.505074721) (* x (* x (+ x 43.3400022514))))))))))
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
    (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.072) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-0.072d0)) .or. (.not. (x <= 5.2d-15))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + (z / (47.066876606d0 + (x * (313.399215894d0 + ((x * 263.505074721d0) + (x * (x * (x + 43.3400022514d0)))))))))
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.072) || !(x <= 5.2e-15)) {
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.072) or not (x <= 5.2e-15):
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.072) || !(x <= 5.2e-15))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(z / Float64(47.066876606 + Float64(x * Float64(313.399215894 + Float64(Float64(x * 263.505074721) + Float64(x * Float64(x * Float64(x + 43.3400022514))))))))));
	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 * 263.505074721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -0.072) || ~((x <= 5.2e-15)))
		tmp = (x + -2.0) * (4.16438922228 + (z / (47.066876606 + (x * (313.399215894 + ((x * 263.505074721) + (x * (x * (x + 43.3400022514)))))))));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.072], N[Not[LessEqual[x, 5.2e-15]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(z / N[(47.066876606 + N[(x * N[(313.399215894 + N[(N[(x * 263.505074721), $MachinePrecision] + N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0719999999999999946 or 5.20000000000000009e-15 < x

   1. Initial program 20.0%

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

      1. associate-/l* 23.7%

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

      2. sub-neg 23.7%

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

      3. metadata-eval 23.7%

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

      4. fma-define 23.7%

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

      5. fma-define 23.7%

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

      6. fma-define 23.7%

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

      7. fma-define 23.7%

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

      8. fma-define 23.6%

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

      9. fma-define 23.6%

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

      10. fma-define 23.6%

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

   3. Simplified 23.6%

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

   5. Taylor expanded in z around 0 23.7%

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

      1. distribute-rgt-in 23.6%

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

      2. *-commutative 23.6%

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

      3. +-commutative 23.6%

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

   7. Applied egg-rr 23.6%

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

   8. Taylor expanded in x around inf 94.8%

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

   if -0.0719999999999999946 < x < 5.20000000000000009e-15

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in x around 0 98.4%

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

      1. *-commutative 98.4%

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

   8. Simplified 98.4%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.072 \lor \neg \left(x \leq 5.2 \cdot 10^{-15}\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{z}{47.066876606 + x \cdot \left(313.399215894 + \left(x \cdot 263.505074721 + x \cdot \left(x \cdot \left(x + 43.3400022514\right)\right)\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000 \lor \neg \left(x \leq 300000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -32000.0) (not (<= x 300000.0)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      (-
       (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
       101.7851458539211)
      x)))
   (/
    (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
    (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -32000.0) || !(x <= 300000.0)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-32000.0d0)) .or. (.not. (x <= 300000.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    else
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -32000.0) || !(x <= 300000.0)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -32000.0) or not (x <= 300000.0):
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	else:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -32000.0) || !(x <= 300000.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	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 * 263.505074721)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -32000.0) || ~((x <= 300000.0)))
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	else
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -32000.0], N[Not[LessEqual[x, 300000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 * 263.505074721), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -32000 or 3e5 < x

   1. Initial program 15.4%

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

      1. associate-/l* 19.3%

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

      2. sub-neg 19.3%

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

      3. metadata-eval 19.3%

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

      4. fma-define 19.3%

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

      5. fma-define 19.3%

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

      6. fma-define 19.3%

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

      7. fma-define 19.3%

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

      8. fma-define 19.3%

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

      9. fma-define 19.3%

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

      10. fma-define 19.3%

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

   3. Simplified 19.3%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

   if -32000 < x < 3e5

   1. Initial program 99.0%

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

   3. Taylor expanded in x around 0 95.6%

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

      1. *-commutative 95.6%

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

   5. Simplified 95.6%

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

   6. Taylor expanded in x around 0 95.5%

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

      1. *-commutative 95.5%

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

   8. Simplified 95.5%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32000 \lor \neg \left(x \leq 300000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976 + x \cdot \left(2.9217875995295866 - y \cdot 0.14147091005106402\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (if (<= x 5e-125)
     (* z (* (+ x -2.0) (+ 0.0212463641547976 (* x -0.14147091005106402))))
     (if (<= x 5.2e-15)
       (*
        (+ x -2.0)
        (*
         x
         (+
          (* y 0.0212463641547976)
          (* x (- 2.9217875995295866 (* y 0.14147091005106402))))))
       (*
        (+ x -2.0)
        (-
         4.16438922228
         (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 5e-125) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 5.2e-15) {
		tmp = (x + -2.0) * (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 - (y * 0.14147091005106402)))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-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) :: tmp
    if (x <= (-420000.0d0)) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else if (x <= 5d-125) then
        tmp = z * ((x + (-2.0d0)) * (0.0212463641547976d0 + (x * (-0.14147091005106402d0))))
    else if (x <= 5.2d-15) then
        tmp = (x + (-2.0d0)) * (x * ((y * 0.0212463641547976d0) + (x * (2.9217875995295866d0 - (y * 0.14147091005106402d0)))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 5e-125) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 5.2e-15) {
		tmp = (x + -2.0) * (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 - (y * 0.14147091005106402)))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	elif x <= 5e-125:
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)))
	elif x <= 5.2e-15:
		tmp = (x + -2.0) * (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 - (y * 0.14147091005106402)))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	elseif (x <= 5e-125)
		tmp = Float64(z * Float64(Float64(x + -2.0) * Float64(0.0212463641547976 + Float64(x * -0.14147091005106402))));
	elseif (x <= 5.2e-15)
		tmp = Float64(Float64(x + -2.0) * Float64(x * Float64(Float64(y * 0.0212463641547976) + Float64(x * Float64(2.9217875995295866 - Float64(y * 0.14147091005106402))))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	elseif (x <= 5e-125)
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	elseif (x <= 5.2e-15)
		tmp = (x + -2.0) * (x * ((y * 0.0212463641547976) + (x * (2.9217875995295866 - (y * 0.14147091005106402)))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e-125], N[(z * N[(N[(x + -2.0), $MachinePrecision] * N[(0.0212463641547976 + N[(x * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.2e-15], N[(N[(x + -2.0), $MachinePrecision] * N[(x * N[(N[(y * 0.0212463641547976), $MachinePrecision] + N[(x * N[(2.9217875995295866 - N[(y * 0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e5

   1. Initial program 6.8%

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

      1. associate-/l* 14.6%

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

      2. sub-neg 14.6%

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

      3. metadata-eval 14.6%

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

      4. fma-define 14.6%

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

      5. fma-define 14.6%

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

      6. fma-define 14.6%

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

      7. fma-define 14.6%

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

      8. fma-define 14.6%

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

      9. fma-define 14.6%

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

      10. fma-define 14.6%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in x around inf 91.4%

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

      1. associate-*r/ 91.4%

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

      2. metadata-eval 91.4%

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

   7. Simplified 91.4%

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

   if -4.2e5 < x < 4.99999999999999967e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 92.5%

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

   6. Taylor expanded in y around 0 73.9%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{-0.14147091005106402 \cdot \left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0212463641547976 + -0.14147091005106402 \cdot x\right) \cdot \left(x - 2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 73.9%

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

       2. sub-neg 73.9%

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

       3. metadata-eval 73.9%

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

   11. Simplified 73.9%

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

   if 4.99999999999999967e-125 < x < 5.20000000000000009e-15

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 79.0%

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

   6. Taylor expanded in x around 0 79.1%

      \[\leadsto \left(x + -2\right) \cdot \color{blue}{\left(x \cdot \left(0.0212463641547976 \cdot y + x \cdot \left(2.9217875995295866 - 0.14147091005106402 \cdot y\right)\right)\right)} \]

   if 5.20000000000000009e-15 < x

   1. Initial program 27.4%

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

      1. associate-/l* 27.5%

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

      2. sub-neg 27.5%

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

      3. metadata-eval 27.5%

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

      4. fma-define 27.5%

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

      5. fma-define 27.5%

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

      6. fma-define 27.5%

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

      7. fma-define 27.5%

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

      8. fma-define 27.5%

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

      9. fma-define 27.5%

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

      10. fma-define 27.4%

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

   3. Simplified 27.4%

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

   5. Taylor expanded in x around -inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. unsub-neg 86.1%

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

      3. sub-neg 86.1%

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

      4. associate-*r/ 86.1%

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

      5. metadata-eval 86.1%

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

      6. distribute-neg-frac 86.1%

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

      7. metadata-eval 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-15}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(x \cdot \left(y \cdot 0.0212463641547976 + x \cdot \left(2.9217875995295866 - y \cdot 0.14147091005106402\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 92.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000 \lor \neg \left(x \leq 300000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - 0.0212463641547976 \cdot \left(z + y \cdot -2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -32000.0) (not (<= x 300000.0)))
   (*
    (+ x -2.0)
    (+
     4.16438922228
     (/
      (-
       (/ (+ 3451.550173699799 (/ (- y 124074.40615218398) x)) x)
       101.7851458539211)
      x)))
   (-
    (* z -0.0424927283095952)
    (*
     x
     (- (* z -0.28294182010212804) (* 0.0212463641547976 (+ z (* y -2.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -32000.0) || !(x <= 300000.0)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-32000.0d0)) .or. (.not. (x <= 300000.0d0))) then
        tmp = (x + (-2.0d0)) * (4.16438922228d0 + ((((3451.550173699799d0 + ((y - 124074.40615218398d0) / x)) / x) - 101.7851458539211d0) / x))
    else
        tmp = (z * (-0.0424927283095952d0)) - (x * ((z * (-0.28294182010212804d0)) - (0.0212463641547976d0 * (z + (y * (-2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -32000.0) || !(x <= 300000.0)) {
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	} else {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -32000.0) or not (x <= 300000.0):
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x))
	else:
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -32000.0) || !(x <= 300000.0))
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 + Float64(Float64(Float64(Float64(3451.550173699799 + Float64(Float64(y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x)));
	else
		tmp = Float64(Float64(z * -0.0424927283095952) - Float64(x * Float64(Float64(z * -0.28294182010212804) - Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -32000.0) || ~((x <= 300000.0)))
		tmp = (x + -2.0) * (4.16438922228 + ((((3451.550173699799 + ((y - 124074.40615218398) / x)) / x) - 101.7851458539211) / x));
	else
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -32000.0], N[Not[LessEqual[x, 300000.0]], $MachinePrecision]], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 + N[(N[(N[(N[(3451.550173699799 + N[(N[(y - 124074.40615218398), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] - 101.7851458539211), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * -0.0424927283095952), $MachinePrecision] - N[(x * N[(N[(z * -0.28294182010212804), $MachinePrecision] - N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -32000 or 3e5 < x

   1. Initial program 15.4%

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

      1. associate-/l* 19.3%

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

      2. sub-neg 19.3%

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

      3. metadata-eval 19.3%

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

      4. fma-define 19.3%

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

      5. fma-define 19.3%

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

      6. fma-define 19.3%

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

      7. fma-define 19.3%

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

      8. fma-define 19.3%

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

      9. fma-define 19.3%

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

      10. fma-define 19.3%

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

   3. Simplified 19.3%

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

   5. Taylor expanded in x around -inf 94.1%

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

      1. mul-1-neg 94.1%

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

      2. unsub-neg 94.1%

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

      3. mul-1-neg 94.1%

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

      4. unsub-neg 94.1%

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

      5. mul-1-neg 94.1%

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

      6. unsub-neg 94.1%

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

      7. mul-1-neg 94.1%

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

      8. unsub-neg 94.1%

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

   7. Simplified 94.1%

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

   if -32000 < x < 3e5

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.6%

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

      5. fma-define 99.6%

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

      6. fma-define 99.6%

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

      7. fma-define 99.6%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 90.8%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32000 \lor \neg \left(x \leq 300000\right):\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 + \frac{\frac{3451.550173699799 + \frac{y - 124074.40615218398}{x}}{x} - 101.7851458539211}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - 0.0212463641547976 \cdot \left(z + y \cdot -2\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (if (<= x 8.5e-126)
     (* z (* (+ x -2.0) (+ 0.0212463641547976 (* x -0.14147091005106402))))
     (if (<= x 2.6e-17)
       (* x (* y -0.0424927283095952))
       (*
        (+ x -2.0)
        (-
         4.16438922228
         (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 8.5e-126) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-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) :: tmp
    if (x <= (-420000.0d0)) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else if (x <= 8.5d-126) then
        tmp = z * ((x + (-2.0d0)) * (0.0212463641547976d0 + (x * (-0.14147091005106402d0))))
    else if (x <= 2.6d-17) then
        tmp = x * (y * (-0.0424927283095952d0))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 8.5e-126) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	elif x <= 8.5e-126:
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)))
	elif x <= 2.6e-17:
		tmp = x * (y * -0.0424927283095952)
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	elseif (x <= 8.5e-126)
		tmp = Float64(z * Float64(Float64(x + -2.0) * Float64(0.0212463641547976 + Float64(x * -0.14147091005106402))));
	elseif (x <= 2.6e-17)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	elseif (x <= 8.5e-126)
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	elseif (x <= 2.6e-17)
		tmp = x * (y * -0.0424927283095952);
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-126], N[(z * N[(N[(x + -2.0), $MachinePrecision] * N[(0.0212463641547976 + N[(x * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-17], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.2e5

   1. Initial program 6.8%

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

      1. associate-/l* 14.6%

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

      2. sub-neg 14.6%

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

      3. metadata-eval 14.6%

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

      4. fma-define 14.6%

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

      5. fma-define 14.6%

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

      6. fma-define 14.6%

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

      7. fma-define 14.6%

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

      8. fma-define 14.6%

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

      9. fma-define 14.6%

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

      10. fma-define 14.6%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in x around inf 91.4%

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

      1. associate-*r/ 91.4%

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

      2. metadata-eval 91.4%

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

   7. Simplified 91.4%

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

   if -4.2e5 < x < 8.49999999999999938e-126

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 92.5%

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

   6. Taylor expanded in y around 0 73.9%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{-0.14147091005106402 \cdot \left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0212463641547976 + -0.14147091005106402 \cdot x\right) \cdot \left(x - 2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 73.9%

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

       2. sub-neg 73.9%

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

       3. metadata-eval 73.9%

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

   11. Simplified 73.9%

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

   if 8.49999999999999938e-126 < x < 2.60000000000000003e-17

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   if 2.60000000000000003e-17 < x

   1. Initial program 28.5%

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

      1. associate-/l* 28.6%

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

      2. sub-neg 28.6%

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

      3. metadata-eval 28.6%

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

      4. fma-define 28.6%

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

      5. fma-define 28.6%

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

      6. fma-define 28.6%

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

      7. fma-define 28.6%

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

      8. fma-define 28.6%

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

      9. fma-define 28.6%

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

      10. fma-define 28.5%

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

   3. Simplified 28.5%

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

   5. Taylor expanded in x around -inf 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. sub-neg 84.9%

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

      4. associate-*r/ 84.9%

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

      5. metadata-eval 84.9%

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

      6. distribute-neg-frac 84.9%

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

      7. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-126}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 89.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (if (<= x 0.33)
     (*
      (+ x -2.0)
      (+
       (* z 0.0212463641547976)
       (* x (- (* y 0.0212463641547976) (* z 0.14147091005106402)))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 0.33) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-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) :: tmp
    if (x <= (-420000.0d0)) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else if (x <= 0.33d0) then
        tmp = (x + (-2.0d0)) * ((z * 0.0212463641547976d0) + (x * ((y * 0.0212463641547976d0) - (z * 0.14147091005106402d0))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 0.33) {
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	elif x <= 0.33:
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	elseif (x <= 0.33)
		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(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	elseif (x <= 0.33)
		tmp = (x + -2.0) * ((z * 0.0212463641547976) + (x * ((y * 0.0212463641547976) - (z * 0.14147091005106402))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.33], 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[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e5

   1. Initial program 6.8%

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

      1. associate-/l* 14.6%

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

      2. sub-neg 14.6%

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

      3. metadata-eval 14.6%

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

      4. fma-define 14.6%

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

      5. fma-define 14.6%

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

      6. fma-define 14.6%

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

      7. fma-define 14.6%

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

      8. fma-define 14.6%

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

      9. fma-define 14.6%

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

      10. fma-define 14.6%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in x around inf 91.4%

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

      1. associate-*r/ 91.4%

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

      2. metadata-eval 91.4%

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

   7. Simplified 91.4%

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

   if -4.2e5 < x < 0.330000000000000016

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 90.9%

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

   if 0.330000000000000016 < x

   1. Initial program 23.9%

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

      1. associate-/l* 24.0%

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

      2. sub-neg 24.0%

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

      3. metadata-eval 24.0%

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

      4. fma-define 24.0%

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

      5. fma-define 24.0%

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

      6. fma-define 24.0%

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

      7. fma-define 24.0%

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

      8. fma-define 24.0%

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

      9. fma-define 24.0%

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

      10. fma-define 24.0%

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

   3. Simplified 24.0%

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

   5. Taylor expanded in x around -inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. unsub-neg 90.0%

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

      3. sub-neg 90.0%

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

      4. associate-*r/ 90.0%

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

      5. metadata-eval 90.0%

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

      6. distribute-neg-frac 90.0%

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

      7. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;\left(x + -2\right) \cdot \left(z \cdot 0.0212463641547976 + x \cdot \left(y \cdot 0.0212463641547976 - z \cdot 0.14147091005106402\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 89.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 300000:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - 0.0212463641547976 \cdot \left(z + y \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x (- 4.16438922228 (/ 110.1139242984811 x)))
   (if (<= x 300000.0)
     (-
      (* z -0.0424927283095952)
      (*
       x
       (- (* z -0.28294182010212804) (* 0.0212463641547976 (+ z (* y -2.0))))))
     (*
      (+ x -2.0)
      (-
       4.16438922228
       (/ (+ 101.7851458539211 (/ -3451.550173699799 x)) x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 300000.0) {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-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) :: tmp
    if (x <= (-420000.0d0)) then
        tmp = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    else if (x <= 300000.0d0) then
        tmp = (z * (-0.0424927283095952d0)) - (x * ((z * (-0.28294182010212804d0)) - (0.0212463641547976d0 * (z + (y * (-2.0d0))))))
    else
        tmp = (x + (-2.0d0)) * (4.16438922228d0 - ((101.7851458539211d0 + ((-3451.550173699799d0) / x)) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	} else if (x <= 300000.0) {
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	} else {
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * (4.16438922228 - (110.1139242984811 / x))
	elif x <= 300000.0:
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))))
	else:
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)));
	elseif (x <= 300000.0)
		tmp = Float64(Float64(z * -0.0424927283095952) - Float64(x * Float64(Float64(z * -0.28294182010212804) - Float64(0.0212463641547976 * Float64(z + Float64(y * -2.0))))));
	else
		tmp = Float64(Float64(x + -2.0) * Float64(4.16438922228 - Float64(Float64(101.7851458539211 + Float64(-3451.550173699799 / x)) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = x * (4.16438922228 - (110.1139242984811 / x));
	elseif (x <= 300000.0)
		tmp = (z * -0.0424927283095952) - (x * ((z * -0.28294182010212804) - (0.0212463641547976 * (z + (y * -2.0)))));
	else
		tmp = (x + -2.0) * (4.16438922228 - ((101.7851458539211 + (-3451.550173699799 / x)) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 300000.0], N[(N[(z * -0.0424927283095952), $MachinePrecision] - N[(x * N[(N[(z * -0.28294182010212804), $MachinePrecision] - N[(0.0212463641547976 * N[(z + N[(y * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + -2.0), $MachinePrecision] * N[(4.16438922228 - N[(N[(101.7851458539211 + N[(-3451.550173699799 / x), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e5

   1. Initial program 6.8%

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

      1. associate-/l* 14.6%

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

      2. sub-neg 14.6%

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

      3. metadata-eval 14.6%

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

      4. fma-define 14.6%

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

      5. fma-define 14.6%

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

      6. fma-define 14.6%

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

      7. fma-define 14.6%

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

      8. fma-define 14.6%

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

      9. fma-define 14.6%

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

      10. fma-define 14.6%

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

   3. Simplified 14.6%

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

   5. Taylor expanded in x around inf 91.4%

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

      1. associate-*r/ 91.4%

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

      2. metadata-eval 91.4%

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

   7. Simplified 91.4%

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

   if -4.2e5 < x < 3e5

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 89.6%

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

   if 3e5 < x

   1. Initial program 21.4%

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

      1. associate-/l* 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. fma-define 21.5%

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

      5. fma-define 21.5%

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

      6. fma-define 21.5%

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

      7. fma-define 21.5%

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

      8. fma-define 21.5%

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

      9. fma-define 21.5%

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

      10. fma-define 21.4%

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

   3. Simplified 21.4%

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

   5. Taylor expanded in x around -inf 92.9%

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

      1. mul-1-neg 92.9%

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

      2. unsub-neg 92.9%

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

      3. sub-neg 92.9%

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

      4. associate-*r/ 92.9%

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

      5. metadata-eval 92.9%

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

      6. distribute-neg-frac 92.9%

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

      7. metadata-eval 92.9%

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

   7. Simplified 92.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 300000:\\ \;\;\;\;z \cdot -0.0424927283095952 - x \cdot \left(z \cdot -0.28294182010212804 - 0.0212463641547976 \cdot \left(z + y \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + -2\right) \cdot \left(4.16438922228 - \frac{101.7851458539211 + \frac{-3451.550173699799}{x}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 74.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 4.16438922228 (/ 110.1139242984811 x)))))
   (if (<= x -1000000.0)
     t_0
     (if (<= x 5.5e-125)
       (* z -0.0424927283095952)
       (if (<= x 2.6e-17) (* x (* y -0.0424927283095952)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	double tmp;
	if (x <= -1000000.0) {
		tmp = t_0;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    if (x <= (-1000000.0d0)) then
        tmp = t_0
    else if (x <= 5.5d-125) then
        tmp = z * (-0.0424927283095952d0)
    else if (x <= 2.6d-17) then
        tmp = x * (y * (-0.0424927283095952d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	double tmp;
	if (x <= -1000000.0) {
		tmp = t_0;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.16438922228 - (110.1139242984811 / x))
	tmp = 0
	if x <= -1000000.0:
		tmp = t_0
	elif x <= 5.5e-125:
		tmp = z * -0.0424927283095952
	elif x <= 2.6e-17:
		tmp = x * (y * -0.0424927283095952)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)))
	tmp = 0.0
	if (x <= -1000000.0)
		tmp = t_0;
	elseif (x <= 5.5e-125)
		tmp = Float64(z * -0.0424927283095952);
	elseif (x <= 2.6e-17)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	tmp = 0.0;
	if (x <= -1000000.0)
		tmp = t_0;
	elseif (x <= 5.5e-125)
		tmp = z * -0.0424927283095952;
	elseif (x <= 2.6e-17)
		tmp = x * (y * -0.0424927283095952);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1000000.0], t$95$0, If[LessEqual[x, 5.5e-125], N[(z * -0.0424927283095952), $MachinePrecision], If[LessEqual[x, 2.6e-17], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e6 or 2.60000000000000003e-17 < x

   1. Initial program 18.1%

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

      1. associate-/l* 21.9%

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

      2. sub-neg 21.9%

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

      3. metadata-eval 21.9%

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

      4. fma-define 21.9%

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

      5. fma-define 21.9%

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

      6. fma-define 21.9%

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

      7. fma-define 21.9%

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

      8. fma-define 21.9%

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

      9. fma-define 21.9%

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

      10. fma-define 21.8%

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

   3. Simplified 21.8%

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

   5. Taylor expanded in x around inf 88.0%

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

      1. associate-*r/ 88.0%

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

      2. metadata-eval 88.0%

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

   7. Simplified 88.0%

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

   if -1e6 < x < 5.4999999999999997e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.8%

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

      1. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   if 5.4999999999999997e-125 < x < 2.60000000000000003e-17

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 75.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{if}\;x \leq -510000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 4.16438922228 (/ 110.1139242984811 x)))))
   (if (<= x -510000.0)
     t_0
     (if (<= x 4.6e-125)
       (* z (* (+ x -2.0) (+ 0.0212463641547976 (* x -0.14147091005106402))))
       (if (<= x 2.6e-17) (* x (* y -0.0424927283095952)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	double tmp;
	if (x <= -510000.0) {
		tmp = t_0;
	} else if (x <= 4.6e-125) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (4.16438922228d0 - (110.1139242984811d0 / x))
    if (x <= (-510000.0d0)) then
        tmp = t_0
    else if (x <= 4.6d-125) then
        tmp = z * ((x + (-2.0d0)) * (0.0212463641547976d0 + (x * (-0.14147091005106402d0))))
    else if (x <= 2.6d-17) then
        tmp = x * (y * (-0.0424927283095952d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	double tmp;
	if (x <= -510000.0) {
		tmp = t_0;
	} else if (x <= 4.6e-125) {
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (4.16438922228 - (110.1139242984811 / x))
	tmp = 0
	if x <= -510000.0:
		tmp = t_0
	elif x <= 4.6e-125:
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)))
	elif x <= 2.6e-17:
		tmp = x * (y * -0.0424927283095952)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(4.16438922228 - Float64(110.1139242984811 / x)))
	tmp = 0.0
	if (x <= -510000.0)
		tmp = t_0;
	elseif (x <= 4.6e-125)
		tmp = Float64(z * Float64(Float64(x + -2.0) * Float64(0.0212463641547976 + Float64(x * -0.14147091005106402))));
	elseif (x <= 2.6e-17)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (4.16438922228 - (110.1139242984811 / x));
	tmp = 0.0;
	if (x <= -510000.0)
		tmp = t_0;
	elseif (x <= 4.6e-125)
		tmp = z * ((x + -2.0) * (0.0212463641547976 + (x * -0.14147091005106402)));
	elseif (x <= 2.6e-17)
		tmp = x * (y * -0.0424927283095952);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(4.16438922228 - N[(110.1139242984811 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -510000.0], t$95$0, If[LessEqual[x, 4.6e-125], N[(z * N[(N[(x + -2.0), $MachinePrecision] * N[(0.0212463641547976 + N[(x * -0.14147091005106402), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e-17], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.1e5 or 2.60000000000000003e-17 < x

   1. Initial program 18.1%

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

      1. associate-/l* 21.9%

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

      2. sub-neg 21.9%

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

      3. metadata-eval 21.9%

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

      4. fma-define 21.9%

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

      5. fma-define 21.9%

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

      6. fma-define 21.9%

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

      7. fma-define 21.9%

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

      8. fma-define 21.9%

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

      9. fma-define 21.9%

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

      10. fma-define 21.8%

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

   3. Simplified 21.8%

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

   5. Taylor expanded in x around inf 88.0%

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

      1. associate-*r/ 88.0%

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

      2. metadata-eval 88.0%

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

   7. Simplified 88.0%

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

   if -5.1e5 < x < 4.5999999999999998e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 92.5%

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

   6. Taylor expanded in y around 0 73.9%

      \[\leadsto \left(x + -2\right) \cdot \left(0.0212463641547976 \cdot z + \color{blue}{-0.14147091005106402 \cdot \left(x \cdot z\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 73.9%

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

      2. *-commutative 73.9%

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

      3. associate-*r* 73.9%

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

   8. Simplified 73.9%

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

   9. Taylor expanded in z around 0 73.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(0.0212463641547976 + -0.14147091005106402 \cdot x\right) \cdot \left(x - 2\right)\right)} \]
   10. Step-by-step derivation

       1. *-commutative 73.9%

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

       2. sub-neg 73.9%

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

       3. metadata-eval 73.9%

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

   11. Simplified 73.9%

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

   if 4.5999999999999998e-125 < x < 2.60000000000000003e-17

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -510000:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(\left(x + -2\right) \cdot \left(0.0212463641547976 + x \cdot -0.14147091005106402\right)\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(4.16438922228 - \frac{110.1139242984811}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x 4.16438922228)
   (if (<= x 5.5e-125)
     (* z -0.0424927283095952)
     (if (<= x 0.33) (* -0.0424927283095952 (* x y)) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 0.33) {
		tmp = -0.0424927283095952 * (x * y);
	} 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 <= (-420000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 5.5d-125) then
        tmp = z * (-0.0424927283095952d0)
    else if (x <= 0.33d0) then
        tmp = (-0.0424927283095952d0) * (x * y)
    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 <= -420000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 0.33) {
		tmp = -0.0424927283095952 * (x * y);
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * 4.16438922228
	elif x <= 5.5e-125:
		tmp = z * -0.0424927283095952
	elif x <= 0.33:
		tmp = -0.0424927283095952 * (x * y)
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 5.5e-125)
		tmp = Float64(z * -0.0424927283095952);
	elseif (x <= 0.33)
		tmp = Float64(-0.0424927283095952 * Float64(x * y));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 5.5e-125)
		tmp = z * -0.0424927283095952;
	elseif (x <= 0.33)
		tmp = -0.0424927283095952 * (x * y);
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 5.5e-125], N[(z * -0.0424927283095952), $MachinePrecision], If[LessEqual[x, 0.33], N[(-0.0424927283095952 * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e5 or 0.330000000000000016 < x

   1. Initial program 15.4%

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

   3. Taylor expanded in x around inf 13.7%

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

   4. Taylor expanded in x around inf 90.1%

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

      1. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if -4.2e5 < x < 5.4999999999999997e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.8%

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

      1. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   if 5.4999999999999997e-125 < x < 0.330000000000000016

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 55.6%

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

   6. Taylor expanded in x around 0 55.6%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;-0.0424927283095952 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 75.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -420000.0)
   (* x 4.16438922228)
   (if (<= x 5.5e-125)
     (* z -0.0424927283095952)
     (if (<= x 0.33) (* x (* y -0.0424927283095952)) (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -420000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 0.33) {
		tmp = x * (y * -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 <= (-420000.0d0)) then
        tmp = x * 4.16438922228d0
    else if (x <= 5.5d-125) then
        tmp = z * (-0.0424927283095952d0)
    else if (x <= 0.33d0) then
        tmp = x * (y * (-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 <= -420000.0) {
		tmp = x * 4.16438922228;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 0.33) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -420000.0:
		tmp = x * 4.16438922228
	elif x <= 5.5e-125:
		tmp = z * -0.0424927283095952
	elif x <= 0.33:
		tmp = x * (y * -0.0424927283095952)
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -420000.0)
		tmp = Float64(x * 4.16438922228);
	elseif (x <= 5.5e-125)
		tmp = Float64(z * -0.0424927283095952);
	elseif (x <= 0.33)
		tmp = Float64(x * Float64(y * -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 <= -420000.0)
		tmp = x * 4.16438922228;
	elseif (x <= 5.5e-125)
		tmp = z * -0.0424927283095952;
	elseif (x <= 0.33)
		tmp = x * (y * -0.0424927283095952);
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -420000.0], N[(x * 4.16438922228), $MachinePrecision], If[LessEqual[x, 5.5e-125], N[(z * -0.0424927283095952), $MachinePrecision], If[LessEqual[x, 0.33], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e5 or 0.330000000000000016 < x

   1. Initial program 15.4%

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

   3. Taylor expanded in x around inf 13.7%

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

   4. Taylor expanded in x around inf 90.1%

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

      1. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   if -4.2e5 < x < 5.4999999999999997e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.8%

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

      1. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   if 5.4999999999999997e-125 < x < 0.330000000000000016

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 55.6%

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

   6. Taylor expanded in x around 0 55.6%

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

      1. *-commutative 55.6%

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

      2. associate-*r* 55.7%

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

      3. *-commutative 55.7%

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

   8. Simplified 55.7%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 0.33:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 74.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{if}\;x \leq -420000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 4.16438922228 (+ x -2.0))))
   (if (<= x -420000.0)
     t_0
     (if (<= x 5.5e-125)
       (* z -0.0424927283095952)
       (if (<= x 2.6e-17) (* x (* y -0.0424927283095952)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x + -2.0);
	double tmp;
	if (x <= -420000.0) {
		tmp = t_0;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} 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 = 4.16438922228d0 * (x + (-2.0d0))
    if (x <= (-420000.0d0)) then
        tmp = t_0
    else if (x <= 5.5d-125) then
        tmp = z * (-0.0424927283095952d0)
    else if (x <= 2.6d-17) then
        tmp = x * (y * (-0.0424927283095952d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 4.16438922228 * (x + -2.0);
	double tmp;
	if (x <= -420000.0) {
		tmp = t_0;
	} else if (x <= 5.5e-125) {
		tmp = z * -0.0424927283095952;
	} else if (x <= 2.6e-17) {
		tmp = x * (y * -0.0424927283095952);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 4.16438922228 * (x + -2.0)
	tmp = 0
	if x <= -420000.0:
		tmp = t_0
	elif x <= 5.5e-125:
		tmp = z * -0.0424927283095952
	elif x <= 2.6e-17:
		tmp = x * (y * -0.0424927283095952)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(4.16438922228 * Float64(x + -2.0))
	tmp = 0.0
	if (x <= -420000.0)
		tmp = t_0;
	elseif (x <= 5.5e-125)
		tmp = Float64(z * -0.0424927283095952);
	elseif (x <= 2.6e-17)
		tmp = Float64(x * Float64(y * -0.0424927283095952));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 4.16438922228 * (x + -2.0);
	tmp = 0.0;
	if (x <= -420000.0)
		tmp = t_0;
	elseif (x <= 5.5e-125)
		tmp = z * -0.0424927283095952;
	elseif (x <= 2.6e-17)
		tmp = x * (y * -0.0424927283095952);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(4.16438922228 * N[(x + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -420000.0], t$95$0, If[LessEqual[x, 5.5e-125], N[(z * -0.0424927283095952), $MachinePrecision], If[LessEqual[x, 2.6e-17], N[(x * N[(y * -0.0424927283095952), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.2e5 or 2.60000000000000003e-17 < x

   1. Initial program 18.1%

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

      1. associate-/l* 21.9%

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

      2. sub-neg 21.9%

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

      3. metadata-eval 21.9%

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

      4. fma-define 21.9%

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

      5. fma-define 21.9%

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

      6. fma-define 21.9%

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

      7. fma-define 21.9%

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

      8. fma-define 21.9%

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

      9. fma-define 21.9%

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

      10. fma-define 21.8%

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

   3. Simplified 21.8%

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

   5. Taylor expanded in x around inf 87.5%

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

   if -4.2e5 < x < 5.4999999999999997e-125

   1. Initial program 98.9%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.7%

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

      9. fma-define 99.7%

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

      10. fma-define 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 73.8%

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

      1. *-commutative 73.8%

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

   7. Simplified 73.8%

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

   if 5.4999999999999997e-125 < x < 2.60000000000000003e-17

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. sub-neg 99.4%

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

      3. metadata-eval 99.4%

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

      4. fma-define 99.4%

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

      5. fma-define 99.4%

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

      6. fma-define 99.4%

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

      7. fma-define 99.4%

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

      8. fma-define 99.4%

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

      9. fma-define 99.4%

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

      10. fma-define 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 67.2%

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

   6. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

      2. associate-*r* 67.3%

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

      3. *-commutative 67.3%

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

   8. Simplified 67.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -420000:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-125}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x \cdot \left(y \cdot -0.0424927283095952\right)\\ \mathbf{else}:\\ \;\;\;\;4.16438922228 \cdot \left(x + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 76.4% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -550000000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -550000000.0) (not (<= x 2.0)))
   (* x 4.16438922228)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -550000000.0) || !(x <= 2.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-550000000.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = x * 4.16438922228d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -550000000.0) || !(x <= 2.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -550000000.0) or not (x <= 2.0):
		tmp = x * 4.16438922228
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -550000000.0) || !(x <= 2.0))
		tmp = Float64(x * 4.16438922228);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -550000000.0) || ~((x <= 2.0)))
		tmp = x * 4.16438922228;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -550000000.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(x * 4.16438922228), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 14.8%

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

   3. Taylor expanded in x around inf 13.6%

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

   4. Taylor expanded in x around inf 90.8%

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

      1. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   if -5.5e8 < x < 2

   1. Initial program 99.0%

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

      1. associate-/l* 99.7%

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

      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. fma-define 99.7%

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

      5. fma-define 99.7%

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

      6. fma-define 99.7%

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

      7. fma-define 99.7%

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

      8. fma-define 99.6%

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

      9. fma-define 99.6%

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

      10. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 66.0%

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

      1. *-commutative 66.0%

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

   7. Simplified 66.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -550000000 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 9.1% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5218852675289308 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 0.5218852675289308))

C

double code(double x, double y, double z) {
	return x * 0.5218852675289308;
}

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 * 0.5218852675289308d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 0.5218852675289308;
}

Python

def code(x, y, z):
	return x * 0.5218852675289308

Julia

function code(x, y, z)
	return Float64(x * 0.5218852675289308)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 0.5218852675289308;
end

Wolfram

code[x_, y_, z_] := N[(x * 0.5218852675289308), $MachinePrecision]

Derivation

1. Initial program 58.9%

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

3. Taylor expanded in x around 0 50.7%

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

   1. *-commutative 50.7%

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

5. Simplified 50.7%

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

6. Taylor expanded in x around 0 51.1%

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

   1. *-commutative 51.1%

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

8. Simplified 51.1%

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

9. Taylor expanded in x around inf 9.0%

   \[\leadsto \color{blue}{0.5218852675289308 \cdot x} \]
10. Step-by-step derivation

    1. *-commutative 9.0%

       \[\leadsto \color{blue}{x \cdot 0.5218852675289308} \]

11. Simplified 9.0%

    \[\leadsto \color{blue}{x \cdot 0.5218852675289308} \]

12. Final simplification 9.0%

    \[\leadsto x \cdot 0.5218852675289308 \]
13. Add Preprocessing

Alternative 22: 45.1% 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 58.9%

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

3. Taylor expanded in x around inf 56.3%

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

4. Taylor expanded in x around inf 45.0%

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

   1. *-commutative 45.0%

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

6. Simplified 45.0%

   \[\leadsto \color{blue}{x \cdot 4.16438922228} \]

7. Final simplification 45.0%

   \[\leadsto x \cdot 4.16438922228 \]
8. Add Preprocessing

Developer target: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(\frac{y}{x \cdot x} + 4.16438922228 \cdot x\right) - 110.1139242984811\\ \mathbf{if}\;x < -3.326128725870005 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 9.429991714554673 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.505074721 \cdot x + \left(43.3400022514 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))
   (if (< x -3.326128725870005e+62)
     t_0
     (if (< x 9.429991714554673e+55)
       (*
        (/ (- x 2.0) 1.0)
        (/
         (+
          (*
           (+
            (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
            y)
           x)
          z)
         (+
          (*
           (+
            (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x))))
            313.399215894)
           x)
          47.066876606)))
       t_0))))

C

double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((y / (x * x)) + (4.16438922228d0 * x)) - 110.1139242984811d0
    if (x < (-3.326128725870005d+62)) then
        tmp = t_0
    else if (x < 9.429991714554673d+55) then
        tmp = ((x - 2.0d0) / 1.0d0) * (((((((((x * 4.16438922228d0) + 78.6994924154d0) * x) + 137.519416416d0) * x) + y) * x) + z) / (((((263.505074721d0 * x) + ((43.3400022514d0 * (x * x)) + (x * (x * x)))) + 313.399215894d0) * x) + 47.066876606d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	double tmp;
	if (x < -3.326128725870005e+62) {
		tmp = t_0;
	} else if (x < 9.429991714554673e+55) {
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811
	tmp = 0
	if x < -3.326128725870005e+62:
		tmp = t_0
	elif x < 9.429991714554673e+55:
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(Float64(y / Float64(x * x)) + Float64(4.16438922228 * x)) - 110.1139242984811)
	tmp = 0.0
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = Float64(Float64(Float64(x - 2.0) / 1.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / Float64(Float64(Float64(Float64(Float64(263.505074721 * x) + Float64(Float64(43.3400022514 * Float64(x * x)) + Float64(x * Float64(x * x)))) + 313.399215894) * x) + 47.066876606)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = ((y / (x * x)) + (4.16438922228 * x)) - 110.1139242984811;
	tmp = 0.0;
	if (x < -3.326128725870005e+62)
		tmp = t_0;
	elseif (x < 9.429991714554673e+55)
		tmp = ((x - 2.0) / 1.0) * (((((((((x * 4.16438922228) + 78.6994924154) * x) + 137.519416416) * x) + y) * x) + z) / (((((263.505074721 * x) + ((43.3400022514 * (x * x)) + (x * (x * x)))) + 313.399215894) * x) + 47.066876606));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(N[(y / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(4.16438922228 * x), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]}, If[Less[x, -3.326128725870005e+62], t$95$0, If[Less[x, 9.429991714554673e+55], N[(N[(N[(x - 2.0), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision] * x), $MachinePrecision] + 137.519416416), $MachinePrecision] * x), $MachinePrecision] + y), $MachinePrecision] * x), $MachinePrecision] + z), $MachinePrecision] / N[(N[(N[(N[(N[(263.505074721 * x), $MachinePrecision] + N[(N[(43.3400022514 * N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision] * x), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :alt
  (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)))