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

Percentage Accurate: 57.6% → 98.8%

Time: 14.4s

Alternatives: 13

Speedup: 5.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 57.6% 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: 98.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot t_0\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 45.3400022514\right)} + \left(\frac{z}{{x}^{2} \cdot \left(x + 45.3400022514\right)} + \frac{t_0}{x + 45.3400022514}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
        (t_1
         (/
          (* (- x 2.0) (+ (* x (+ y (* x t_0))) z))
          (+
           (*
            x
            (+
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))
             313.399215894))
           47.066876606))))
   (if (<= t_1 (- INFINITY))
     (+
      (/ y (* x (+ x 45.3400022514)))
      (+
       (/ z (* (pow x 2.0) (+ x 45.3400022514)))
       (/ t_0 (+ x 45.3400022514))))
     (if (<= t_1 5e+302)
       t_1
       (-
        (+
         (/ (- y 130977.50649958357) (pow x 2.0))
         (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
        110.1139242984811)))))

C

double code(double x, double y, double z) {
	double t_0 = (x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416;
	double t_1 = ((x - 2.0) * ((x * (y + (x * t_0))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / (x * (x + 45.3400022514))) + ((z / (pow(x, 2.0) * (x + 45.3400022514))) + (t_0 / (x + 45.3400022514)));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416;
	double t_1 = ((x - 2.0) * ((x * (y + (x * t_0))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / (x * (x + 45.3400022514))) + ((z / (Math.pow(x, 2.0) * (x + 45.3400022514))) + (t_0 / (x + 45.3400022514)));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else {
		tmp = (((y - 130977.50649958357) / Math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416
	t_1 = ((x - 2.0) * ((x * (y + (x * t_0))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / (x * (x + 45.3400022514))) + ((z / (math.pow(x, 2.0) * (x + 45.3400022514))) + (t_0 / (x + 45.3400022514)))
	elif t_1 <= 5e+302:
		tmp = t_1
	else:
		tmp = (((y - 130977.50649958357) / math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)
	t_1 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(y + Float64(x * t_0))) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / Float64(x * Float64(x + 45.3400022514))) + Float64(Float64(z / Float64((x ^ 2.0) * Float64(x + 45.3400022514))) + Float64(t_0 / Float64(x + 45.3400022514))));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416;
	t_1 = ((x - 2.0) * ((x * (y + (x * t_0))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / (x * (x + 45.3400022514))) + ((z / ((x ^ 2.0) * (x + 45.3400022514))) + (t_0 / (x + 45.3400022514)));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	else
		tmp = (((y - 130977.50649958357) / (x ^ 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(y + N[(x * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 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]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / N[(x * N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(N[Power[x, 2.0], $MachinePrecision] * N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 / N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], t$95$1, N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 3.9%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around inf 85.5%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{45.3400022514 \cdot {x}^{2} + {x}^{3}}} \]
   5. Step-by-step derivation

      1. +-commutative 85.5%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{3} + 45.3400022514 \cdot {x}^{2}}} \]

      2. cube-mult 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(x \cdot x\right)} + 45.3400022514 \cdot {x}^{2}} \]

      3. unpow2 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{x \cdot \color{blue}{{x}^{2}} + 45.3400022514 \cdot {x}^{2}} \]

      4. distribute-rgt-out 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   6. Simplified 85.7%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   7. Taylor expanded in y around 0 99.3%

      \[\leadsto \color{blue}{\frac{y}{x \cdot \left(45.3400022514 + x\right)} + \left(\frac{z}{{x}^{2} \cdot \left(45.3400022514 + x\right)} + \frac{137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)}{45.3400022514 + x}\right)} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5e302

   1. Initial program 99.6%

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

   if 5e302 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.1%

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

   2. Taylor expanded in x around -inf 99.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 45.3400022514\right)} + \left(\frac{z}{{x}^{2} \cdot \left(x + 45.3400022514\right)} + \frac{x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416}{x + 45.3400022514}\right)\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternative 2: 98.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<=
      (/
       (*
        (- x 2.0)
        (+
         (*
          x
          (+
           y
           (*
            x
            (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))))
         z))
       (+
        (*
         x
         (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
        47.066876606))
      5e+302)
   (/
    (fma
     x
     (fma x (fma x (fma x 4.16438922228 78.6994924154) 137.519416416) y)
     z)
    (/
     (fma
      x
      (fma x (fma x (+ x 43.3400022514) 263.505074721) 313.399215894)
      47.066876606)
     (+ x -2.0)))
   (-
    (+
     (/ (- y 130977.50649958357) (pow x 2.0))
     (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
    110.1139242984811)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((((x - 2.0) * ((x * (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+302) {
		tmp = fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / (fma(x, fma(x, fma(x, (x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / (x + -2.0));
	} else {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(y + Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)) <= 5e+302)
		tmp = Float64(fma(x, fma(x, fma(x, fma(x, 4.16438922228, 78.6994924154), 137.519416416), y), z) / Float64(fma(x, fma(x, fma(x, Float64(x + 43.3400022514), 263.505074721), 313.399215894), 47.066876606) / Float64(x + -2.0)));
	else
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(y + N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 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]), $MachinePrecision], 5e+302], N[(N[(x * N[(x * N[(x * N[(x * 4.16438922228 + 78.6994924154), $MachinePrecision] + 137.519416416), $MachinePrecision] + y), $MachinePrecision] + z), $MachinePrecision] / N[(N[(x * N[(x * N[(x * N[(x + 43.3400022514), $MachinePrecision] + 263.505074721), $MachinePrecision] + 313.399215894), $MachinePrecision] + 47.066876606), $MachinePrecision] / N[(x + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5e302

   1. Initial program 95.3%

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

   3. Simplified 99.0%

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

   if 5e302 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.1%

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

   2. Taylor expanded in x around -inf 99.0%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, x + 43.3400022514, 263.505074721\right), 313.399215894\right), 47.066876606\right)}{x + -2}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+25} \lor \neg \left(x \leq 7.5 \cdot 10^{+54}\right):\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.05e+25) (not (<= x 7.5e+54)))
   (-
    (+
     (/ (- y 130977.50649958357) (pow x 2.0))
     (+ (* x 4.16438922228) (* 3655.1204654076414 (/ 1.0 x))))
    110.1139242984811)
   (/
    (*
     (- x 2.0)
     (+
      (*
       x
       (+
        y
        (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))))
      z))
    (+
     (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
     47.066876606))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+25) || !(x <= 7.5e+54)) {
		tmp = (((y - 130977.50649958357) / pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	} else {
		tmp = ((x - 2.0) * ((x * (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.05d+25)) .or. (.not. (x <= 7.5d+54))) then
        tmp = (((y - 130977.50649958357d0) / (x ** 2.0d0)) + ((x * 4.16438922228d0) + (3655.1204654076414d0 * (1.0d0 / x)))) - 110.1139242984811d0
    else
        tmp = ((x - 2.0d0) * ((x * (y + (x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.05e+25) || !(x <= 7.5e+54)) {
		tmp = (((y - 130977.50649958357) / Math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	} else {
		tmp = ((x - 2.0) * ((x * (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.05e+25) or not (x <= 7.5e+54):
		tmp = (((y - 130977.50649958357) / math.pow(x, 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811
	else:
		tmp = ((x - 2.0) * ((x * (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.05e+25) || !(x <= 7.5e+54))
		tmp = Float64(Float64(Float64(Float64(y - 130977.50649958357) / (x ^ 2.0)) + Float64(Float64(x * 4.16438922228) + Float64(3655.1204654076414 * Float64(1.0 / x)))) - 110.1139242984811);
	else
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * Float64(y + Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.05e+25) || ~((x <= 7.5e+54)))
		tmp = (((y - 130977.50649958357) / (x ^ 2.0)) + ((x * 4.16438922228) + (3655.1204654076414 * (1.0 / x)))) - 110.1139242984811;
	else
		tmp = ((x - 2.0) * ((x * (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416)))) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.05e+25], N[Not[LessEqual[x, 7.5e+54]], $MachinePrecision]], N[(N[(N[(N[(y - 130977.50649958357), $MachinePrecision] / N[Power[x, 2.0], $MachinePrecision]), $MachinePrecision] + N[(N[(x * 4.16438922228), $MachinePrecision] + N[(3655.1204654076414 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * N[(y + N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 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]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e25 or 7.50000000000000042e54 < x

   1. Initial program 2.1%

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

   2. Taylor expanded in x around -inf 98.1%

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

   if -1.05e25 < x < 7.50000000000000042e54

   1. Initial program 99.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+25} \lor \neg \left(x \leq 7.5 \cdot 10^{+54}\right):\\ \;\;\;\;\left(\frac{y - 130977.50649958357}{{x}^{2}} + \left(x \cdot 4.16438922228 + 3655.1204654076414 \cdot \frac{1}{x}\right)\right) - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \end{array} \]

Alternative 4: 97.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\\ t_1 := \frac{\left(x - 2\right) \cdot \left(x \cdot t_0 + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_0}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          y
          (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))))
        (t_1
         (/
          (* (- x 2.0) (+ (* x t_0) z))
          (+
           (*
            x
            (+
             (* x (+ (* x (+ x 43.3400022514)) 263.505074721))
             313.399215894))
           47.066876606))))
   (if (<= t_1 (- INFINITY))
     (/ t_0 (* x (+ x 45.3400022514)))
     (if (<= t_1 5e+302) t_1 (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double t_0 = y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416));
	double t_1 = ((x - 2.0) * ((x * t_0) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_0 / (x * (x + 45.3400022514));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416));
	double t_1 = ((x - 2.0) * ((x * t_0) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_0 / (x * (x + 45.3400022514));
	} else if (t_1 <= 5e+302) {
		tmp = t_1;
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))
	t_1 = ((x - 2.0) * ((x * t_0) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_0 / (x * (x + 45.3400022514))
	elif t_1 <= 5e+302:
		tmp = t_1
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y + Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416)))
	t_1 = Float64(Float64(Float64(x - 2.0) * Float64(Float64(x * t_0) + z)) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_0 / Float64(x * Float64(x + 45.3400022514)));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416));
	t_1 = ((x - 2.0) * ((x * t_0) + z)) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_0 / (x * (x + 45.3400022514));
	elseif (t_1 <= 5e+302)
		tmp = t_1;
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y + N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(x - 2.0), $MachinePrecision] * N[(N[(x * t$95$0), $MachinePrecision] + z), $MachinePrecision]), $MachinePrecision] / 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]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$0 / N[(x * N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+302], t$95$1, N[(x * 4.16438922228), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 3.9%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in x around inf 85.5%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{45.3400022514 \cdot {x}^{2} + {x}^{3}}} \]
   5. Step-by-step derivation

      1. +-commutative 85.5%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{3} + 45.3400022514 \cdot {x}^{2}}} \]

      2. cube-mult 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(x \cdot x\right)} + 45.3400022514 \cdot {x}^{2}} \]

      3. unpow2 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{x \cdot \color{blue}{{x}^{2}} + 45.3400022514 \cdot {x}^{2}} \]

      4. distribute-rgt-out 85.7%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   6. Simplified 85.7%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   7. Taylor expanded in z around 0 85.0%

      \[\leadsto \color{blue}{\frac{y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right)}{x \cdot \left(45.3400022514 + x\right)}} \]

   if -inf.0 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000)) < 5e302

   1. Initial program 99.6%

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

   if 5e302 < (/.f64 (*.f64 (-.f64 x 2) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 x 104109730557/25000000000) 393497462077/5000000000) x) 4297481763/31250000) x) y) x) z)) (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 (*.f64 (+.f64 x 216700011257/5000000000) x) 263505074721/1000000000) x) 156699607947/500000000) x) 23533438303/500000000))

   1. Initial program 0.1%

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

   2. Taylor expanded in x around inf 97.1%

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

      1. *-commutative 97.1%

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

   4. Simplified 97.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq -\infty:\\ \;\;\;\;\frac{y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{elif}\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606} \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(x \cdot \left(y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)\right) + z\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 5: 94.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -41000000:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -41000000.0)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 6e+47)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+
       (*
        x
        (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
       47.066876606))
     (* x 4.16438922228))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -41000000.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 6e+47) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} 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 <= (-41000000.0d0)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 6d+47) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / ((x * ((x * ((x * (x + 43.3400022514d0)) + 263.505074721d0)) + 313.399215894d0)) + 47.066876606d0)
    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 <= -41000000.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 6e+47) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -41000000.0:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 6e+47:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606)
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -41000000.0)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 6e+47)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(Float64(x * Float64(Float64(x * Float64(Float64(x * Float64(x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -41000000.0)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 6e+47)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / ((x * ((x * ((x * (x + 43.3400022514)) + 263.505074721)) + 313.399215894)) + 47.066876606);
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -41000000.0], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+47], 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[(N[(x * N[(x + 43.3400022514), $MachinePrecision]), $MachinePrecision] + 263.505074721), $MachinePrecision]), $MachinePrecision] + 313.399215894), $MachinePrecision]), $MachinePrecision] + 47.066876606), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1e7

   1. Initial program 13.8%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. *-commutative 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -4.1e7 < x < 6.0000000000000003e47

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 96.6%

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

      1. *-commutative 96.6%

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

   4. Simplified 96.6%

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

   if 6.0000000000000003e47 < x

   1. Initial program 2.3%

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

   2. Taylor expanded in x around inf 91.7%

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

      1. *-commutative 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -41000000:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{x \cdot \left(x \cdot \left(x \cdot \left(x + 43.3400022514\right) + 263.505074721\right) + 313.399215894\right) + 47.066876606}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 6: 94.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -430:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 39:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -430.0)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 39.0)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+ 47.066876606 (* x (+ 313.399215894 (* x 263.505074721)))))
     (if (<= x 1.5e+83)
       (/
        (+
         y
         (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)))
        (* x (+ x 45.3400022514)))
       (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -430.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 39.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else if (x <= 1.5e+83) {
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	} 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 <= (-430.0d0)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 39.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * (313.399215894d0 + (x * 263.505074721d0))))
    else if (x <= 1.5d+83) then
        tmp = (y + (x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0))) / (x * (x + 45.3400022514d0))
    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 <= -430.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 39.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	} else if (x <= 1.5e+83) {
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -430.0:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 39.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))))
	elif x <= 1.5e+83:
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514))
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -430.0)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 39.0)
		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)))));
	elseif (x <= 1.5e+83)
		tmp = Float64(Float64(y + Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / Float64(x * Float64(x + 45.3400022514)));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -430.0)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 39.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * (313.399215894 + (x * 263.505074721))));
	elseif (x <= 1.5e+83)
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -430.0], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 39.0], 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], If[LessEqual[x, 1.5e+83], N[(N[(y + N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -430

   1. Initial program 13.8%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. *-commutative 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -430 < x < 39

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 98.9%

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

      1. *-commutative 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around 0 98.5%

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

      1. *-commutative 99.2%

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

   7. Simplified 98.5%

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

   if 39 < x < 1.5e83

   1. Initial program 69.5%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around inf 85.8%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{45.3400022514 \cdot {x}^{2} + {x}^{3}}} \]
   5. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{3} + 45.3400022514 \cdot {x}^{2}}} \]

      2. cube-mult 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(x \cdot x\right)} + 45.3400022514 \cdot {x}^{2}} \]

      3. unpow2 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{x \cdot \color{blue}{{x}^{2}} + 45.3400022514 \cdot {x}^{2}} \]

      4. distribute-rgt-out 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   6. Simplified 85.9%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   7. Taylor expanded in z around 0 69.0%

      \[\leadsto \color{blue}{\frac{y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right)}{x \cdot \left(45.3400022514 + x\right)}} \]

   if 1.5e83 < x

   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. Taylor expanded in x around inf 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -430:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 39:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot \left(313.399215894 + x \cdot 263.505074721\right)}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 7: 94.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+82}:\\ \;\;\;\;\frac{y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 14.5)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+ 47.066876606 (* x 313.399215894)))
     (if (<= x 8e+82)
       (/
        (+
         y
         (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)))
        (* x (+ x 45.3400022514)))
       (* x 4.16438922228)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 14.5) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} else if (x <= 8e+82) {
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	} 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 <= (-36.0d0)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 14.5d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * 313.399215894d0))
    else if (x <= 8d+82) then
        tmp = (y + (x * ((x * ((x * 4.16438922228d0) + 78.6994924154d0)) + 137.519416416d0))) / (x * (x + 45.3400022514d0))
    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 <= -36.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 14.5) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} else if (x <= 8e+82) {
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	} else {
		tmp = x * 4.16438922228;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -36.0:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 14.5:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894))
	elif x <= 8e+82:
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514))
	else:
		tmp = x * 4.16438922228
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 14.5)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * 313.399215894)));
	elseif (x <= 8e+82)
		tmp = Float64(Float64(y + Float64(x * Float64(Float64(x * Float64(Float64(x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / Float64(x * Float64(x + 45.3400022514)));
	else
		tmp = Float64(x * 4.16438922228);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -36.0)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 14.5)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	elseif (x <= 8e+82)
		tmp = (y + (x * ((x * ((x * 4.16438922228) + 78.6994924154)) + 137.519416416))) / (x * (x + 45.3400022514));
	else
		tmp = x * 4.16438922228;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 14.5], 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 * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+82], N[(N[(y + N[(x * N[(N[(x * N[(N[(x * 4.16438922228), $MachinePrecision] + 78.6994924154), $MachinePrecision]), $MachinePrecision] + 137.519416416), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * N[(x + 45.3400022514), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 4.16438922228), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -36

   1. Initial program 13.8%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. *-commutative 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -36 < x < 14.5

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.2%

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

      1. *-commutative 98.2%

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

   7. Simplified 98.2%

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

   if 14.5 < x < 7.9999999999999997e82

   1. Initial program 69.5%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around inf 85.8%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{45.3400022514 \cdot {x}^{2} + {x}^{3}}} \]
   5. Step-by-step derivation

      1. +-commutative 85.8%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{3} + 45.3400022514 \cdot {x}^{2}}} \]

      2. cube-mult 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{x \cdot \left(x \cdot x\right)} + 45.3400022514 \cdot {x}^{2}} \]

      3. unpow2 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{x \cdot \color{blue}{{x}^{2}} + 45.3400022514 \cdot {x}^{2}} \]

      4. distribute-rgt-out 85.9%

         \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   6. Simplified 85.9%

      \[\leadsto \frac{\mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)}{\color{blue}{{x}^{2} \cdot \left(x + 45.3400022514\right)}} \]

   7. Taylor expanded in z around 0 69.0%

      \[\leadsto \color{blue}{\frac{y + x \cdot \left(137.519416416 + x \cdot \left(78.6994924154 + 4.16438922228 \cdot x\right)\right)}{x \cdot \left(45.3400022514 + x\right)}} \]

   if 7.9999999999999997e82 < x

   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. Taylor expanded in x around inf 99.0%

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

      1. *-commutative 99.0%

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

   4. Simplified 99.0%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 14.5:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+82}:\\ \;\;\;\;\frac{y + x \cdot \left(x \cdot \left(x \cdot 4.16438922228 + 78.6994924154\right) + 137.519416416\right)}{x \cdot \left(x + 45.3400022514\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228\\ \end{array} \]

Alternative 8: 92.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 6600000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -36.0)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 6600000.0)
     (/
      (* (- x 2.0) (+ z (* x (+ y (* x 137.519416416)))))
      (+ 47.066876606 (* x 313.399215894)))
     (- (* x 4.16438922228) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 6600000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-36.0d0)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 6600000.0d0) then
        tmp = ((x - 2.0d0) * (z + (x * (y + (x * 137.519416416d0))))) / (47.066876606d0 + (x * 313.399215894d0))
    else
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -36.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 6600000.0) {
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -36.0:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 6600000.0:
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894))
	else:
		tmp = (x * 4.16438922228) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -36.0)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 6600000.0)
		tmp = Float64(Float64(Float64(x - 2.0) * Float64(z + Float64(x * Float64(y + Float64(x * 137.519416416))))) / Float64(47.066876606 + Float64(x * 313.399215894)));
	else
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -36.0)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 6600000.0)
		tmp = ((x - 2.0) * (z + (x * (y + (x * 137.519416416))))) / (47.066876606 + (x * 313.399215894));
	else
		tmp = (x * 4.16438922228) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -36.0], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6600000.0], 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 * 313.399215894), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -36

   1. Initial program 13.8%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. *-commutative 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -36 < x < 6.6e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around 0 97.6%

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

      1. *-commutative 97.6%

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

   7. Simplified 97.6%

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

   if 6.6e6 < x

   1. Initial program 16.9%

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

   2. Taylor expanded in x around inf 83.7%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 6600000:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(z + x \cdot \left(y + x \cdot 137.519416416\right)\right)}{47.066876606 + x \cdot 313.399215894}\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 9: 90.1% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 24:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(y \cdot -0.0424927283095952 + z \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -310.0)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 24.0)
     (+
      (* z -0.0424927283095952)
      (* x (+ (* y -0.0424927283095952) (* z 0.3041881842569256))))
     (- (* x 4.16438922228) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -310.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 24.0) {
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256)));
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-310.0d0)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 24.0d0) then
        tmp = (z * (-0.0424927283095952d0)) + (x * ((y * (-0.0424927283095952d0)) + (z * 0.3041881842569256d0)))
    else
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -310.0) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 24.0) {
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256)));
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -310.0:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 24.0:
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256)))
	else:
		tmp = (x * 4.16438922228) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -310.0)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 24.0)
		tmp = Float64(Float64(z * -0.0424927283095952) + Float64(x * Float64(Float64(y * -0.0424927283095952) + Float64(z * 0.3041881842569256))));
	else
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -310.0)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 24.0)
		tmp = (z * -0.0424927283095952) + (x * ((y * -0.0424927283095952) + (z * 0.3041881842569256)));
	else
		tmp = (x * 4.16438922228) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -310.0], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 24.0], N[(N[(z * -0.0424927283095952), $MachinePrecision] + N[(x * N[(N[(y * -0.0424927283095952), $MachinePrecision] + N[(z * 0.3041881842569256), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -310

   1. Initial program 13.8%

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

   2. Taylor expanded in x around inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. *-commutative 92.7%

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

      3. un-div-inv 92.7%

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

   4. Applied egg-rr 92.7%

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

   if -310 < x < 24

   1. Initial program 99.6%

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

   2. Taylor expanded in x around inf 98.4%

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

      1. +-commutative 98.4%

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

      2. cube-mult 98.4%

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

      3. unpow2 98.4%

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

      4. distribute-rgt-out 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in x around 0 97.8%

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

   6. Taylor expanded in y around 0 97.4%

      \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + \color{blue}{-1 \cdot \left({x}^{2} \cdot \left(5.843575199059173 + 6.658593866711955 \cdot \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right)\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + \color{blue}{\left(-{x}^{2} \cdot \left(5.843575199059173 + 6.658593866711955 \cdot \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right)\right)\right)}\right) \]

      2. distribute-rgt-neg-in 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + \color{blue}{{x}^{2} \cdot \left(-\left(5.843575199059173 + 6.658593866711955 \cdot \left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right)\right)\right)}\right) \]

      3. *-commutative 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + {x}^{2} \cdot \left(-\left(5.843575199059173 + \color{blue}{\left(0.0212463641547976 \cdot z - -0.28294182010212804 \cdot z\right) \cdot 6.658593866711955}\right)\right)\right) \]

      4. distribute-rgt-out-- 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + {x}^{2} \cdot \left(-\left(5.843575199059173 + \color{blue}{\left(z \cdot \left(0.0212463641547976 - -0.28294182010212804\right)\right)} \cdot 6.658593866711955\right)\right)\right) \]

      5. metadata-eval 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + {x}^{2} \cdot \left(-\left(5.843575199059173 + \left(z \cdot \color{blue}{0.3041881842569256}\right) \cdot 6.658593866711955\right)\right)\right) \]

      6. associate-*l* 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + {x}^{2} \cdot \left(-\left(5.843575199059173 + \color{blue}{z \cdot \left(0.3041881842569256 \cdot 6.658593866711955\right)}\right)\right)\right) \]

      7. metadata-eval 97.4%

         \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + {x}^{2} \cdot \left(-\left(5.843575199059173 + z \cdot \color{blue}{2.025465578019411}\right)\right)\right) \]

   8. Simplified 97.4%

      \[\leadsto -0.0424927283095952 \cdot z + \left(x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right) + \color{blue}{{x}^{2} \cdot \left(-\left(5.843575199059173 + z \cdot 2.025465578019411\right)\right)}\right) \]

   9. Taylor expanded in x around 0 89.2%

      \[\leadsto -0.0424927283095952 \cdot z + \color{blue}{x \cdot \left(0.0212463641547976 \cdot \left(z + -2 \cdot y\right) - -0.28294182010212804 \cdot z\right)} \]
   10. Step-by-step derivation

       1. +-commutative 89.2%

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

       2. distribute-rgt-in 89.2%

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

       3. *-commutative 89.2%

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

       4. associate-*l* 89.2%

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

       5. metadata-eval 89.2%

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

       6. *-commutative 89.2%

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

       7. associate--l+ 89.2%

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

       8. *-commutative 89.2%

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

       9. distribute-rgt-out-- 89.2%

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

       10. metadata-eval 89.2%

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

   11. Simplified 89.2%

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

   if 24 < x

   1. Initial program 18.2%

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

   2. Taylor expanded in x around inf 82.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 24:\\ \;\;\;\;z \cdot -0.0424927283095952 + x \cdot \left(y \cdot -0.0424927283095952 + z \cdot 0.3041881842569256\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 10: 76.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e-12)
   (+ (* x 4.16438922228) (- (/ 3655.1204654076414 x) 110.1139242984811))
   (if (<= x 1.9e-25)
     (* z -0.0424927283095952)
     (- (* x 4.16438922228) 110.1139242984811))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-12) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 1.9e-25) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1d-12)) then
        tmp = (x * 4.16438922228d0) + ((3655.1204654076414d0 / x) - 110.1139242984811d0)
    else if (x <= 1.9d-25) then
        tmp = z * (-0.0424927283095952d0)
    else
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-12) {
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	} else if (x <= 1.9e-25) {
		tmp = z * -0.0424927283095952;
	} else {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e-12:
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811)
	elif x <= 1.9e-25:
		tmp = z * -0.0424927283095952
	else:
		tmp = (x * 4.16438922228) - 110.1139242984811
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e-12)
		tmp = Float64(Float64(x * 4.16438922228) + Float64(Float64(3655.1204654076414 / x) - 110.1139242984811));
	elseif (x <= 1.9e-25)
		tmp = Float64(z * -0.0424927283095952);
	else
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e-12)
		tmp = (x * 4.16438922228) + ((3655.1204654076414 / x) - 110.1139242984811);
	elseif (x <= 1.9e-25)
		tmp = z * -0.0424927283095952;
	else
		tmp = (x * 4.16438922228) - 110.1139242984811;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e-12], N[(N[(x * 4.16438922228), $MachinePrecision] + N[(N[(3655.1204654076414 / x), $MachinePrecision] - 110.1139242984811), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-25], N[(z * -0.0424927283095952), $MachinePrecision], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999998e-13

   1. Initial program 15.1%

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

   2. Taylor expanded in x around inf 91.3%

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

      1. associate--l+ 91.4%

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

      2. *-commutative 91.4%

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

      3. un-div-inv 91.4%

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

   4. Applied egg-rr 91.4%

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

   if -9.9999999999999998e-13 < x < 1.8999999999999999e-25

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 66.0%

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

   if 1.8999999999999999e-25 < x

   1. Initial program 26.6%

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

   2. Taylor expanded in x around inf 74.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12}:\\ \;\;\;\;x \cdot 4.16438922228 + \left(\frac{3655.1204654076414}{x} - 110.1139242984811\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-25}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \mathbf{else}:\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \end{array} \]

Alternative 11: 76.8% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-12) (not (<= x 1.9e-25)))
   (- (* x 4.16438922228) 110.1139242984811)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-12) || !(x <= 1.9e-25)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1d-12)) .or. (.not. (x <= 1.9d-25))) then
        tmp = (x * 4.16438922228d0) - 110.1139242984811d0
    else
        tmp = z * (-0.0424927283095952d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-12) || !(x <= 1.9e-25)) {
		tmp = (x * 4.16438922228) - 110.1139242984811;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-12) or not (x <= 1.9e-25):
		tmp = (x * 4.16438922228) - 110.1139242984811
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-12) || !(x <= 1.9e-25))
		tmp = Float64(Float64(x * 4.16438922228) - 110.1139242984811);
	else
		tmp = Float64(z * -0.0424927283095952);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-12) || ~((x <= 1.9e-25)))
		tmp = (x * 4.16438922228) - 110.1139242984811;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-12], N[Not[LessEqual[x, 1.9e-25]], $MachinePrecision]], N[(N[(x * 4.16438922228), $MachinePrecision] - 110.1139242984811), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999998e-13 or 1.8999999999999999e-25 < x

   1. Initial program 20.9%

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

   2. Taylor expanded in x around inf 82.8%

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

   if -9.9999999999999998e-13 < x < 1.8999999999999999e-25

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 66.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 1.9 \cdot 10^{-25}\right):\\ \;\;\;\;x \cdot 4.16438922228 - 110.1139242984811\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 12: 77.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 6600000\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-12) (not (<= x 6600000.0)))
   (* x 4.16438922228)
   (* z -0.0424927283095952)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-12) || !(x <= 6600000.0)) {
		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 <= (-1d-12)) .or. (.not. (x <= 6600000.0d0))) 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 <= -1e-12) || !(x <= 6600000.0)) {
		tmp = x * 4.16438922228;
	} else {
		tmp = z * -0.0424927283095952;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-12) or not (x <= 6600000.0):
		tmp = x * 4.16438922228
	else:
		tmp = z * -0.0424927283095952
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-12) || !(x <= 6600000.0))
		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 <= -1e-12) || ~((x <= 6600000.0)))
		tmp = x * 4.16438922228;
	else
		tmp = z * -0.0424927283095952;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-12], N[Not[LessEqual[x, 6600000.0]], $MachinePrecision]], N[(x * 4.16438922228), $MachinePrecision], N[(z * -0.0424927283095952), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.9999999999999998e-13 or 6.6e6 < x

   1. Initial program 15.9%

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

   2. Taylor expanded in x around inf 87.0%

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

      1. *-commutative 87.0%

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

   4. Simplified 87.0%

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

   if -9.9999999999999998e-13 < x < 6.6e6

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 62.2%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-12} \lor \neg \left(x \leq 6600000\right):\\ \;\;\;\;x \cdot 4.16438922228\\ \mathbf{else}:\\ \;\;\;\;z \cdot -0.0424927283095952\\ \end{array} \]

Alternative 13: 34.8% accurate, 12.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 58.1%

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

2. Taylor expanded in x around 0 32.9%

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

3. Final simplification 32.9%

   \[\leadsto z \cdot -0.0424927283095952 \]

Developer target: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 1.0) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

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