Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.4% → 93.8%

Time: 1.4min

Alternatives: 24

Speedup: 1.4×

• 46.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) \cdot t_1 + t_0 \cdot t_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Initial Program: 70.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) \cdot t_1 + t_0 \cdot t_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\right) \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* (* 3.0 x1) x1))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (+
    x1
    (+
     (+
      (+
       (+
        (*
         (+
          (* (* (* 2.0 x1) t_2) (- t_2 3.0))
          (* (* x1 x1) (- (* 4.0 t_2) 6.0)))
         t_1)
        (* t_0 t_2))
       (* (* x1 x1) x1))
      x1)
     (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    t_0 = (3.0d0 * x1) * x1
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    code = x1 + (((((((((2.0d0 * x1) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)))
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (3.0 * x1) * x1;
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
}

Python

def code(x1, x2):
	t_0 = (3.0 * x1) * x1
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	return x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))

Julia

function code(x1, x2)
	t_0 = Float64(Float64(3.0 * x1) * x1)
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	return Float64(x1 + Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(2.0 * x1) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0))) * t_1) + Float64(t_0 * t_2)) + Float64(Float64(x1 * x1) * x1)) + x1) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
end

MATLAB

function tmp = code(x1, x2)
	t_0 = (3.0 * x1) * x1;
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = x1 + (((((((((2.0 * x1) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0))) * t_1) + (t_0 * t_2)) + ((x1 * x1) * x1)) + x1) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(3.0 * x1), $MachinePrecision] * x1), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, N[(x1 + N[(N[(N[(N[(N[(N[(N[(N[(N[(2.0 * x1), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * x1), $MachinePrecision]), $MachinePrecision] + x1), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Alternative 1: 93.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot -6\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t_2, 4, -6\right), t_2 \cdot \left(\left(-3 + t_2\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(t_1, t_2, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 -6.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (fma x1 (* x1 3.0) (- (* x2 2.0) x1)) (fma x1 x1 1.0))))
   (if (<= x1 -4.2e+155)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        x1
        (fma (* x2 4.0) (fma 2.0 x2 -3.0) -2.0)
        (* (* x1 x1) (* 3.0 (+ x2 (+ x2 3.0)))))))
     (if (<= x1 -5.5e+102)
       (+
        x1
        (+
         (+ x1 (* (pow x1 4.0) 6.0))
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) (+ (* x1 x1) 1.0)))))
       (if (<= x1 1.5e+133)
         (+
          x1
          (fma
           3.0
           (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
           (+
            x1
            (fma
             (fma x1 x1 1.0)
             (fma
              x1
              (* x1 (fma t_2 4.0 -6.0))
              (* t_2 (* (+ -3.0 t_2) (* x1 2.0))))
             (fma t_1 t_2 (pow x1 3.0))))))
         (cbrt (* t_0 (* t_0 t_0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * -6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = fma(x1, (x1 * 3.0), ((x2 * 2.0) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + fma(x2, -6.0, fma(x1, fma((x2 * 4.0), fma(2.0, x2, -3.0), -2.0), ((x1 * x1) * (3.0 * (x2 + (x2 + 3.0))))));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_1 - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_2, 4.0, -6.0)), (t_2 * ((-3.0 + t_2) * (x1 * 2.0)))), fma(t_1, t_2, pow(x1, 3.0)))));
	} else {
		tmp = cbrt((t_0 * (t_0 * t_0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * -6.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 * 2.0) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -4.2e+155)
		tmp = Float64(x1 + fma(x2, -6.0, fma(x1, fma(Float64(x2 * 4.0), fma(2.0, x2, -3.0), -2.0), Float64(Float64(x1 * x1) * Float64(3.0 * Float64(x2 + Float64(x2 + 3.0)))))));
	elseif (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / Float64(Float64(x1 * x1) + 1.0)))));
	elseif (x1 <= 1.5e+133)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_2, 4.0, -6.0)), Float64(t_2 * Float64(Float64(-3.0 + t_2) * Float64(x1 * 2.0)))), fma(t_1, t_2, (x1 ^ 3.0))))));
	else
		tmp = cbrt(Float64(t_0 * Float64(t_0 * t_0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.2e+155], N[(x1 + N[(x2 * -6.0 + N[(x1 * N[(N[(x2 * 4.0), $MachinePrecision] * N[(2.0 * x2 + -3.0), $MachinePrecision] + -2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 * N[(x2 + N[(x2 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+133], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$2 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(-3.0 + t$95$2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$2 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2e155

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.2%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. fma-def 54.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

      3. +-commutative 54.2%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. associate-*r* 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      10. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      11. associate-*r* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      12. *-commutative 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*l* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      14. unpow2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      15. cancel-sign-sub-inv 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      16. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      17. count-2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{\left(x2 + x2\right)}\right)\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(3 + x2\right) + x2\right)\right)\right)\right)} \]

   if -4.2e155 < x1 < -5.49999999999999981e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{6 \cdot {x1}^{4}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -5.49999999999999981e102 < x1 < 1.50000000000000003e133

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\left(x1 \cdot 2\right) \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right)\right), \mathsf{fma}\left(x1 \cdot \left(x1 \cdot 3\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)} \]

   if 1.50000000000000003e133 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1 \cdot \left(x1 \cdot 3\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 2: 93.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)\\ t_1 := \frac{t_0}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_2 := x1 + x2 \cdot -6\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{\left(t_3 + x2 \cdot 2\right) - x1}{t_4}\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_3 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \frac{3 \cdot \left(x1 \cdot t_0\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t_1 \cdot \left(-3 + t_1\right)\right) + x1 \cdot \mathsf{fma}\left(t_1, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_4 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_5\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_5 - 6\right)\right) + 3 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_2 \cdot \left(t_2 \cdot t_2\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (- (+ x2 x2) x1)))
        (t_1 (/ t_0 (fma x1 x1 1.0)))
        (t_2 (+ x1 (* x2 -6.0)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- (+ t_3 (* x2 2.0)) x1) t_4)))
   (if (<= x1 -4.2e+155)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        x1
        (fma (* x2 4.0) (fma 2.0 x2 -3.0) -2.0)
        (* (* x1 x1) (* 3.0 (+ x2 (+ x2 3.0)))))))
     (if (<= x1 -5.5e-103)
       (+
        x1
        (fma
         3.0
         (/ (- t_3 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* x1 (/ (* 3.0 (* x1 t_0)) (fma x1 x1 1.0)))
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_1 (+ -3.0 t_1))) (* x1 (fma t_1 4.0 -6.0)))))))))
       (if (<= x1 1.5e+133)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_4
               (+
                (* (* (* x1 2.0) t_5) (- t_5 3.0))
                (* (* x1 x1) (- (* 4.0 t_5) 6.0))))
              (* 3.0 t_3))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (cbrt (* t_2 (* t_2 t_2))))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), ((x2 + x2) - x1));
	double t_1 = t_0 / fma(x1, x1, 1.0);
	double t_2 = x1 + (x2 * -6.0);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = ((t_3 + (x2 * 2.0)) - x1) / t_4;
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + fma(x2, -6.0, fma(x1, fma((x2 * 4.0), fma(2.0, x2, -3.0), -2.0), ((x1 * x1) * (3.0 * (x2 + (x2 + 3.0))))));
	} else if (x1 <= -5.5e-103) {
		tmp = x1 + fma(3.0, ((t_3 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((x1 * ((3.0 * (x1 * t_0)) / fma(x1, x1, 1.0))) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_1 * (-3.0 + t_1))) + (x1 * fma(t_1, 4.0, -6.0))))))));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + ((x1 + (((t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((4.0 * t_5) - 6.0)))) + (3.0 * t_3)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_2 * (t_2 * t_2)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 + x2) - x1))
	t_1 = Float64(t_0 / fma(x1, x1, 1.0))
	t_2 = Float64(x1 + Float64(x2 * -6.0))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(Float64(t_3 + Float64(x2 * 2.0)) - x1) / t_4)
	tmp = 0.0
	if (x1 <= -4.2e+155)
		tmp = Float64(x1 + fma(x2, -6.0, fma(x1, fma(Float64(x2 * 4.0), fma(2.0, x2, -3.0), -2.0), Float64(Float64(x1 * x1) * Float64(3.0 * Float64(x2 + Float64(x2 + 3.0)))))));
	elseif (x1 <= -5.5e-103)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_3 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(x1 * Float64(Float64(3.0 * Float64(x1 * t_0)) / fma(x1, x1, 1.0))) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_1 * Float64(-3.0 + t_1))) + Float64(x1 * fma(t_1, 4.0, -6.0)))))))));
	elseif (x1 <= 1.5e+133)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_4 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_5) - 6.0)))) + Float64(3.0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_2 * Float64(t_2 * t_2)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$3 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[x1, -4.2e+155], N[(x1 + N[(x2 * -6.0 + N[(x1 * N[(N[(x2 * 4.0), $MachinePrecision] * N[(2.0 * x2 + -3.0), $MachinePrecision] + -2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 * N[(x2 + N[(x2 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e-103], N[(x1 + N[(3.0 * N[(N[(t$95$3 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(N[(3.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$1 * N[(-3.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$1 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+133], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$4 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$2 * N[(t$95$2 * t$95$2), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2e155

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.2%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. fma-def 54.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

      3. +-commutative 54.2%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. associate-*r* 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      10. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      11. associate-*r* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      12. *-commutative 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*l* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      14. unpow2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      15. cancel-sign-sub-inv 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      16. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      17. count-2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{\left(x2 + x2\right)}\right)\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(3 + x2\right) + x2\right)\right)\right)\right)} \]

   if -4.2e155 < x1 < -5.50000000000000032e-103

   1. Initial program 85.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \frac{3 \cdot \left(x1 \cdot \mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right) + x1\right)\right)} \]

   if -5.50000000000000032e-103 < x1 < 1.50000000000000003e133

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 98.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.4%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.4%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 1.50000000000000003e133 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \frac{3 \cdot \left(x1 \cdot \mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 3: 93.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + x2 \cdot 2\right) - x1}{t_1}\\ t_4 := x1 + x2 \cdot -6\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2200000:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_2 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t_0 \cdot \left(-3 + t_0\right)\right) + x1 \cdot \mathsf{fma}\left(t_0, 4, -6\right)\right)\right) + x1 \cdot \left(x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + 3 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_4 \cdot \left(t_4 \cdot t_4\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (fma x1 (* x1 3.0) (- (+ x2 x2) x1)) (fma x1 x1 1.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* x2 2.0)) x1) t_1))
        (t_4 (+ x1 (* x2 -6.0))))
   (if (<= x1 -4.2e+155)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        x1
        (fma (* x2 4.0) (fma 2.0 x2 -3.0) -2.0)
        (* (* x1 x1) (* 3.0 (+ x2 (+ x2 3.0)))))))
     (if (<= x1 -2200000.0)
       (+
        x1
        (fma
         3.0
         (/ (- t_2 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (* x1 (+ (* 2.0 (* t_0 (+ -3.0 t_0))) (* x1 (fma t_0 4.0 -6.0))))))
          (* x1 (* x1 9.0)))))
       (if (<= x1 1.5e+133)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* 3.0 t_2))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (cbrt (* t_4 (* t_4 t_4))))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), ((x2 + x2) - x1)) / fma(x1, x1, 1.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (x2 * 2.0)) - x1) / t_1;
	double t_4 = x1 + (x2 * -6.0);
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + fma(x2, -6.0, fma(x1, fma((x2 * 4.0), fma(2.0, x2, -3.0), -2.0), ((x1 * x1) * (3.0 * (x2 + (x2 + 3.0))))));
	} else if (x1 <= -2200000.0) {
		tmp = x1 + fma(3.0, ((t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_0 * (-3.0 + t_0))) + (x1 * fma(t_0, 4.0, -6.0)))))) + (x1 * (x1 * 9.0))));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_4 * (t_4 * t_4)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 + x2) - x1)) / fma(x1, x1, 1.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(x2 * 2.0)) - x1) / t_1)
	t_4 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x1 <= -4.2e+155)
		tmp = Float64(x1 + fma(x2, -6.0, fma(x1, fma(Float64(x2 * 4.0), fma(2.0, x2, -3.0), -2.0), Float64(Float64(x1 * x1) * Float64(3.0 * Float64(x2 + Float64(x2 + 3.0)))))));
	elseif (x1 <= -2200000.0)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_0 * Float64(-3.0 + t_0))) + Float64(x1 * fma(t_0, 4.0, -6.0)))))) + Float64(x1 * Float64(x1 * 9.0)))));
	elseif (x1 <= 1.5e+133)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(3.0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_4 * Float64(t_4 * t_4)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.2e+155], N[(x1 + N[(x2 * -6.0 + N[(x1 * N[(N[(x2 * 4.0), $MachinePrecision] * N[(2.0 * x2 + -3.0), $MachinePrecision] + -2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 * N[(x2 + N[(x2 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2200000.0], N[(x1 + N[(3.0 * N[(N[(t$95$2 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$0 * N[(-3.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+133], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$4 * N[(t$95$4 * t$95$4), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2e155

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.2%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. fma-def 54.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

      3. +-commutative 54.2%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. associate-*r* 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      10. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      11. associate-*r* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      12. *-commutative 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*l* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      14. unpow2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      15. cancel-sign-sub-inv 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      16. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      17. count-2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{\left(x2 + x2\right)}\right)\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(3 + x2\right) + x2\right)\right)\right)\right)} \]

   if -4.2e155 < x1 < -2.2e6

   1. Initial program 71.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \frac{3 \cdot \left(x1 \cdot \mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right) + x1\right)\right)} \]

   4. Taylor expanded in x1 around inf 95.9%

      \[\leadsto x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \color{blue}{\left(9 \cdot x1\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right) + x1\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 95.9%

         \[\leadsto x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right) + x1\right)\right) \]

   6. Simplified 95.9%

      \[\leadsto x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \color{blue}{\left(x1 \cdot 9\right)} + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right) + x1\right)\right) \]

   if -2.2e6 < x1 < 1.50000000000000003e133

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 1.50000000000000003e133 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2200000:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right) + x1 \cdot \left(x1 \cdot 9\right)\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 4: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ t_3 := x1 + x2 \cdot -6\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_1\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_3 \cdot \left(t_3 \cdot t_3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* x2 2.0)) x1) t_0))
        (t_3 (+ x1 (* x2 -6.0))))
   (if (<= x1 -4.2e+155)
     (+
      x1
      (fma
       x2
       -6.0
       (fma
        x1
        (fma (* x2 4.0) (fma 2.0 x2 -3.0) -2.0)
        (* (* x1 x1) (* 3.0 (+ x2 (+ x2 3.0)))))))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         (+ x1 (* (pow x1 4.0) 6.0))
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))))
       (if (<= x1 1.5e+133)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_0
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* 3.0 t_1))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (cbrt (* t_3 (* t_3 t_3))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double t_3 = x1 + (x2 * -6.0);
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + fma(x2, -6.0, fma(x1, fma((x2 * 4.0), fma(2.0, x2, -3.0), -2.0), ((x1 * x1) * (3.0 * (x2 + (x2 + 3.0))))));
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + ((x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_3 * (t_3 * t_3)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x1 <= -4.2e+155)
		tmp = Float64(x1 + fma(x2, -6.0, fma(x1, fma(Float64(x2 * 4.0), fma(2.0, x2, -3.0), -2.0), Float64(Float64(x1 * x1) * Float64(3.0 * Float64(x2 + Float64(x2 + 3.0)))))));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0))));
	elseif (x1 <= 1.5e+133)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_1)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_3 * Float64(t_3 * t_3)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.2e+155], N[(x1 + N[(x2 * -6.0 + N[(x1 * N[(N[(x2 * 4.0), $MachinePrecision] * N[(2.0 * x2 + -3.0), $MachinePrecision] + -2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(3.0 * N[(x2 + N[(x2 + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+133], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$3 * N[(t$95$3 * t$95$3), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2e155

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.2%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 54.2%

         \[\leadsto x1 + \left(\color{blue}{x2 \cdot -6} + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right) \]

      2. fma-def 54.2%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

      3. +-commutative 54.2%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)}\right) \]

      4. fma-def 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      5. associate-*r* 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      6. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      7. metadata-eval 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      8. *-commutative 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      9. fma-neg 70.8%

         \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      10. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      11. associate-*r* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      12. *-commutative 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*l* 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{{x1}^{2} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      14. unpow2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\left(x1 \cdot x1\right)} \cdot \left(3 \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      15. cancel-sign-sub-inv 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right)\right) \]

      16. metadata-eval 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right)\right) \]

      17. count-2 70.8%

          \[\leadsto x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(3 + \color{blue}{\left(x2 + x2\right)}\right)\right)\right)\right) \]

   5. Simplified 70.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(\left(3 + x2\right) + x2\right)\right)\right)\right)} \]

   if -4.2e155 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{6 \cdot {x1}^{4}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -5.60000000000000037e102 < x1 < 1.50000000000000003e133

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 1.50000000000000003e133 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \mathsf{fma}\left(x2, -6, \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \left(x1 \cdot x1\right) \cdot \left(3 \cdot \left(x2 + \left(x2 + 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 5: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x2 \cdot -6\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + x2 \cdot 2\right) - x1}{t_0}\\ t_5 := t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\right)\\ \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(t_3 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(t_2 + \left(t_5 + t_3 \cdot t_4\right)\right)\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_5 + 3 \cdot t_3\right) + t_2\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x2 -6.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* x2 2.0)) x1) t_0))
        (t_5
         (*
          t_0
          (+
           (* (* (* x1 2.0) t_4) (- t_4 3.0))
           (* (* x1 x1) (- (* 4.0 t_4) 6.0))))))
   (if (<=
        (+
         x1
         (+
          (* 3.0 (/ (- (- t_3 (* x2 2.0)) x1) t_0))
          (+ x1 (+ t_2 (+ t_5 (* t_3 t_4))))))
        INFINITY)
     (+ x1 (+ (+ x1 (+ (+ t_5 (* 3.0 t_3)) t_2)) (* 3.0 (- (* x2 -2.0) x1))))
     (cbrt (* t_1 (* t_1 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * -6.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)));
	double tmp;
	if ((x1 + ((3.0 * (((t_3 - (x2 * 2.0)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_3 * t_4)))))) <= ((double) INFINITY)) {
		tmp = x1 + ((x1 + ((t_5 + (3.0 * t_3)) + t_2)) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * -6.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (x2 * 2.0)) - x1) / t_0;
	double t_5 = t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((4.0 * t_4) - 6.0)));
	double tmp;
	if ((x1 + ((3.0 * (((t_3 - (x2 * 2.0)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_3 * t_4)))))) <= Double.POSITIVE_INFINITY) {
		tmp = x1 + ((x1 + ((t_5 + (3.0 * t_3)) + t_2)) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = Math.cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(x2 * 2.0)) - x1) / t_0)
	t_5 = Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_3 * t_4)))))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_5 + Float64(3.0 * t_3)) + t_2)) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_1 * Float64(t_1 * t_1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(N[(x1 + N[(N[(t$95$5 + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$1 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))))) < +inf.0

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 2 x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)) 3)) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 4 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1))) 6))) (+.f64 (*.f64 x1 x1) 1)) (*.f64 (*.f64 (*.f64 3 x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 3 (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 3 x1) x1) (*.f64 2 x2)) x1) (+.f64 (*.f64 x1 x1) 1)))))

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 4.8%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 4.8%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 4.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 48.3%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 48.3%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 48.3%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 48.3%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\right)\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 6: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot -6\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_2}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + 3 \cdot t_1\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_0 \cdot \left(t_0 \cdot t_0\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 -6.0)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* x2 2.0)) x1) t_2)))
   (if (<= x1 -4.2e+155)
     (+
      x1
      (+
       (* x2 -6.0)
       (+
        (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
        (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))))
     (if (<= x1 -5.6e+102)
       (+
        x1
        (+
         (+ x1 (* (pow x1 4.0) 6.0))
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_2))))
       (if (<= x1 1.5e+133)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_2
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* 3.0 t_1))
             (* x1 (* x1 x1))))
           (* 3.0 (- (* x2 -2.0) x1))))
         (cbrt (* t_0 (* t_0 t_0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * -6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + ((x2 * -6.0) + ((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))));
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_0 * (t_0 * t_0)));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * -6.0);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.2e+155) {
		tmp = x1 + ((x2 * -6.0) + ((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))));
	} else if (x1 <= -5.6e+102) {
		tmp = x1 + ((x1 + (Math.pow(x1, 4.0) * 6.0)) + (3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 1.5e+133) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_1)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = Math.cbrt((t_0 * (t_0 * t_0)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * -6.0))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4.2e+155)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0)))));
	elseif (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_2))));
	elseif (x1 <= 1.5e+133)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(3.0 * t_1)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_0 * Float64(t_0 * t_0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.2e+155], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.6e+102], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.5e+133], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$0 * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.2e155

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.2%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\right)} \]

   if -4.2e155 < x1 < -5.60000000000000037e102

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{6 \cdot {x1}^{4}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 87.5%

      \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -5.60000000000000037e102 < x1 < 1.50000000000000003e133

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 1.50000000000000003e133 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{+155}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 1.5 \cdot 10^{+133}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 7: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + x2 \cdot -6\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_2}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{t_1 \cdot \left(t_1 \cdot t_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (* x2 -6.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* x2 2.0)) x1) t_2)))
   (if (<= x1 -1e+103)
     (+
      x1
      (+
       (+ x1 (* (pow x1 4.0) 6.0))
       (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_2))))
     (if (<= x1 5e+131)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_2
             (+
              (* (* (* x1 2.0) t_3) (- t_3 3.0))
              (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
            (* 3.0 t_0))
           (* x1 (* x1 x1))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (cbrt (* t_1 (* t_1 t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * -6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 5e+131) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * -6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -1e+103) {
		tmp = x1 + ((x1 + (Math.pow(x1, 4.0) * 6.0)) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)));
	} else if (x1 <= 5e+131) {
		tmp = x1 + ((x1 + (((t_2 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = Math.cbrt((t_1 * (t_1 * t_1)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_2))));
	elseif (x1 <= 5e+131)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = cbrt(Float64(t_1 * Float64(t_1 * t_1)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -1e+103], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+131], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Power[N[(t$95$1 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e103

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 21.9%

      \[\leadsto x1 + \left(\left(\color{blue}{6 \cdot {x1}^{4}} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   3. Step-by-step derivation

      1. *-commutative 21.9%

         \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Simplified 21.9%

      \[\leadsto x1 + \left(\left(\color{blue}{{x1}^{4} \cdot 6} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -1e103 < x1 < 4.99999999999999995e131

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 99.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 99.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 4.99999999999999995e131 < x1

   1. Initial program 9.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.5%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.4%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. add-cbrt-cube 96.8%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]

   7. Applied egg-rr 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right) \cdot \left(x1 + x2 \cdot -6\right)}} \]
   8. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \sqrt[3]{\color{blue}{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]

   9. Simplified 96.8%

      \[\leadsto \color{blue}{\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+131}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(x1 + x2 \cdot -6\right) \cdot \left(\left(x1 + x2 \cdot -6\right) \cdot \left(x1 + x2 \cdot -6\right)\right)}\\ \end{array} \]

Alternative 8: 80.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (<= x1 5.5e+144)
     (+
      x1
      (+
       (+
        x1
        (+
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
          (* 3.0 t_0))
         (* x1 (* x1 x1))))
       (* 3.0 (- (* x2 -2.0) x1))))
     (/ (fma x1 x1 (* (* x2 x2) -36.0)) (+ x1 (* x2 6.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= 5.5e+144) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = fma(x1, x1, ((x2 * x2) * -36.0)) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= 5.5e+144)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(fma(x1, x1, Float64(Float64(x2 * x2) * -36.0)) / Float64(x1 + Float64(x2 * 6.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, 5.5e+144], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1 + N[(N[(x2 * x2), $MachinePrecision] * -36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < 5.50000000000000022e144

   1. Initial program 85.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 83.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 85.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 85.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. fma-neg 79.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. *-commutative 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 - \color{blue}{-6 \cdot x2}} \]

      9. cancel-sign-sub-inv 79.3%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(--6\right) \cdot x2}} \]

      10. metadata-eval 79.3%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{6} \cdot x2} \]

      11. *-commutative 79.3%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot 6}} \]

   9. Simplified 79.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + x2 \cdot 2\right) - x1}{t_0}\\ t_4 := 3 \cdot \frac{\left(t_2 - x2 \cdot 2\right) - x1}{t_0}\\ t_5 := x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(3 \cdot t_2 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right) + \left(t_3 - 3\right) \cdot \left(3 \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ t_6 := x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_2 \cdot t_3 + t_0 \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -16000:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq -1.25 \cdot 10^{-232}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 195:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* x2 2.0)) x1) t_0))
        (t_4 (* 3.0 (/ (- (- t_2 (* x2 2.0)) x1) t_0)))
        (t_5
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             t_1
             (+
              (* 3.0 t_2)
              (*
               t_0
               (+
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))
                (* (- t_3 3.0) (* 3.0 (* x1 2.0)))))))))))
        (t_6
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             t_1
             (+
              (* t_2 t_3)
              (* t_0 (* 4.0 (* x1 (* x2 (- (* x2 2.0) 3.0))))))))))))
   (if (<= x1 -16000.0)
     t_5
     (if (<= x1 -1.25e-232)
       t_6
       (if (<= x1 6.8e-252)
         (+ x1 (+ t_4 (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
         (if (<= x1 195.0)
           t_6
           (if (<= x1 5.5e+144)
             t_5
             (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_4 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_5 = x1 + (t_4 + (x1 + (t_1 + ((3.0 * t_2) + (t_0 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (3.0 * (x1 * 2.0)))))))));
	double t_6 = x1 + (t_4 + (x1 + (t_1 + ((t_2 * t_3) + (t_0 * (4.0 * (x1 * (x2 * ((x2 * 2.0) - 3.0)))))))));
	double tmp;
	if (x1 <= -16000.0) {
		tmp = t_5;
	} else if (x1 <= -1.25e-232) {
		tmp = t_6;
	} else if (x1 <= 6.8e-252) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 195.0) {
		tmp = t_6;
	} else if (x1 <= 5.5e+144) {
		tmp = t_5;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (x2 * 2.0d0)) - x1) / t_0
    t_4 = 3.0d0 * (((t_2 - (x2 * 2.0d0)) - x1) / t_0)
    t_5 = x1 + (t_4 + (x1 + (t_1 + ((3.0d0 * t_2) + (t_0 * (((x1 * x1) * ((4.0d0 * t_3) - 6.0d0)) + ((t_3 - 3.0d0) * (3.0d0 * (x1 * 2.0d0)))))))))
    t_6 = x1 + (t_4 + (x1 + (t_1 + ((t_2 * t_3) + (t_0 * (4.0d0 * (x1 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))))))
    if (x1 <= (-16000.0d0)) then
        tmp = t_5
    else if (x1 <= (-1.25d-232)) then
        tmp = t_6
    else if (x1 <= 6.8d-252) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 195.0d0) then
        tmp = t_6
    else if (x1 <= 5.5d+144) then
        tmp = t_5
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	double t_4 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	double t_5 = x1 + (t_4 + (x1 + (t_1 + ((3.0 * t_2) + (t_0 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (3.0 * (x1 * 2.0)))))))));
	double t_6 = x1 + (t_4 + (x1 + (t_1 + ((t_2 * t_3) + (t_0 * (4.0 * (x1 * (x2 * ((x2 * 2.0) - 3.0)))))))));
	double tmp;
	if (x1 <= -16000.0) {
		tmp = t_5;
	} else if (x1 <= -1.25e-232) {
		tmp = t_6;
	} else if (x1 <= 6.8e-252) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 195.0) {
		tmp = t_6;
	} else if (x1 <= 5.5e+144) {
		tmp = t_5;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (x2 * 2.0)) - x1) / t_0
	t_4 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0)
	t_5 = x1 + (t_4 + (x1 + (t_1 + ((3.0 * t_2) + (t_0 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (3.0 * (x1 * 2.0)))))))))
	t_6 = x1 + (t_4 + (x1 + (t_1 + ((t_2 * t_3) + (t_0 * (4.0 * (x1 * (x2 * ((x2 * 2.0) - 3.0)))))))))
	tmp = 0
	if x1 <= -16000.0:
		tmp = t_5
	elif x1 <= -1.25e-232:
		tmp = t_6
	elif x1 <= 6.8e-252:
		tmp = x1 + (t_4 + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 195.0:
		tmp = t_6
	elif x1 <= 5.5e+144:
		tmp = t_5
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(x2 * 2.0)) - x1) / t_0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(x2 * 2.0)) - x1) / t_0))
	t_5 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_1 + Float64(Float64(3.0 * t_2) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)) + Float64(Float64(t_3 - 3.0) * Float64(3.0 * Float64(x1 * 2.0))))))))))
	t_6 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_1 + Float64(Float64(t_2 * t_3) + Float64(t_0 * Float64(4.0 * Float64(x1 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))))))))
	tmp = 0.0
	if (x1 <= -16000.0)
		tmp = t_5;
	elseif (x1 <= -1.25e-232)
		tmp = t_6;
	elseif (x1 <= 6.8e-252)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 195.0)
		tmp = t_6;
	elseif (x1 <= 5.5e+144)
		tmp = t_5;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (x2 * 2.0)) - x1) / t_0;
	t_4 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_0);
	t_5 = x1 + (t_4 + (x1 + (t_1 + ((3.0 * t_2) + (t_0 * (((x1 * x1) * ((4.0 * t_3) - 6.0)) + ((t_3 - 3.0) * (3.0 * (x1 * 2.0)))))))));
	t_6 = x1 + (t_4 + (x1 + (t_1 + ((t_2 * t_3) + (t_0 * (4.0 * (x1 * (x2 * ((x2 * 2.0) - 3.0)))))))));
	tmp = 0.0;
	if (x1 <= -16000.0)
		tmp = t_5;
	elseif (x1 <= -1.25e-232)
		tmp = t_6;
	elseif (x1 <= 6.8e-252)
		tmp = x1 + (t_4 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 195.0)
		tmp = t_6;
	elseif (x1 <= 5.5e+144)
		tmp = t_5;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$2 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$1 + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - 3.0), $MachinePrecision] * N[(3.0 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$1 + N[(N[(t$95$2 * t$95$3), $MachinePrecision] + N[(t$95$0 * N[(4.0 * N[(x1 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -16000.0], t$95$5, If[LessEqual[x1, -1.25e-232], t$95$6, If[LessEqual[x1, 6.8e-252], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 195.0], t$95$6, If[LessEqual[x1, 5.5e+144], t$95$5, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -16000 or 195 < x1 < 5.50000000000000022e144

   1. Initial program 62.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 62.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 48.4%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{3}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -16000 < x1 < -1.25e-232 or 6.7999999999999999e-252 < x1 < 195

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 98.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 86.5%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -1.25e-232 < x1 < 6.7999999999999999e-252

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -16000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(3 \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.25 \cdot 10^{-232}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-252}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 195:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(3 \cdot \left(x1 \cdot 2\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 10: 64.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x2 \cdot 2 - x1\\ t_2 := x2 \cdot \left(x2 \cdot 2 - 3\right)\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot \left(x1 \cdot 3\right)\\ t_5 := 3 \cdot \frac{\left(t_4 - x2 \cdot 2\right) - x1}{t_0}\\ t_6 := \frac{\left(t_4 + x2 \cdot 2\right) - x1}{t_0}\\ t_7 := t_4 \cdot t_6\\ t_8 := x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(3 \cdot t_4 + t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_6\right) \cdot \left(t_6 - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+61}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(t_7 + t_0 \cdot \left(\left(3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_1 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_1 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -210000:\\ \;\;\;\;t_8\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-236}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_3 + \left(t_7 + t_0 \cdot \left(4 \cdot \left(x1 \cdot t_2\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.4 \cdot 10^{-74}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_2 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;t_8\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (- (* x2 2.0) x1))
        (t_2 (* x2 (- (* x2 2.0) 3.0)))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (* x1 (* x1 3.0)))
        (t_5 (* 3.0 (/ (- (- t_4 (* x2 2.0)) x1) t_0)))
        (t_6 (/ (- (+ t_4 (* x2 2.0)) x1) t_0))
        (t_7 (* t_4 t_6))
        (t_8
         (+
          x1
          (+
           t_5
           (+
            x1
            (+
             t_3
             (+
              (* 3.0 t_4)
              (* t_0 (+ (* (* (* x1 2.0) t_6) (- t_6 3.0)) (* x2 8.0))))))))))
   (if (<= x1 -7.6e+61)
     (+
      x1
      (+
       t_5
       (+
        x1
        (+
         t_3
         (+
          t_7
          (*
           t_0
           (+
            (* (* 3.0 (* x1 2.0)) (- t_1 3.0))
            (* (* x1 x1) (- (* 4.0 t_1) 6.0)))))))))
     (if (<= x1 -210000.0)
       t_8
       (if (<= x1 -5.5e-236)
         (+ x1 (+ t_5 (+ x1 (+ t_3 (+ t_7 (* t_0 (* 4.0 (* x1 t_2))))))))
         (if (<= x1 6.8e-251)
           (+ x1 (+ t_5 (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
           (if (<= x1 8.4e-74)
             (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_2) 2.0))))
             (if (<= x1 3.5e+144)
               t_8
               (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * 2.0) - x1;
	double t_2 = x2 * ((x2 * 2.0) - 3.0);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = 3.0 * (((t_4 - (x2 * 2.0)) - x1) / t_0);
	double t_6 = ((t_4 + (x2 * 2.0)) - x1) / t_0;
	double t_7 = t_4 * t_6;
	double t_8 = x1 + (t_5 + (x1 + (t_3 + ((3.0 * t_4) + (t_0 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + (x2 * 8.0)))))));
	double tmp;
	if (x1 <= -7.6e+61) {
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (((3.0 * (x1 * 2.0)) * (t_1 - 3.0)) + ((x1 * x1) * ((4.0 * t_1) - 6.0))))))));
	} else if (x1 <= -210000.0) {
		tmp = t_8;
	} else if (x1 <= -5.5e-236) {
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (4.0 * (x1 * t_2)))))));
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 8.4e-74) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_2) - 2.0)));
	} else if (x1 <= 3.5e+144) {
		tmp = t_8;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: t_8
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = (x2 * 2.0d0) - x1
    t_2 = x2 * ((x2 * 2.0d0) - 3.0d0)
    t_3 = x1 * (x1 * x1)
    t_4 = x1 * (x1 * 3.0d0)
    t_5 = 3.0d0 * (((t_4 - (x2 * 2.0d0)) - x1) / t_0)
    t_6 = ((t_4 + (x2 * 2.0d0)) - x1) / t_0
    t_7 = t_4 * t_6
    t_8 = x1 + (t_5 + (x1 + (t_3 + ((3.0d0 * t_4) + (t_0 * ((((x1 * 2.0d0) * t_6) * (t_6 - 3.0d0)) + (x2 * 8.0d0)))))))
    if (x1 <= (-7.6d+61)) then
        tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (((3.0d0 * (x1 * 2.0d0)) * (t_1 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_1) - 6.0d0))))))))
    else if (x1 <= (-210000.0d0)) then
        tmp = t_8
    else if (x1 <= (-5.5d-236)) then
        tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (4.0d0 * (x1 * t_2)))))))
    else if (x1 <= 6.8d-251) then
        tmp = x1 + (t_5 + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 8.4d-74) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_2) - 2.0d0)))
    else if (x1 <= 3.5d+144) then
        tmp = t_8
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = (x2 * 2.0) - x1;
	double t_2 = x2 * ((x2 * 2.0) - 3.0);
	double t_3 = x1 * (x1 * x1);
	double t_4 = x1 * (x1 * 3.0);
	double t_5 = 3.0 * (((t_4 - (x2 * 2.0)) - x1) / t_0);
	double t_6 = ((t_4 + (x2 * 2.0)) - x1) / t_0;
	double t_7 = t_4 * t_6;
	double t_8 = x1 + (t_5 + (x1 + (t_3 + ((3.0 * t_4) + (t_0 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + (x2 * 8.0)))))));
	double tmp;
	if (x1 <= -7.6e+61) {
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (((3.0 * (x1 * 2.0)) * (t_1 - 3.0)) + ((x1 * x1) * ((4.0 * t_1) - 6.0))))))));
	} else if (x1 <= -210000.0) {
		tmp = t_8;
	} else if (x1 <= -5.5e-236) {
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (4.0 * (x1 * t_2)))))));
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 8.4e-74) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_2) - 2.0)));
	} else if (x1 <= 3.5e+144) {
		tmp = t_8;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = (x2 * 2.0) - x1
	t_2 = x2 * ((x2 * 2.0) - 3.0)
	t_3 = x1 * (x1 * x1)
	t_4 = x1 * (x1 * 3.0)
	t_5 = 3.0 * (((t_4 - (x2 * 2.0)) - x1) / t_0)
	t_6 = ((t_4 + (x2 * 2.0)) - x1) / t_0
	t_7 = t_4 * t_6
	t_8 = x1 + (t_5 + (x1 + (t_3 + ((3.0 * t_4) + (t_0 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + (x2 * 8.0)))))))
	tmp = 0
	if x1 <= -7.6e+61:
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (((3.0 * (x1 * 2.0)) * (t_1 - 3.0)) + ((x1 * x1) * ((4.0 * t_1) - 6.0))))))))
	elif x1 <= -210000.0:
		tmp = t_8
	elif x1 <= -5.5e-236:
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (4.0 * (x1 * t_2)))))))
	elif x1 <= 6.8e-251:
		tmp = x1 + (t_5 + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 8.4e-74:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_2) - 2.0)))
	elif x1 <= 3.5e+144:
		tmp = t_8
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(Float64(x2 * 2.0) - x1)
	t_2 = Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(x1 * Float64(x1 * 3.0))
	t_5 = Float64(3.0 * Float64(Float64(Float64(t_4 - Float64(x2 * 2.0)) - x1) / t_0))
	t_6 = Float64(Float64(Float64(t_4 + Float64(x2 * 2.0)) - x1) / t_0)
	t_7 = Float64(t_4 * t_6)
	t_8 = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_3 + Float64(Float64(3.0 * t_4) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_6) * Float64(t_6 - 3.0)) + Float64(x2 * 8.0))))))))
	tmp = 0.0
	if (x1 <= -7.6e+61)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_3 + Float64(t_7 + Float64(t_0 * Float64(Float64(Float64(3.0 * Float64(x1 * 2.0)) * Float64(t_1 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_1) - 6.0)))))))));
	elseif (x1 <= -210000.0)
		tmp = t_8;
	elseif (x1 <= -5.5e-236)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_3 + Float64(t_7 + Float64(t_0 * Float64(4.0 * Float64(x1 * t_2))))))));
	elseif (x1 <= 6.8e-251)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 8.4e-74)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_2) - 2.0))));
	elseif (x1 <= 3.5e+144)
		tmp = t_8;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = (x2 * 2.0) - x1;
	t_2 = x2 * ((x2 * 2.0) - 3.0);
	t_3 = x1 * (x1 * x1);
	t_4 = x1 * (x1 * 3.0);
	t_5 = 3.0 * (((t_4 - (x2 * 2.0)) - x1) / t_0);
	t_6 = ((t_4 + (x2 * 2.0)) - x1) / t_0;
	t_7 = t_4 * t_6;
	t_8 = x1 + (t_5 + (x1 + (t_3 + ((3.0 * t_4) + (t_0 * ((((x1 * 2.0) * t_6) * (t_6 - 3.0)) + (x2 * 8.0)))))));
	tmp = 0.0;
	if (x1 <= -7.6e+61)
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (((3.0 * (x1 * 2.0)) * (t_1 - 3.0)) + ((x1 * x1) * ((4.0 * t_1) - 6.0))))))));
	elseif (x1 <= -210000.0)
		tmp = t_8;
	elseif (x1 <= -5.5e-236)
		tmp = x1 + (t_5 + (x1 + (t_3 + (t_7 + (t_0 * (4.0 * (x1 * t_2)))))));
	elseif (x1 <= 6.8e-251)
		tmp = x1 + (t_5 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 8.4e-74)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_2) - 2.0)));
	elseif (x1 <= 3.5e+144)
		tmp = t_8;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]}, Block[{t$95$2 = N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(t$95$4 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(N[(N[(t$95$4 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$7 = N[(t$95$4 * t$95$6), $MachinePrecision]}, Block[{t$95$8 = N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$3 + N[(N[(3.0 * t$95$4), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$6), $MachinePrecision] * N[(t$95$6 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.6e+61], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$3 + N[(t$95$7 + N[(t$95$0 * N[(N[(N[(3.0 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$1 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$1), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -210000.0], t$95$8, If[LessEqual[x1, -5.5e-236], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$3 + N[(t$95$7 + N[(t$95$0 * N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.8e-251], N[(x1 + N[(t$95$5 + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 8.4e-74], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$2), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.5e+144], t$95$8, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x1 < -7.5999999999999999e61

   1. Initial program 21.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 2.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 0.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{3}\right) \cdot \left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   4. Taylor expanded in x1 around 0 12.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot 3\right) \cdot \left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -7.5999999999999999e61 < x1 < -2.1e5 or 8.4e-74 < x1 < 3.4999999999999998e144

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 91.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\left(3 + 2 \cdot \frac{x2}{{x1}^{2}}\right) - \left(3 \cdot \frac{1}{{x1}^{2}} + \frac{1}{x1}\right)\right)} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 61.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{8 \cdot x2}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 61.8%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 61.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x1 around inf 61.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -2.1e5 < x1 < -5.49999999999999959e-236

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 97.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 86.8%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -5.49999999999999959e-236 < x1 < 6.80000000000000034e-251

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 6.80000000000000034e-251 < x1 < 8.4e-74

   1. Initial program 99.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 88.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 88.6%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if 3.4999999999999998e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.6 \cdot 10^{+61}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\left(x2 \cdot 2 - x1\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(x2 \cdot 2 - x1\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -210000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-236}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.4 \cdot 10^{-74}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11: 79.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + 3 \cdot t_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* x2 2.0)) x1) t_1)))
   (if (<= x1 5.5e+144)
     (+
      x1
      (+
       (+
        x1
        (+
         (+
          (*
           t_1
           (+
            (* (* (* x1 2.0) t_2) (- t_2 3.0))
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
          (* 3.0 t_0))
         (* x1 (* x1 x1))))
       (* 3.0 (- (* x2 -2.0) x1))))
     (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= 5.5e+144) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (x2 * 2.0d0)) - x1) / t_1
    if (x1 <= 5.5d+144) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (3.0d0 * t_0)) + (x1 * (x1 * x1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	double tmp;
	if (x1 <= 5.5e+144) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1
	tmp = 0
	if x1 <= 5.5e+144:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= 5.5e+144)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(3.0 * t_0)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (x2 * 2.0)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= 5.5e+144)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (3.0 * t_0)) + (x1 * (x1 * x1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, 5.5e+144], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < 5.50000000000000022e144

   1. Initial program 85.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 83.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 85.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]
   4. Step-by-step derivation

      1. mul-1-neg 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      2. unsub-neg 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      3. *-commutative 85.3%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 85.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12: 63.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.36 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_2)))
        (t_4 (/ (- (+ t_1 (* x2 2.0)) x1) t_2)))
   (if (<= x1 -4.2e-234)
     t_0
     (if (<= x1 6.8e-251)
       (+ x1 (+ t_3 (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
       (if (<= x1 1.36e-74)
         t_0
         (if (<= x1 3.5e+144)
           (+
            x1
            (+
             t_3
             (+
              x1
              (+
               (* x1 (* x1 x1))
               (+
                (* 3.0 t_1)
                (* t_2 (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* x2 8.0))))))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.2e-234) {
		tmp = t_0;
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 1.36e-74) {
		tmp = t_0;
	} else if (x1 <= 3.5e+144) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x2 * 8.0)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_2)
    t_4 = ((t_1 + (x2 * 2.0d0)) - x1) / t_2
    if (x1 <= (-4.2d-234)) then
        tmp = t_0
    else if (x1 <= 6.8d-251) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 1.36d-74) then
        tmp = t_0
    else if (x1 <= 3.5d+144) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + (x2 * 8.0d0)))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	double tmp;
	if (x1 <= -4.2e-234) {
		tmp = t_0;
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 1.36e-74) {
		tmp = t_0;
	} else if (x1 <= 3.5e+144) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x2 * 8.0)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2)
	t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2
	tmp = 0
	if x1 <= -4.2e-234:
		tmp = t_0
	elif x1 <= 6.8e-251:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 1.36e-74:
		tmp = t_0
	elif x1 <= 3.5e+144:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x2 * 8.0)))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -4.2e-234)
		tmp = t_0;
	elseif (x1 <= 6.8e-251)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 1.36e-74)
		tmp = t_0;
	elseif (x1 <= 3.5e+144)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(x2 * 8.0))))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	t_4 = ((t_1 + (x2 * 2.0)) - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -4.2e-234)
		tmp = t_0;
	elseif (x1 <= 6.8e-251)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 1.36e-74)
		tmp = t_0;
	elseif (x1 <= 3.5e+144)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + (x2 * 8.0)))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -4.2e-234], t$95$0, If[LessEqual[x1, 6.8e-251], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.36e-74], t$95$0, If[LessEqual[x1, 3.5e+144], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.19999999999999982e-234 or 6.80000000000000034e-251 < x1 < 1.36000000000000006e-74

   1. Initial program 78.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 59.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if -4.19999999999999982e-234 < x1 < 6.80000000000000034e-251

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 1.36000000000000006e-74 < x1 < 3.4999999999999998e144

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 89.5%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\left(3 + 2 \cdot \frac{x2}{{x1}^{2}}\right) - \left(3 \cdot \frac{1}{{x1}^{2}} + \frac{1}{x1}\right)\right)} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 66.4%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{8 \cdot x2}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 66.4%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 66.4%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x1 around inf 66.3%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 3.4999999999999998e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.2 \cdot 10^{-234}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.36 \cdot 10^{-74}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + x2 \cdot 8\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 77.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + x2 \cdot 2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* x2 2.0)) x1) t_0)))
   (if (<= x1 5.5e+144)
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* 3.0 t_1)
          (* t_0 (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0))))))))
     (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double tmp;
	if (x1 <= 5.5e+144) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (x2 * 2.0d0)) - x1) / t_0
    if (x1 <= 5.5d+144) then
        tmp = x1 + ((3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	double tmp;
	if (x1 <= 5.5e+144) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0
	tmp = 0
	if x1 <= 5.5e+144:
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(x2 * 2.0)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= 5.5e+144)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (x2 * 2.0)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= 5.5e+144)
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, 5.5e+144], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < 5.50000000000000022e144

   1. Initial program 85.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 83.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{3}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 79.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{3} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot 3\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14: 64.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x2 \cdot \left(x2 \cdot 2 - 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -4.7 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot t_1 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \frac{\left(t_0 + x2 \cdot 2\right) - x1}{t_2} + t_2 \cdot \left(4 \cdot \left(x1 \cdot t_1\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x2 (- (* x2 2.0) 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_2))))
   (if (<= x1 -4.7e-233)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 t_1) 2.0))))
     (if (<= x1 3.8e-251)
       (+ x1 (+ t_3 (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
       (if (<= x1 5.5e+144)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (/ (- (+ t_0 (* x2 2.0)) x1) t_2))
              (* t_2 (* 4.0 (* x1 t_1))))))))
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x2 * ((x2 * 2.0) - 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.7e-233) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 3.8e-251) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 5.5e+144) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (x2 * 2.0)) - x1) / t_2)) + (t_2 * (4.0 * (x1 * t_1)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x2 * ((x2 * 2.0d0) - 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_2)
    if (x1 <= (-4.7d-233)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * t_1) - 2.0d0)))
    else if (x1 <= 3.8d-251) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 5.5d+144) then
        tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (x2 * 2.0d0)) - x1) / t_2)) + (t_2 * (4.0d0 * (x1 * t_1)))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x2 * ((x2 * 2.0) - 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double tmp;
	if (x1 <= -4.7e-233) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	} else if (x1 <= 3.8e-251) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 5.5e+144) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (x2 * 2.0)) - x1) / t_2)) + (t_2 * (4.0 * (x1 * t_1)))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x2 * ((x2 * 2.0) - 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)
	tmp = 0
	if x1 <= -4.7e-233:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)))
	elif x1 <= 3.8e-251:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 5.5e+144:
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (x2 * 2.0)) - x1) / t_2)) + (t_2 * (4.0 * (x1 * t_1)))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_2))
	tmp = 0.0
	if (x1 <= -4.7e-233)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * t_1) - 2.0))));
	elseif (x1 <= 3.8e-251)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 5.5e+144)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(t_0 + Float64(x2 * 2.0)) - x1) / t_2)) + Float64(t_2 * Float64(4.0 * Float64(x1 * t_1))))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x2 * ((x2 * 2.0) - 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	tmp = 0.0;
	if (x1 <= -4.7e-233)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * t_1) - 2.0)));
	elseif (x1 <= 3.8e-251)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 5.5e+144)
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (x2 * 2.0)) - x1) / t_2)) + (t_2 * (4.0 * (x1 * t_1)))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.7e-233], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * t$95$1), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.8e-251], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e+144], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(t$95$0 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.6999999999999996e-233

   1. Initial program 70.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 48.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if -4.6999999999999996e-233 < x1 < 3.7999999999999997e-251

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 3.7999999999999997e-251 < x1 < 5.50000000000000022e144

   1. Initial program 99.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 77.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \color{blue}{\left(\left(-1 \cdot x1 + 2 \cdot x2\right) - 3\right)} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 70.2%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.7 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 15: 63.6% accurate, 3.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\\ \mathbf{if}\;x1 \leq -1.8 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + x2 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (*
          3.0
          (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ (* x1 x1) 1.0)))))
   (if (<= x1 -1.8e-233)
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0))))
     (if (<= x1 6.8e-251)
       (+ x1 (+ t_0 (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
       (if (<= x1 1.32e+93)
         (+ x1 (+ t_0 (+ x1 (* 4.0 (* (* x1 2.0) (* x2 x2))))))
         (if (<= x1 5.5e+144)
           (+ x1 (+ t_0 (+ x1 (+ (* x1 (* x1 x1)) (* x2 8.0)))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -1.8e-233) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 1.32e+93) {
		tmp = x1 + (t_0 + (x1 + (4.0 * ((x1 * 2.0) * (x2 * x2)))));
	} else if (x1 <= 5.5e+144) {
		tmp = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / ((x1 * x1) + 1.0d0))
    if (x1 <= (-1.8d-233)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    else if (x1 <= 6.8d-251) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 1.32d+93) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * ((x1 * 2.0d0) * (x2 * x2)))))
    else if (x1 <= 5.5d+144) then
        tmp = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0d0))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0));
	double tmp;
	if (x1 <= -1.8e-233) {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 1.32e+93) {
		tmp = x1 + (t_0 + (x1 + (4.0 * ((x1 * 2.0) * (x2 * x2)))));
	} else if (x1 <= 5.5e+144) {
		tmp = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))
	tmp = 0
	if x1 <= -1.8e-233:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	elif x1 <= 6.8e-251:
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 1.32e+93:
		tmp = x1 + (t_0 + (x1 + (4.0 * ((x1 * 2.0) * (x2 * x2)))))
	elif x1 <= 5.5e+144:
		tmp = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(Float64(x1 * x1) + 1.0)))
	tmp = 0.0
	if (x1 <= -1.8e-233)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))));
	elseif (x1 <= 6.8e-251)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 1.32e+93)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(Float64(x1 * 2.0) * Float64(x2 * x2))))));
	elseif (x1 <= 5.5e+144)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(x2 * 8.0)))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0));
	tmp = 0.0;
	if (x1 <= -1.8e-233)
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	elseif (x1 <= 6.8e-251)
		tmp = x1 + (t_0 + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 1.32e+93)
		tmp = x1 + (t_0 + (x1 + (4.0 * ((x1 * 2.0) * (x2 * x2)))));
	elseif (x1 <= 5.5e+144)
		tmp = x1 + (t_0 + (x1 + ((x1 * (x1 * x1)) + (x2 * 8.0))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.8e-233], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6.8e-251], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+93], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.5e+144], N[(x1 + N[(t$95$0 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.80000000000000004e-233

   1. Initial program 70.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 47.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 48.7%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if -1.80000000000000004e-233 < x1 < 6.80000000000000034e-251

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 6.80000000000000034e-251 < x1 < 1.3199999999999999e93

   1. Initial program 99.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 69.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 69.1%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(2 \cdot \left(x1 \cdot {x2}^{2}\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot {x2}^{2}\right) \cdot 2\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. *-commutative 69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(\color{blue}{\left({x2}^{2} \cdot x1\right)} \cdot 2\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      3. associate-*l* 69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left({x2}^{2} \cdot \left(x1 \cdot 2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      4. unpow2 69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 2\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      5. *-commutative 69.1%

         \[\leadsto x1 + \left(\left(4 \cdot \left(\left(x2 \cdot x2\right) \cdot \color{blue}{\left(2 \cdot x1\right)}\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 69.1%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x2 \cdot x2\right) \cdot \left(2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 1.3199999999999999e93 < x1 < 5.50000000000000022e144

   1. Initial program 100.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around inf 100.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \color{blue}{\left(\left(3 + 2 \cdot \frac{x2}{{x1}^{2}}\right) - \left(3 \cdot \frac{1}{{x1}^{2}} + \frac{1}{x1}\right)\right)} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 68.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{8 \cdot x2}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 68.2%

         \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 68.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \color{blue}{x2 \cdot 8}\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   6. Taylor expanded in x1 around 0 84.9%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{8 \cdot x2} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   7. Step-by-step derivation

      1. *-commutative 84.9%

         \[\leadsto x1 + \left(\left(\left(\color{blue}{x2 \cdot 8} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   8. Simplified 84.9%

      \[\leadsto x1 + \left(\left(\left(\color{blue}{x2 \cdot 8} + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 5.50000000000000022e144 < x1

   1. Initial program 3.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.4%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 9.7%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 9.7%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 9.7%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 75.9%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 75.9%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.8 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+93}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+144}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + x2 \cdot 8\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 16: 61.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0))))))
   (if (<= x1 -7.5e-233)
     t_0
     (if (<= x1 6.8e-251)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (* 4.0 (* x1 (* x2 -3.0))))))
       (if (<= x1 3.05e+168)
         t_0
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -7.5e-233) {
		tmp = t_0;
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-7.5d-233)) then
        tmp = t_0
    else if (x1 <= 6.8d-251) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * (x2 * (-3.0d0))))))
    else if (x1 <= 3.05d+168) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -7.5e-233) {
		tmp = t_0;
	} else if (x1 <= 6.8e-251) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -7.5e-233:
		tmp = t_0
	elif x1 <= 6.8e-251:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))))
	elif x1 <= 3.05e+168:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -7.5e-233)
		tmp = t_0;
	elseif (x1 <= 6.8e-251)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * Float64(x2 * -3.0))))));
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -7.5e-233)
		tmp = t_0;
	elseif (x1 <= 6.8e-251)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * (x2 * -3.0)))));
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e-233], t$95$0, If[LessEqual[x1, 6.8e-251], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * N[(x2 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.05e+168], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.49999999999999974e-233 or 6.80000000000000034e-251 < x1 < 3.0500000000000001e168

   1. Initial program 81.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 53.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.8%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if -7.49999999999999974e-233 < x1 < 6.80000000000000034e-251

   1. Initial program 99.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 75.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around 0 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(-3 \cdot \left(x1 \cdot x2\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
   4. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot -3\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

      2. associate-*l* 94.3%

         \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   5. Simplified 94.3%

      \[\leadsto x1 + \left(\left(4 \cdot \color{blue}{\left(x1 \cdot \left(x2 \cdot -3\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if 3.0500000000000001e168 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 10.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 10.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 10.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 80.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-233}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 6.8 \cdot 10^{-251}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot -3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 17: 59.8% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -1.3 \cdot 10^{-234}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{-286}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0))))))
   (if (<= x1 -1.3e-234)
     t_0
     (if (<= x1 -1.02e-286)
       (* x2 -6.0)
       (if (<= x1 3.05e+168)
         t_0
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -1.3e-234) {
		tmp = t_0;
	} else if (x1 <= -1.02e-286) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-1.3d-234)) then
        tmp = t_0
    else if (x1 <= (-1.02d-286)) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 3.05d+168) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double tmp;
	if (x1 <= -1.3e-234) {
		tmp = t_0;
	} else if (x1 <= -1.02e-286) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -1.3e-234:
		tmp = t_0
	elif x1 <= -1.02e-286:
		tmp = x2 * -6.0
	elif x1 <= 3.05e+168:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))))
	tmp = 0.0
	if (x1 <= -1.3e-234)
		tmp = t_0;
	elseif (x1 <= -1.02e-286)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	tmp = 0.0;
	if (x1 <= -1.3e-234)
		tmp = t_0;
	elseif (x1 <= -1.02e-286)
		tmp = x2 * -6.0;
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.3e-234], t$95$0, If[LessEqual[x1, -1.02e-286], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 3.05e+168], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.29999999999999995e-234 or -1.01999999999999996e-286 < x1 < 3.0500000000000001e168

   1. Initial program 83.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 57.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 58.0%

      \[\leadsto x1 + \color{blue}{\left(-6 \cdot x2 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)} \]

   if -1.29999999999999995e-234 < x1 < -1.01999999999999996e-286

   1. Initial program 99.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 48.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 87.1%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 87.1%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 87.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 87.1%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 87.1%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 87.1%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 3.0500000000000001e168 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 10.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 10.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 10.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 80.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.3 \cdot 10^{-234}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq -1.02 \cdot 10^{-286}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 18: 43.4% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))))
   (if (<= x1 -7.5e-143)
     t_0
     (if (<= x1 2.45e-86)
       (* x2 -6.0)
       (if (<= x1 3.05e+168)
         t_0
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	double tmp;
	if (x1 <= -7.5e-143) {
		tmp = t_0;
	} else if (x1 <= 2.45e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    if (x1 <= (-7.5d-143)) then
        tmp = t_0
    else if (x1 <= 2.45d-86) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 3.05d+168) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	double tmp;
	if (x1 <= -7.5e-143) {
		tmp = t_0;
	} else if (x1 <= 2.45e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	tmp = 0
	if x1 <= -7.5e-143:
		tmp = t_0
	elif x1 <= 2.45e-86:
		tmp = x2 * -6.0
	elif x1 <= 3.05e+168:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))))
	tmp = 0.0
	if (x1 <= -7.5e-143)
		tmp = t_0;
	elseif (x1 <= 2.45e-86)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	tmp = 0.0;
	if (x1 <= -7.5e-143)
		tmp = t_0;
	elseif (x1 <= 2.45e-86)
		tmp = x2 * -6.0;
	elseif (x1 <= 3.05e+168)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e-143], t$95$0, If[LessEqual[x1, 2.45e-86], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 3.05e+168], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.5000000000000003e-143 or 2.44999999999999986e-86 < x1 < 3.0500000000000001e168

   1. Initial program 75.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 42.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 25.9%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]

   if -7.5000000000000003e-143 < x1 < 2.44999999999999986e-86

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 66.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 3.0500000000000001e168 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 10.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 10.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 10.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 80.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.45 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 19: 43.7% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;x1 + \left(9 + t_0\right)\\ \mathbf{elif}\;x1 \leq 3.15 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;x1 + t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0)))))))
   (if (<= x1 -7.5e-143)
     (+ x1 (+ 9.0 t_0))
     (if (<= x1 3.15e-86)
       (* x2 -6.0)
       (if (<= x1 3.05e+168)
         (+ x1 t_0)
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0))));
	double tmp;
	if (x1 <= -7.5e-143) {
		tmp = x1 + (9.0 + t_0);
	} else if (x1 <= 3.15e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = x1 + t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))))
    if (x1 <= (-7.5d-143)) then
        tmp = x1 + (9.0d0 + t_0)
    else if (x1 <= 3.15d-86) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 3.05d+168) then
        tmp = x1 + t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0))));
	double tmp;
	if (x1 <= -7.5e-143) {
		tmp = x1 + (9.0 + t_0);
	} else if (x1 <= 3.15e-86) {
		tmp = x2 * -6.0;
	} else if (x1 <= 3.05e+168) {
		tmp = x1 + t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0))))
	tmp = 0
	if x1 <= -7.5e-143:
		tmp = x1 + (9.0 + t_0)
	elif x1 <= 3.15e-86:
		tmp = x2 * -6.0
	elif x1 <= 3.05e+168:
		tmp = x1 + t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0)))))
	tmp = 0.0
	if (x1 <= -7.5e-143)
		tmp = Float64(x1 + Float64(9.0 + t_0));
	elseif (x1 <= 3.15e-86)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 3.05e+168)
		tmp = Float64(x1 + t_0);
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0))));
	tmp = 0.0;
	if (x1 <= -7.5e-143)
		tmp = x1 + (9.0 + t_0);
	elseif (x1 <= 3.15e-86)
		tmp = x2 * -6.0;
	elseif (x1 <= 3.05e+168)
		tmp = x1 + t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e-143], N[(x1 + N[(9.0 + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.15e-86], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 3.05e+168], N[(x1 + t$95$0), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -7.5000000000000003e-143

   1. Initial program 64.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 42.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 19.9%

      \[\leadsto x1 + \color{blue}{\left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \]

   if -7.5000000000000003e-143 < x1 < 3.15e-86

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 66.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 3.15e-86 < x1 < 3.0500000000000001e168

   1. Initial program 93.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 41.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 38.5%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]

   if 3.0500000000000001e168 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 10.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 10.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 10.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
   6. Step-by-step derivation

      1. flip-+ 80.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]

   7. Applied egg-rr 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   8. Step-by-step derivation

      1. swap-sqr 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}}{x1 - x2 \cdot -6} \]

      2. metadata-eval 80.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot \color{blue}{36}}{x1 - x2 \cdot -6} \]

   9. Simplified 80.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{-143}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.15 \cdot 10^{-86}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 3.05 \cdot 10^{+168}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 20: 40.0% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.9 \cdot 10^{-143} \lor \neg \left(x1 \leq 2.6 \cdot 10^{-86}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6.9e-143) (not (<= x1 2.6e-86)))
   (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.9e-143) || !(x1 <= 2.6e-86)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6.9d-143)) .or. (.not. (x1 <= 2.6d-86))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.9e-143) || !(x1 <= 2.6e-86)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6.9e-143) or not (x1 <= 2.6e-86):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6.9e-143) || !(x1 <= 2.6e-86))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6.9e-143) || ~((x1 <= 2.6e-86)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6.9e-143], N[Not[LessEqual[x1, 2.6e-86]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.89999999999999989e-143 or 2.6000000000000001e-86 < x1

   1. Initial program 64.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 35.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 28.6%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]

   if -6.89999999999999989e-143 < x1 < 2.6000000000000001e-86

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 66.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.9 \cdot 10^{-143} \lor \neg \left(x1 \leq 2.6 \cdot 10^{-86}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 21: 40.0% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6.9 \cdot 10^{-143} \lor \neg \left(x1 \leq 2.65 \cdot 10^{-86}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6.9e-143) (not (<= x1 2.65e-86)))
   (+ x1 (* (* x2 x2) (* x1 8.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.9e-143) || !(x1 <= 2.65e-86)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6.9d-143)) .or. (.not. (x1 <= 2.65d-86))) then
        tmp = x1 + ((x2 * x2) * (x1 * 8.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6.9e-143) || !(x1 <= 2.65e-86)) {
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6.9e-143) or not (x1 <= 2.65e-86):
		tmp = x1 + ((x2 * x2) * (x1 * 8.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6.9e-143) || !(x1 <= 2.65e-86))
		tmp = Float64(x1 + Float64(Float64(x2 * x2) * Float64(x1 * 8.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6.9e-143) || ~((x1 <= 2.65e-86)))
		tmp = x1 + ((x2 * x2) * (x1 * 8.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6.9e-143], N[Not[LessEqual[x1, 2.65e-86]], $MachinePrecision]], N[(x1 + N[(N[(x2 * x2), $MachinePrecision] * N[(x1 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.89999999999999989e-143 or 2.6499999999999998e-86 < x1

   1. Initial program 64.2%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 35.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 28.6%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot {x2}^{2}\right)} \]
   4. Step-by-step derivation

      1. *-commutative 28.6%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right) \cdot 8} \]

      2. *-commutative 28.6%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right)} \cdot 8 \]

      3. associate-*l* 28.6%

         \[\leadsto x1 + \color{blue}{{x2}^{2} \cdot \left(x1 \cdot 8\right)} \]

      4. unpow2 28.6%

         \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(x1 \cdot 8\right) \]

   5. Simplified 28.6%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)} \]

   if -6.89999999999999989e-143 < x1 < 2.6499999999999998e-86

   1. Initial program 99.4%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 80.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 66.5%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 66.5%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   6. Taylor expanded in x1 around 0 66.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   7. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   8. Simplified 66.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.9 \cdot 10^{-143} \lor \neg \left(x1 \leq 2.65 \cdot 10^{-86}\right):\\ \;\;\;\;x1 + \left(x2 \cdot x2\right) \cdot \left(x1 \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 22: 27.1% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -6.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -6.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -6.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 51.0%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.4%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.4%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Final simplification 26.4%

   \[\leadsto x1 + x2 \cdot -6 \]

Alternative 23: 26.9% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 76.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 51.0%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.4%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.4%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around 0 26.2%

   \[\leadsto \color{blue}{-6 \cdot x2} \]
7. Step-by-step derivation

   1. *-commutative 26.2%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

8. Simplified 26.2%

   \[\leadsto \color{blue}{x2 \cdot -6} \]

9. Final simplification 26.2%

   \[\leadsto x2 \cdot -6 \]

Alternative 24: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

double code(double x1, double x2) {
	return x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1
end function

Java

public static double code(double x1, double x2) {
	return x1;
}

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1;
end

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 76.0%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 51.0%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 26.4%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 26.4%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 26.4%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around inf 3.3%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.3%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  :precision binary64
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) (- (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)) 3.0)) (* (* x1 x1) (- (* 4.0 (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))) 6.0))) (+ (* x1 x1) 1.0)) (* (* (* 3.0 x1) x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (* (* x1 x1) x1)) x1) (* 3.0 (/ (- (- (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0))))))