Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 71.3% → 98.8%

Time: 1.4min

Alternatives: 30

Speedup: 4.7×

• 45.8% 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: 71.3% 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: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_1 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -1.55 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_2 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t_0, 4, -6\right), t_0 \cdot \left(\left(t_0 + -3\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(t_2, t_0, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (fma x1 (* x1 3.0) (- (* 2.0 x2) x1)) (fma x1 x1 1.0)))
        (t_1 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_2 (* x1 (* x1 3.0))))
   (if (<= x1 -1e+154)
     t_1
     (if (<= x1 -1.55e+70)
       (+
        x1
        (+
         (+ x1 (* (pow x1 4.0) 6.0))
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))))
       (if (<= x1 5e+153)
         (+
          x1
          (fma
           3.0
           (/ (- t_2 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
           (+
            x1
            (fma
             (fma x1 x1 1.0)
             (fma
              x1
              (* x1 (fma t_0 4.0 -6.0))
              (* t_0 (* (+ t_0 -3.0) (* x1 2.0))))
             (fma t_2 t_0 (pow x1 3.0))))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), ((2.0 * x2) - x1)) / fma(x1, x1, 1.0);
	double t_1 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_2 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_1;
	} else if (x1 <= -1.55e+70) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + (3.0 * (((t_2 - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + fma(3.0, ((t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_0, 4.0, -6.0)), (t_0 * ((t_0 + -3.0) * (x1 * 2.0)))), fma(t_2, t_0, pow(x1, 3.0)))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(2.0 * x2) - x1)) / fma(x1, x1, 1.0))
	t_1 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_1;
	elseif (x1 <= -1.55e+70)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0)))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_0, 4.0, -6.0)), Float64(t_0 * Float64(Float64(t_0 + -3.0) * Float64(x1 * 2.0)))), fma(t_2, t_0, (x1 ^ 3.0))))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$1, If[LessEqual[x1, -1.55e+70], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], 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[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(t$95$0 + -3.0), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$0 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 74.0%

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

      1. fma-def 78.1%

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

      2. associate-*r* 78.1%

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

      3. fma-neg 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-commutative 78.1%

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

      6. fma-neg 78.1%

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

      7. metadata-eval 78.1%

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

      8. *-commutative 78.1%

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

      9. fma-def 78.1%

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

      10. associate-*r* 78.1%

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

      11. *-commutative 78.1%

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

      12. unpow2 78.1%

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

      13. associate-*r* 78.1%

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

      14. associate-*l* 78.1%

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

      15. *-commutative 78.1%

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

      16. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -1.00000000000000004e154 < x1 < -1.55000000000000015e70

   1. Initial program 37.3%

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

   2. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -1.55000000000000015e70 < x1 < 5.00000000000000018e153

   1. Initial program 97.7%

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

   3. Simplified 97.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -1.55 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} + -3\right) \cdot \left(x1 \cdot 2\right)\right)\right), \mathsf{fma}\left(x1 \cdot \left(x1 \cdot 3\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 2: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_1 := \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_2 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \left(x1 \cdot 9\right) + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t_3 \cdot \left(-3 + t_3\right)\right) + x1 \cdot \mathsf{fma}\left(t_3, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(t_1 \cdot \left(x1 \cdot 2\right), -3 + t_1, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, t_1, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t_2 \cdot t_1\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{\left(t_2 + -2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_1 (/ (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (fma x1 (* x1 3.0) (- (+ x2 x2) x1)) (fma x1 x1 1.0))))
   (if (<= x1 -1e+154)
     t_0
     (if (<= x1 -1e+38)
       (+
        x1
        (fma
         3.0
         (/ (- t_2 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* x1 (* x1 9.0))
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_3 (+ -3.0 t_3))) (* x1 (fma t_3 4.0 -6.0)))))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (+
            (fma
             (fma
              (* t_1 (* x1 2.0))
              (+ -3.0 t_1)
              (* (* x1 x1) (fma 4.0 t_1 -6.0)))
             (fma x1 x1 1.0)
             (* t_2 t_1))
            (* x1 (* x1 x1)))
           (+ x1 (* 3.0 (/ (- (+ t_2 (* -2.0 x2)) x1) (fma x1 x1 1.0))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_1 = (fma((x1 * 3.0), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = fma(x1, (x1 * 3.0), ((x2 + x2) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_0;
	} else if (x1 <= -1e+38) {
		tmp = x1 + fma(3.0, ((t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((x1 * (x1 * 9.0)) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_3 * (-3.0 + t_3))) + (x1 * fma(t_3, 4.0, -6.0))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((fma(fma((t_1 * (x1 * 2.0)), (-3.0 + t_1), ((x1 * x1) * fma(4.0, t_1, -6.0))), fma(x1, x1, 1.0), (t_2 * t_1)) + (x1 * (x1 * x1))) + (x1 + (3.0 * (((t_2 + (-2.0 * x2)) - x1) / fma(x1, x1, 1.0)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_1 = Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 + x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_0;
	elseif (x1 <= -1e+38)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_3 * Float64(-3.0 + t_3))) + Float64(x1 * fma(t_3, 4.0, -6.0)))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(fma(fma(Float64(t_1 * Float64(x1 * 2.0)), Float64(-3.0 + t_1), Float64(Float64(x1 * x1) * fma(4.0, t_1, -6.0))), fma(x1, x1, 1.0), Float64(t_2 * t_1)) + Float64(x1 * Float64(x1 * x1))) + Float64(x1 + Float64(3.0 * Float64(Float64(Float64(t_2 + Float64(-2.0 * x2)) - x1) / fma(x1, x1, 1.0))))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$0, If[LessEqual[x1, -1e+38], 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[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$3 * N[(-3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$3 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(N[(N[(N[(t$95$1 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$1), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$1 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$2 * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(N[(t$95$2 + N[(-2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 74.0%

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

      1. fma-def 78.1%

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

      2. associate-*r* 78.1%

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

      3. fma-neg 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-commutative 78.1%

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

      6. fma-neg 78.1%

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

      7. metadata-eval 78.1%

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

      8. *-commutative 78.1%

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

      9. fma-def 78.1%

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

      10. associate-*r* 78.1%

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

      11. *-commutative 78.1%

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

      12. unpow2 78.1%

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

      13. associate-*r* 78.1%

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

      14. associate-*l* 78.1%

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

      15. *-commutative 78.1%

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

      16. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -1.00000000000000004e154 < x1 < -9.99999999999999977e37

   1. Initial program 56.1%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x1 around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -9.99999999999999977e37 < x1 < 5.00000000000000018e153

   1. Initial program 97.7%

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

   3. Simplified 97.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \left(x1 \cdot 9\right) + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right), -3 + \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + -2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 3: 99.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ t_4 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t_2 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \left(x1 \cdot 9\right) + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(t_4 \cdot \left(-3 + t_4\right)\right) + x1 \cdot \mathsf{fma}\left(t_4, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right) + t_2 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4 (/ (fma x1 (* x1 3.0) (- (+ x2 x2) x1)) (fma x1 x1 1.0))))
   (if (<= x1 -1e+154)
     t_0
     (if (<= x1 -1e+38)
       (+
        x1
        (fma
         3.0
         (/ (- t_2 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          (* x1 (* x1 9.0))
          (*
           (fma x1 x1 1.0)
           (+
            x1
            (*
             x1
             (+ (* 2.0 (* t_4 (+ -3.0 t_4))) (* x1 (fma t_4 4.0 -6.0)))))))))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* 4.0 t_3) 6.0))))
              (* t_2 t_3))
             (* x1 (* x1 x1))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = fma(x1, (x1 * 3.0), ((x2 + x2) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_0;
	} else if (x1 <= -1e+38) {
		tmp = x1 + fma(3.0, ((t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), ((x1 * (x1 * 9.0)) + (fma(x1, x1, 1.0) * (x1 + (x1 * ((2.0 * (t_4 * (-3.0 + t_4))) + (x1 * fma(t_4, 4.0, -6.0))))))));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((4.0 * t_3) - 6.0)))) + (t_2 * t_3)) + (x1 * (x1 * x1)))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 + x2) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_0;
	elseif (x1 <= -1e+38)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_2 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(Float64(x1 * Float64(x1 * 9.0)) + Float64(fma(x1, x1, 1.0) * Float64(x1 + Float64(x1 * Float64(Float64(2.0 * Float64(t_4 * Float64(-3.0 + t_4))) + Float64(x1 * fma(t_4, 4.0, -6.0)))))))));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + 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(t_2 * t_3)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 + x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$0, If[LessEqual[x1, -1e+38], 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[(x1 * N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(x1 * N[(N[(2.0 * N[(t$95$4 * N[(-3.0 + t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(t$95$4 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + 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[(t$95$2 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 74.0%

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

      1. fma-def 78.1%

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

      2. associate-*r* 78.1%

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

      3. fma-neg 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-commutative 78.1%

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

      6. fma-neg 78.1%

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

      7. metadata-eval 78.1%

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

      8. *-commutative 78.1%

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

      9. fma-def 78.1%

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

      10. associate-*r* 78.1%

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

      11. *-commutative 78.1%

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

      12. unpow2 78.1%

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

      13. associate-*r* 78.1%

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

      14. associate-*l* 78.1%

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

      15. *-commutative 78.1%

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

      16. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -1.00000000000000004e154 < x1 < -9.99999999999999977e37

   1. Initial program 56.1%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x1 around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   if -9.99999999999999977e37 < x1 < 5.00000000000000018e153

   1. Initial program 97.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+38}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{x1 \cdot \left(x1 \cdot 3\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 \cdot \left(x1 \cdot 9\right) + \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + x1 \cdot \left(2 \cdot \left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) + x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, \left(x2 + x2\right) - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 4: 95.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ t_3 := x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{if}\;t_3 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+
             (+
              (*
               t_0
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* t_1 t_2))
             (* x1 (* x1 x1))))))))
   (if (<= t_3 INFINITY) t_3 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))))

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 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))));
	double tmp;
	if (t_3 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	}
	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(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + 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(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1))))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)));
	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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + 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[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $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 99.5%

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

   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%

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

   3. Taylor expanded in x1 around 0 64.6%

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

      1. fma-def 69.2%

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

      2. associate-*r* 69.2%

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

      3. fma-neg 69.2%

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

      4. metadata-eval 69.2%

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

      5. *-commutative 69.2%

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

      6. fma-neg 69.2%

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

      7. metadata-eval 69.2%

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

      8. *-commutative 69.2%

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

      9. fma-def 69.2%

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

      10. associate-*r* 69.2%

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

      11. *-commutative 69.2%

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

      12. unpow2 69.2%

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

      13. associate-*r* 69.2%

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

      14. associate-*l* 69.2%

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

      15. *-commutative 69.2%

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

      16. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in x2 around 0 85.8%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 85.8%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 85.8%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 85.8%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 85.8%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right) \leq \infty:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 5: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ t_3 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + t_4\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(\left(t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_1 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
        (t_3 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))
   (if (<= x1 -1e+154)
     t_3
     (if (<= x1 -1.75e+70)
       (+ x1 (+ (+ x1 (* (pow x1 4.0) 6.0)) t_4))
       (if (<= x1 5e+153)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+
             (+
              (*
               t_0
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* t_1 t_2))
             (* x1 (* x1 x1))))))
         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 + (2.0 * x2)) - x1) / t_0;
	double t_3 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -1e+154) {
		tmp = t_3;
	} else if (x1 <= -1.75e+70) {
		tmp = x1 + ((x1 + (pow(x1, 4.0) * 6.0)) + t_4);
	} else if (x1 <= 5e+153) {
		tmp = x1 + (t_4 + (x1 + (((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))));
	} else {
		tmp = 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(2.0 * x2)) - x1) / t_0)
	t_3 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))
	tmp = 0.0
	if (x1 <= -1e+154)
		tmp = t_3;
	elseif (x1 <= -1.75e+70)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64((x1 ^ 4.0) * 6.0)) + t_4));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(t_4 + 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(t_1 * t_2)) + Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = 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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+154], t$95$3, If[LessEqual[x1, -1.75e+70], N[(x1 + N[(N[(x1 + N[(N[Power[x1, 4.0], $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(t$95$4 + 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[(t$95$1 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.00000000000000004e154 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 74.0%

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

      1. fma-def 78.1%

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

      2. associate-*r* 78.1%

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

      3. fma-neg 78.1%

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

      4. metadata-eval 78.1%

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

      5. *-commutative 78.1%

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

      6. fma-neg 78.1%

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

      7. metadata-eval 78.1%

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

      8. *-commutative 78.1%

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

      9. fma-def 78.1%

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

      10. associate-*r* 78.1%

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

      11. *-commutative 78.1%

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

      12. unpow2 78.1%

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

      13. associate-*r* 78.1%

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

      14. associate-*l* 78.1%

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

      15. *-commutative 78.1%

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

      16. *-commutative 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 100.0%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 100.0%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -1.00000000000000004e154 < x1 < -1.75000000000000001e70

   1. Initial program 37.3%

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

   2. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -1.75000000000000001e70 < x1 < 5.00000000000000018e153

   1. Initial program 97.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+154}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -1.75 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(\left(x1 + {x1}^{4} \cdot 6\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 6: 95.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := \left(x1 \cdot 2\right) \cdot t_4\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ t_7 := x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(t_5 \cdot \left(t_4 - 3\right) + t_6\right) + t_3 \cdot t_4\right) + t_1\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -0.014:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 0.014:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_1 + \left(t_2 \cdot \left(t_6 + t_5 \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_3 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_2))
        (t_5 (* (* x1 2.0) t_4))
        (t_6 (* (* x1 x1) (- (* 4.0 t_4) 6.0)))
        (t_7
         (+
          x1
          (+
           (+ x1 (+ (+ (* t_2 (+ (* t_5 (- t_4 3.0)) t_6)) (* t_3 t_4)) t_1))
           (* 3.0 (+ 3.0 (/ -1.0 x1)))))))
   (if (<= x1 -5.8e+102)
     t_0
     (if (<= x1 -0.014)
       t_7
       (if (<= x1 0.014)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             t_1
             (+
              (* t_2 (+ t_6 (* t_5 (- (+ x2 x2) 3.0))))
              (* t_3 (+ x2 x2)))))))
         (if (<= x1 5e+153) t_7 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_7 = x1 + ((x1 + (((t_2 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_3 * t_4)) + t_1)) + (3.0 * (3.0 + (-1.0 / x1))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = t_0;
	} else if (x1 <= -0.014) {
		tmp = t_7;
	} else if (x1 <= 0.014) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_1 + ((t_2 * (t_6 + (t_5 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_7;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(Float64(x1 * 2.0) * t_4)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	t_7 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_5 * Float64(t_4 - 3.0)) + t_6)) + Float64(t_3 * t_4)) + t_1)) + Float64(3.0 * Float64(3.0 + Float64(-1.0 / x1)))))
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = t_0;
	elseif (x1 <= -0.014)
		tmp = t_7;
	elseif (x1 <= 0.014)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_1 + Float64(Float64(t_2 * Float64(t_6 + Float64(t_5 * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_3 * Float64(x2 + x2)))))));
	elseif (x1 <= 5e+153)
		tmp = t_7;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], t$95$0, If[LessEqual[x1, -0.014], t$95$7, If[LessEqual[x1, 0.014], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(N[(t$95$2 * N[(t$95$6 + N[(t$95$5 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$7, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.8000000000000005e102 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 66.9%

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

      1. fma-def 71.7%

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

      2. associate-*r* 71.7%

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

      3. fma-neg 71.7%

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

      4. metadata-eval 71.7%

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

      5. *-commutative 71.7%

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

      6. fma-neg 71.7%

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

      7. metadata-eval 71.7%

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

      8. *-commutative 71.7%

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

      9. fma-def 71.7%

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

      10. associate-*r* 71.7%

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

      11. *-commutative 71.7%

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

      12. unpow2 71.7%

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

      13. associate-*r* 71.7%

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

      14. associate-*l* 71.7%

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

      15. *-commutative 71.7%

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

      16. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in x2 around 0 88.9%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 88.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 88.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 88.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 88.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -5.8000000000000005e102 < x1 < -0.0140000000000000003 or 0.0140000000000000003 < x1 < 5.00000000000000018e153

   1. Initial program 93.6%

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

   2. Taylor expanded in x1 around inf 92.8%

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

   if -0.0140000000000000003 < x1 < 0.0140000000000000003

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 98.9%

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

      1. count-2 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x1 around 0 99.0%

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

      1. count-2 98.9%

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

   7. Simplified 99.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -0.014:\\ \;\;\;\;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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\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) + 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 0.014:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\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) + 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 7: 93.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := t_4 - 3\\ t_6 := t_2 \cdot t_4\\ t_7 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -0.05:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot t_5 + t_7\right) + t_6\right) + t_1\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + \left(t_1 + \left(t_6 + t_3 \cdot \left(t_7 + t_5 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_2 (* 2.0 x2)) x1) t_3))
        (t_5 (- t_4 3.0))
        (t_6 (* t_2 t_4))
        (t_7 (* (* x1 x1) (- (* 4.0 t_4) 6.0))))
   (if (<= x1 -6.4e+102)
     t_0
     (if (<= x1 -0.05)
       (+
        x1
        (+
         (+ x1 (+ (+ (* t_3 (+ (* (* (* x1 2.0) t_4) t_5) t_7)) t_6) t_1))
         (* 3.0 (+ 3.0 (/ -1.0 x1)))))
       (if (<= x1 7.5e+149)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_3))
           (+
            x1
            (+
             t_1
             (+
              t_6
              (* t_3 (+ t_7 (* t_5 (* (* x1 2.0) (- (* 2.0 x2) x1))))))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_2 + (2.0 * x2)) - x1) / t_3;
	double t_5 = t_4 - 3.0;
	double t_6 = t_2 * t_4;
	double t_7 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double tmp;
	if (x1 <= -6.4e+102) {
		tmp = t_0;
	} else if (x1 <= -0.05) {
		tmp = x1 + ((x1 + (((t_3 * ((((x1 * 2.0) * t_4) * t_5) + t_7)) + t_6) + t_1)) + (3.0 * (3.0 + (-1.0 / x1))));
	} else if (x1 <= 7.5e+149) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_1 + (t_6 + (t_3 * (t_7 + (t_5 * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(t_4 - 3.0)
	t_6 = Float64(t_2 * t_4)
	t_7 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	tmp = 0.0
	if (x1 <= -6.4e+102)
		tmp = t_0;
	elseif (x1 <= -0.05)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * t_5) + t_7)) + t_6) + t_1)) + Float64(3.0 * Float64(3.0 + Float64(-1.0 / x1)))));
	elseif (x1 <= 7.5e+149)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(t_1 + Float64(t_6 + Float64(t_3 * Float64(t_7 + Float64(t_5 * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $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[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$4 - 3.0), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$2 * t$95$4), $MachinePrecision]}, Block[{t$95$7 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.4e+102], t$95$0, If[LessEqual[x1, -0.05], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * t$95$5), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.5e+149], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(t$95$6 + N[(t$95$3 * N[(t$95$7 + N[(t$95$5 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.3999999999999999e102 or 7.50000000000000031e149 < x1

   1. Initial program 1.2%

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

   2. Taylor expanded in x1 around 0 1.2%

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

   3. Taylor expanded in x1 around 0 66.1%

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

      1. fma-def 70.8%

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

      2. associate-*r* 70.8%

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

      3. fma-neg 70.8%

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

      4. metadata-eval 70.8%

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

      5. *-commutative 70.8%

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

      6. fma-neg 70.8%

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

      7. metadata-eval 70.8%

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

      8. *-commutative 70.8%

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

      9. fma-def 70.8%

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

      10. associate-*r* 70.8%

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

      11. *-commutative 70.8%

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

      12. unpow2 70.8%

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

      13. associate-*r* 70.8%

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

      14. associate-*l* 70.8%

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

      15. *-commutative 70.8%

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

      16. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x2 around 0 87.9%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 87.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 87.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 87.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 87.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -6.3999999999999999e102 < x1 < -0.050000000000000003

   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 99.3%

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

   if -0.050000000000000003 < x1 < 7.50000000000000031e149

   1. Initial program 97.5%

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

   2. Taylor expanded in x1 around 0 95.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \color{blue}{\left(-1 \cdot x1 + 2 \cdot x2\right)}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+102}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -0.05:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 8: 95.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := \left(x1 \cdot 2\right) \cdot t_4\\ t_6 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ t_7 := x1 + \left(9 + \left(x1 + \left(\left(t_2 \cdot \left(t_5 \cdot \left(t_4 - 3\right) + t_6\right) + t_3 \cdot t_4\right) + t_1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -0.0096:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 0.0115:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_1 + \left(t_2 \cdot \left(t_6 + t_5 \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_3 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0))))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_2))
        (t_5 (* (* x1 2.0) t_4))
        (t_6 (* (* x1 x1) (- (* 4.0 t_4) 6.0)))
        (t_7
         (+
          x1
          (+
           9.0
           (+
            x1
            (+ (+ (* t_2 (+ (* t_5 (- t_4 3.0)) t_6)) (* t_3 t_4)) t_1))))))
   (if (<= x1 -1.4e+103)
     t_0
     (if (<= x1 -0.0096)
       t_7
       (if (<= x1 0.0115)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_2))
           (+
            x1
            (+
             t_1
             (+
              (* t_2 (+ t_6 (* t_5 (- (+ x2 x2) 3.0))))
              (* t_3 (+ x2 x2)))))))
         (if (<= x1 5e+153) t_7 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	double t_1 = x1 * (x1 * x1);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2;
	double t_5 = (x1 * 2.0) * t_4;
	double t_6 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double t_7 = x1 + (9.0 + (x1 + (((t_2 * ((t_5 * (t_4 - 3.0)) + t_6)) + (t_3 * t_4)) + t_1)));
	double tmp;
	if (x1 <= -1.4e+103) {
		tmp = t_0;
	} else if (x1 <= -0.0096) {
		tmp = t_7;
	} else if (x1 <= 0.0115) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_1 + ((t_2 * (t_6 + (t_5 * ((x2 + x2) - 3.0)))) + (t_3 * (x2 + x2))))));
	} else if (x1 <= 5e+153) {
		tmp = t_7;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(Float64(x1 * 2.0) * t_4)
	t_6 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	t_7 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_5 * Float64(t_4 - 3.0)) + t_6)) + Float64(t_3 * t_4)) + t_1))))
	tmp = 0.0
	if (x1 <= -1.4e+103)
		tmp = t_0;
	elseif (x1 <= -0.0096)
		tmp = t_7;
	elseif (x1 <= 0.0115)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_1 + Float64(Float64(t_2 * Float64(t_6 + Float64(t_5 * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_3 * Float64(x2 + x2)))))));
	elseif (x1 <= 5e+153)
		tmp = t_7;
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(9.0 + N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$5 * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.4e+103], t$95$0, If[LessEqual[x1, -0.0096], t$95$7, If[LessEqual[x1, 0.0115], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$1 + N[(N[(t$95$2 * N[(t$95$6 + N[(t$95$5 * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], t$95$7, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.40000000000000004e103 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x1 around 0 66.9%

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

      1. fma-def 71.7%

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

      2. associate-*r* 71.7%

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

      3. fma-neg 71.7%

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

      4. metadata-eval 71.7%

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

      5. *-commutative 71.7%

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

      6. fma-neg 71.7%

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

      7. metadata-eval 71.7%

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

      8. *-commutative 71.7%

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

      9. fma-def 71.7%

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

      10. associate-*r* 71.7%

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

      11. *-commutative 71.7%

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

      12. unpow2 71.7%

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

      13. associate-*r* 71.7%

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

      14. associate-*l* 71.7%

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

      15. *-commutative 71.7%

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

      16. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in x2 around 0 88.9%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 88.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 88.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 88.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 88.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -1.40000000000000004e103 < x1 < -0.00959999999999999916 or 0.0115 < x1 < 5.00000000000000018e153

   1. Initial program 93.6%

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

   2. Taylor expanded in x1 around inf 92.5%

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

   if -0.00959999999999999916 < x1 < 0.0115

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 98.9%

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

      1. count-2 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x1 around 0 99.0%

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

      1. count-2 98.9%

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

   7. Simplified 99.0%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.4 \cdot 10^{+103}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq -0.0096:\\ \;\;\;\;x1 + \left(9 + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\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) + 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.0115:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(9 + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\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) + 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \end{array} \]

Alternative 9: 89.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+102} \lor \neg \left(x1 \leq 7.5 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_0 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -6.4e+102) (not (<= x1 7.5e+149)))
     (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))
            (* (* (* x1 2.0) t_2) (- (+ x2 x2) 3.0))))
          (* t_0 (+ x2 x2))))))))))

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 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -6.4e+102) || !(x1 <= 7.5e+149)) {
		tmp = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	}
	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(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -6.4e+102) || !(x1 <= 7.5e+149))
		tmp = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_0 * Float64(x2 + x2)))))));
	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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -6.4e+102], N[Not[LessEqual[x1, 7.5e+149]], $MachinePrecision]], N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -6.3999999999999999e102 or 7.50000000000000031e149 < x1

   1. Initial program 1.2%

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

   2. Taylor expanded in x1 around 0 1.2%

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

   3. Taylor expanded in x1 around 0 66.1%

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

      1. fma-def 70.8%

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

      2. associate-*r* 70.8%

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

      3. fma-neg 70.8%

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

      4. metadata-eval 70.8%

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

      5. *-commutative 70.8%

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

      6. fma-neg 70.8%

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

      7. metadata-eval 70.8%

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

      8. *-commutative 70.8%

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

      9. fma-def 70.8%

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

      10. associate-*r* 70.8%

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

      11. *-commutative 70.8%

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

      12. unpow2 70.8%

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

      13. associate-*r* 70.8%

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

      14. associate-*l* 70.8%

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

      15. *-commutative 70.8%

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

      16. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in x2 around 0 87.9%

      \[\leadsto x1 + \color{blue}{\left(9 \cdot {x1}^{2} + -2 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. fma-def 87.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, {x1}^{2}, -2 \cdot x1\right)} \]

      2. unpow2 87.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, \color{blue}{x1 \cdot x1}, -2 \cdot x1\right) \]

      3. *-commutative 87.9%

         \[\leadsto x1 + \mathsf{fma}\left(9, x1 \cdot x1, \color{blue}{x1 \cdot -2}\right) \]

   8. Simplified 87.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)} \]

   if -6.3999999999999999e102 < x1 < 7.50000000000000031e149

   1. Initial program 97.8%

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

   2. Taylor expanded in x1 around 0 92.0%

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

      1. count-2 92.0%

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

   4. Simplified 92.0%

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

   5. Taylor expanded in x1 around 0 90.9%

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

      1. count-2 92.0%

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

   7. Simplified 90.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.4 \cdot 10^{+102} \lor \neg \left(x1 \leq 7.5 \cdot 10^{+149}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 10: 84.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := t_3 \cdot t_4\\ t_6 := x1 + \left(9 + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right) + \left(t_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -0.48:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 0.039:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5 (* t_3 t_4))
        (t_6
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_2
             (+
              t_5
              (*
               t_0
               (+
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))
                (* (- t_4 3.0) (* (* x1 2.0) (- (* 2.0 x2) x1))))))))))))
   (if (<= x1 -5.6e+102)
     t_1
     (if (<= x1 -0.48)
       t_6
       (if (<= x1 0.039)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+ t_2 (+ t_5 (* t_0 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113) t_6 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_3 * t_4;
	double t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -0.48) {
		tmp = t_6;
	} else if (x1 <= 0.039) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_1;
	}
	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 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = t_3 * t_4
    t_6 = x1 + (9.0d0 + (x1 + (t_2 + (t_5 + (t_0 * (((x1 * x1) * ((4.0d0 * t_4) - 6.0d0)) + ((t_4 - 3.0d0) * ((x1 * 2.0d0) * ((2.0d0 * x2) - x1)))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_1
    else if (x1 <= (-0.48d0)) then
        tmp = t_6
    else if (x1 <= 0.039d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = t_6
    else
        tmp = t_1
    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 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_3 * t_4;
	double t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -0.48) {
		tmp = t_6;
	} else if (x1 <= 0.039) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = t_3 * t_4
	t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_1
	elif x1 <= -0.48:
		tmp = t_6
	elif x1 <= 0.039:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = t_6
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(t_3 * t_4)
	t_6 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(2.0 * x2) - x1))))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -0.48)
		tmp = t_6;
	elseif (x1 <= 0.039)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = t_3 * t_4;
	t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * ((2.0 * x2) - x1)))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -0.48)
		tmp = t_6;
	elseif (x1 <= 0.039)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_1;
	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 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$1, If[LessEqual[x1, -0.48], t$95$6, If[LessEqual[x1, 0.039], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$6, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -0.47999999999999998 or 0.0389999999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x1 around 0 81.9%

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

   3. Taylor expanded in x1 around inf 81.9%

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

   if -0.47999999999999998 < x1 < 0.0389999999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.8%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -0.48:\\ \;\;\;\;x1 + \left(9 + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.039:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(9 + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(2 \cdot x2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 11: 82.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+113}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + t_0 \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -5.6e+102) (not (<= x1 2.1e+113)))
     (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))
            (* (* (* x1 2.0) t_2) (- (+ x2 x2) 3.0))))
          (* t_0 (+ x2 x2))))))))))

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 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2.1e+113)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	}
	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 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-5.6d+102)) .or. (.not. (x1 <= 2.1d+113))) then
        tmp = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)) + (((x1 * 2.0d0) * t_2) * ((x2 + x2) - 3.0d0)))) + (t_0 * (x2 + x2))))))
    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 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.6e+102) || !(x1 <= 2.1e+113)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -5.6e+102) or not (x1 <= 2.1e+113):
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))))
	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(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5.6e+102) || !(x1 <= 2.1e+113))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(Float64(x2 + x2) - 3.0)))) + Float64(t_0 * Float64(x2 + x2)))))));
	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 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -5.6e+102) || ~((x1 <= 2.1e+113)))
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + (((x1 * 2.0) * t_2) * ((x2 + x2) - 3.0)))) + (t_0 * (x2 + x2))))));
	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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5.6e+102], N[Not[LessEqual[x1, 2.1e+113]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(N[(x2 + x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < 2.0999999999999999e113

   1. Initial program 98.9%

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

   2. Taylor expanded in x1 around 0 93.0%

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

      1. count-2 93.0%

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

   4. Simplified 93.0%

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

   5. Taylor expanded in x1 around 0 91.9%

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

      1. count-2 93.0%

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

   7. Simplified 91.9%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+113}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\left(x2 + x2\right) - 3\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 84.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 \cdot \left(x1 \cdot x1\right)\\ t_5 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_6 := t_1 \cdot t_5\\ t_7 := x1 + \left(t_3 + \left(x1 + \left(t_4 + \left(t_6 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_5 - 6\right) + 12 \cdot \frac{x2}{x1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -70:\\ \;\;\;\;t_7\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_4 + \left(t_6 + t_2 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (* x1 (* x1 x1)))
        (t_5 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_6 (* t_1 t_5))
        (t_7
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             t_4
             (+
              t_6
              (*
               t_2
               (+ (* (* x1 x1) (- (* 4.0 t_5) 6.0)) (* 12.0 (/ x2 x1)))))))))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -70.0)
       t_7
       (if (<= x1 13.2)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+ t_4 (+ t_6 (* t_2 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113) t_7 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_6 = t_1 * t_5;
	double t_7 = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_5) - 6.0)) + (12.0 * (x2 / x1))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -70.0) {
		tmp = t_7;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_7;
	} else {
		tmp = t_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) :: tmp
    t_0 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = x1 * (x1 * x1)
    t_5 = ((t_1 + (2.0d0 * x2)) - x1) / t_2
    t_6 = t_1 * t_5
    t_7 = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (((x1 * x1) * ((4.0d0 * t_5) - 6.0d0)) + (12.0d0 * (x2 / x1))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-70.0d0)) then
        tmp = t_7
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = t_7
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 * (x1 * x1);
	double t_5 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_6 = t_1 * t_5;
	double t_7 = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_5) - 6.0)) + (12.0 * (x2 / x1))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -70.0) {
		tmp = t_7;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_7;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = x1 * (x1 * x1)
	t_5 = ((t_1 + (2.0 * x2)) - x1) / t_2
	t_6 = t_1 * t_5
	t_7 = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_5) - 6.0)) + (12.0 * (x2 / x1))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -70.0:
		tmp = t_7
	elif x1 <= 13.2:
		tmp = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = t_7
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	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(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(x1 * Float64(x1 * x1))
	t_5 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_6 = Float64(t_1 * t_5)
	t_7 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_4 + Float64(t_6 + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_5) - 6.0)) + Float64(12.0 * Float64(x2 / x1)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -70.0)
		tmp = t_7;
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_4 + Float64(t_6 + Float64(t_2 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_7;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = x1 * (x1 * x1);
	t_5 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	t_6 = t_1 * t_5;
	t_7 = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (((x1 * x1) * ((4.0 * t_5) - 6.0)) + (12.0 * (x2 / x1))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -70.0)
		tmp = t_7;
	elseif (x1 <= 13.2)
		tmp = x1 + (t_3 + (x1 + (t_4 + (t_6 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_7;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * t$95$5), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$4 + N[(t$95$6 + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$5), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(12.0 * N[(x2 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -70.0], t$95$7, If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$4 + N[(t$95$6 + N[(t$95$2 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$7, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -70 or 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x2 around inf 94.6%

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

      1. associate-*r/ 94.6%

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

      2. associate-/l* 94.6%

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

      3. +-commutative 94.6%

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

      4. unpow2 94.6%

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

      5. fma-udef 94.6%

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

   4. Simplified 94.6%

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

   5. Taylor expanded in x1 around inf 77.7%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\color{blue}{12 \cdot \frac{x2}{x1}} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -70 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -70:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + 12 \cdot \frac{x2}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \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) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right) + 12 \cdot \frac{x2}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 13: 83.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_5 := t_2 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\\ t_6 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -195:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_6 + \left(t_3 + t_5\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_6 + \left(t_3 + t_2 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_6 + \left(t_1 \cdot \left(x2 + x2\right) + t_5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_5
         (*
          t_2
          (+
           (* x1 2.0)
           (*
            (* x1 x1)
            (-
             (*
              4.0
              (+
               3.0
               (+ (* 2.0 (/ x2 (* x1 x1))) (- (/ -1.0 x1) (/ 3.0 (* x1 x1))))))
             6.0)))))
        (t_6 (* x1 (* x1 x1))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -195.0)
       (+ x1 (+ t_4 (+ x1 (+ t_6 (+ t_3 t_5)))))
       (if (<= x1 13.2)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+ t_6 (+ t_3 (* t_2 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113)
           (+ x1 (+ t_4 (+ x1 (+ t_6 (+ (* t_1 (+ x2 x2)) t_5)))))
           t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_5 = t_2 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -195.0) {
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + t_5))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_4 + (x1 + (t_6 + ((t_1 * (x2 + x2)) + t_5))));
	} else {
		tmp = t_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 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_2)
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_5 = t_2 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * (3.0d0 + ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))) - 6.0d0)))
    t_6 = x1 * (x1 * x1)
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-195.0d0)) then
        tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + t_5))))
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + (t_2 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = x1 + (t_4 + (x1 + (t_6 + ((t_1 * (x2 + x2)) + t_5))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_5 = t_2 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	double t_6 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -195.0) {
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + t_5))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_4 + (x1 + (t_6 + ((t_1 * (x2 + x2)) + t_5))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_5 = t_2 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)))
	t_6 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -195.0:
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + t_5))))
	elif x1 <= 13.2:
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = x1 + (t_4 + (x1 + (t_6 + ((t_1 * (x2 + x2)) + t_5))))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_5 = Float64(t_2 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1)))))) - 6.0))))
	t_6 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -195.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_6 + Float64(t_3 + t_5)))));
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_6 + Float64(t_3 + Float64(t_2 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_6 + Float64(Float64(t_1 * Float64(x2 + x2)) + t_5)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_5 = t_2 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	t_6 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -195.0)
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + t_5))));
	elseif (x1 <= 13.2)
		tmp = x1 + (t_4 + (x1 + (t_6 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = x1 + (t_4 + (x1 + (t_6 + ((t_1 * (x2 + x2)) + t_5))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -195.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$6 + N[(t$95$3 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$6 + N[(t$95$3 + N[(t$95$2 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$6 + N[(N[(t$95$1 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -195

   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 0 77.3%

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

   3. Taylor expanded in x1 around inf 72.3%

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

   4. Taylor expanded in x1 around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. unpow2 72.4%

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

      3. +-commutative 72.4%

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

      4. associate-*r/ 72.4%

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

      5. metadata-eval 72.4%

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

      6. unpow2 72.4%

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

   6. Simplified 72.4%

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

   if -195 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

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

   if 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 94.8%

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

   2. Taylor expanded in x1 around 0 86.1%

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

   3. Taylor expanded in x1 around inf 81.8%

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

   4. Taylor expanded in x1 around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. unpow2 81.8%

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

      3. +-commutative 81.8%

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

      4. associate-*r/ 81.8%

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

      5. metadata-eval 81.8%

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

      6. unpow2 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in x1 around 0 81.8%

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

      1. count-2 77.9%

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

   9. Simplified 81.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(2 \cdot x1 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} - \left(\frac{1}{x1} + \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -195:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 14: 83.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := t_0 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\\ t_2 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t_3 \cdot \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := 3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x1 \leq -490:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_5 + \left(t_4 + t_1\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_4 + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_3 \cdot \left(x2 + x2\right) + t_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1
         (*
          t_0
          (+
           (* x1 2.0)
           (*
            (* x1 x1)
            (-
             (*
              4.0
              (+
               3.0
               (+ (* 2.0 (/ x2 (* x1 x1))) (- (/ -1.0 x1) (/ 3.0 (* x1 x1))))))
             6.0)))))
        (t_2 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* t_3 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))))
   (if (<= x1 -5.6e+102)
     t_2
     (if (<= x1 -490.0)
       (+ x1 (+ 9.0 (+ x1 (+ t_5 (+ t_4 t_1)))))
       (if (<= x1 13.2)
         (+
          x1
          (+
           t_6
           (+
            x1
            (+ t_5 (+ t_4 (* t_0 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113)
           (+ x1 (+ t_6 (+ x1 (+ t_5 (+ (* t_3 (+ x2 x2)) t_1)))))
           t_2))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	double t_2 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -490.0) {
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + t_1))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_3 * (x2 + x2)) + t_1))));
	} else {
		tmp = t_2;
	}
	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 = t_0 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * (3.0d0 + ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))) - 6.0d0)))
    t_2 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 * (((t_3 + (2.0d0 * x2)) - x1) / t_0)
    t_5 = x1 * (x1 * x1)
    t_6 = 3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)
    if (x1 <= (-5.6d+102)) then
        tmp = t_2
    else if (x1 <= (-490.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_5 + (t_4 + t_1))))
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = x1 + (t_6 + (x1 + (t_5 + ((t_3 * (x2 + x2)) + t_1))))
    else
        tmp = t_2
    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 = t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	double t_2 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_2;
	} else if (x1 <= -490.0) {
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + t_1))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_3 * (x2 + x2)) + t_1))));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)))
	t_2 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0)
	t_5 = x1 * (x1 * x1)
	t_6 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_2
	elif x1 <= -490.0:
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + t_1))))
	elif x1 <= 13.2:
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_3 * (x2 + x2)) + t_1))))
	else:
		tmp = t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(t_0 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1)))))) - 6.0))))
	t_2 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 * Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -490.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_5 + Float64(t_4 + t_1)))));
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_0 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(Float64(t_3 * Float64(x2 + x2)) + t_1)))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0)));
	t_2 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	t_5 = x1 * (x1 * x1);
	t_6 = 3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_2;
	elseif (x1 <= -490.0)
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + t_1))));
	elseif (x1 <= 13.2)
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_3 * (x2 + x2)) + t_1))));
	else
		tmp = t_2;
	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[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 * N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$2, If[LessEqual[x1, -490.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$5 + N[(t$95$4 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$0 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(N[(t$95$3 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -490

   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 0 77.3%

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

   3. Taylor expanded in x1 around inf 72.3%

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

   4. Taylor expanded in x1 around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. unpow2 72.4%

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

      3. +-commutative 72.4%

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

      4. associate-*r/ 72.4%

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

      5. metadata-eval 72.4%

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

      6. unpow2 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x1 around inf 72.4%

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

   if -490 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

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

   if 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 94.8%

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

   2. Taylor expanded in x1 around 0 86.1%

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

   3. Taylor expanded in x1 around inf 81.8%

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

   4. Taylor expanded in x1 around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. unpow2 81.8%

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

      3. +-commutative 81.8%

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

      4. associate-*r/ 81.8%

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

      5. metadata-eval 81.8%

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

      6. unpow2 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in x1 around 0 81.8%

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

      1. count-2 77.9%

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

   9. Simplified 81.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(2 \cdot x1 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} - \left(\frac{1}{x1} + \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -490:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 15: 83.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_0}\\ t_4 := t_2 \cdot t_3\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -300:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(t_5 + \left(t_4 + t_0 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_4 + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_5 + \left(t_2 \cdot \left(x2 + x2\right) + t_0 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_3 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0))
        (t_4 (* t_2 t_3))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))))
   (if (<= x1 -5.6e+102)
     t_1
     (if (<= x1 -300.0)
       (+
        x1
        (+
         9.0
         (+
          x1
          (+
           t_5
           (+
            t_4
            (*
             t_0
             (+
              (* x1 2.0)
              (*
               (* x1 x1)
               (-
                (*
                 4.0
                 (+
                  3.0
                  (+
                   (* 2.0 (/ x2 (* x1 x1)))
                   (- (/ -1.0 x1) (/ 3.0 (* x1 x1))))))
                6.0)))))))))
       (if (<= x1 13.2)
         (+
          x1
          (+
           t_6
           (+
            x1
            (+ t_5 (+ t_4 (* t_0 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113)
           (+
            x1
            (+
             t_6
             (+
              x1
              (+
               t_5
               (+
                (* t_2 (+ x2 x2))
                (* t_0 (+ (* x1 2.0) (* (* x1 x1) (- (* 4.0 t_3) 6.0)))))))))
           t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = t_2 * t_3;
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -300.0) {
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_2 * (x2 + x2)) + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_3) - 6.0))))))));
	} else {
		tmp = t_1;
	}
	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 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    t_4 = t_2 * t_3
    t_5 = x1 * (x1 * x1)
    t_6 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    if (x1 <= (-5.6d+102)) then
        tmp = t_1
    else if (x1 <= (-300.0d0)) then
        tmp = x1 + (9.0d0 + (x1 + (t_5 + (t_4 + (t_0 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * (3.0d0 + ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))) - 6.0d0))))))))
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = x1 + (t_6 + (x1 + (t_5 + ((t_2 * (x2 + x2)) + (t_0 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * t_3) - 6.0d0))))))))
    else
        tmp = t_1
    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 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double t_4 = t_2 * t_3;
	double t_5 = x1 * (x1 * x1);
	double t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -300.0) {
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_2 * (x2 + x2)) + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_3) - 6.0))))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	t_4 = t_2 * t_3
	t_5 = x1 * (x1 * x1)
	t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_1
	elif x1 <= -300.0:
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))))
	elif x1 <= 13.2:
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_2 * (x2 + x2)) + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_3) - 6.0))))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	t_4 = Float64(t_2 * t_3)
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -300.0)
		tmp = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_0 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1)))))) - 6.0)))))))));
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(t_4 + Float64(t_0 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_5 + Float64(Float64(t_2 * Float64(x2 + x2)) + Float64(t_0 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_3) - 6.0)))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	t_4 = t_2 * t_3;
	t_5 = x1 * (x1 * x1);
	t_6 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -300.0)
		tmp = x1 + (9.0 + (x1 + (t_5 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	elseif (x1 <= 13.2)
		tmp = x1 + (t_6 + (x1 + (t_5 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = x1 + (t_6 + (x1 + (t_5 + ((t_2 * (x2 + x2)) + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_3) - 6.0))))))));
	else
		tmp = t_1;
	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 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$1, If[LessEqual[x1, -300.0], N[(x1 + N[(9.0 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(t$95$4 + N[(t$95$0 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$5 + N[(N[(t$95$2 * N[(x2 + x2), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$3), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -300

   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 0 77.3%

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

   3. Taylor expanded in x1 around inf 72.3%

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

   4. Taylor expanded in x1 around inf 72.4%

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

      1. associate--l+ 72.4%

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

      2. unpow2 72.4%

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

      3. +-commutative 72.4%

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

      4. associate-*r/ 72.4%

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

      5. metadata-eval 72.4%

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

      6. unpow2 72.4%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x1 around inf 72.4%

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

   if -300 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

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

   if 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 94.8%

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

   2. Taylor expanded in x1 around 0 86.1%

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

   3. Taylor expanded in x1 around inf 81.8%

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

   4. Taylor expanded in x1 around 0 81.8%

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

      1. count-2 77.9%

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

   6. Simplified 81.8%

      \[\leadsto x1 + \left(\left(\left(\left(\left(2 \cdot x1 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \color{blue}{\left(x2 + x2\right)}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -300:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(x2 + x2\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 16: 83.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := t_3 \cdot \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := x1 + \left(9 + \left(x1 + \left(t_2 + \left(t_4 + t_0 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -60:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(t_2 + \left(t_4 + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* t_3 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0)))
        (t_5
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_2
             (+
              t_4
              (*
               t_0
               (+
                (* x1 2.0)
                (*
                 (* x1 x1)
                 (-
                  (*
                   4.0
                   (+
                    3.0
                    (+
                     (* 2.0 (/ x2 (* x1 x1)))
                     (- (/ -1.0 x1) (/ 3.0 (* x1 x1))))))
                  6.0)))))))))))
   (if (<= x1 -5.6e+102)
     t_1
     (if (<= x1 -60.0)
       t_5
       (if (<= x1 13.2)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+ t_2 (+ t_4 (* t_0 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113) t_5 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	double t_5 = x1 + (9.0 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -60.0) {
		tmp = t_5;
	} else if (x1 <= 13.2) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = t_3 * (((t_3 + (2.0d0 * x2)) - x1) / t_0)
    t_5 = x1 + (9.0d0 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * (3.0d0 + ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))) - 6.0d0))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_1
    else if (x1 <= (-60.0d0)) then
        tmp = t_5
    else if (x1 <= 13.2d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_4 + (t_0 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = t_5
    else
        tmp = t_1
    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 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	double t_5 = x1 + (9.0 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -60.0) {
		tmp = t_5;
	} else if (x1 <= 13.2) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0)
	t_5 = x1 + (9.0 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_1
	elif x1 <= -60.0:
		tmp = t_5
	elif x1 <= 13.2:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(t_3 * Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0))
	t_5 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(t_0 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1)))))) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -60.0)
		tmp = t_5;
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(t_0 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = t_3 * (((t_3 + (2.0 * x2)) - x1) / t_0);
	t_5 = x1 + (9.0 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -60.0)
		tmp = t_5;
	elseif (x1 <= 13.2)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_4 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_5;
	else
		tmp = t_1;
	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 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(t$95$3 * N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$1, If[LessEqual[x1, -60.0], t$95$5, If[LessEqual[x1, 13.2], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(t$95$0 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$5, t$95$1]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -60 or 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around inf 76.8%

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

   4. Taylor expanded in x1 around inf 76.9%

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

      1. associate--l+ 76.9%

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

      2. unpow2 76.9%

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

      3. +-commutative 76.9%

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

      4. associate-*r/ 76.9%

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

      5. metadata-eval 76.9%

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

      6. unpow2 76.9%

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

   6. Simplified 76.9%

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

   7. Taylor expanded in x1 around inf 76.9%

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

   if -60 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -60:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 17: 83.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := t_3 \cdot t_4\\ t_6 := x1 + \left(9 + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -430:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5 (* t_3 t_4))
        (t_6
         (+
          x1
          (+
           9.0
           (+
            x1
            (+
             t_2
             (+
              t_5
              (* t_0 (+ (* x1 2.0) (* (* x1 x1) (- (* 4.0 t_4) 6.0)))))))))))
   (if (<= x1 -5.6e+102)
     t_1
     (if (<= x1 -430.0)
       t_6
       (if (<= x1 13.2)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
           (+
            x1
            (+ t_2 (+ t_5 (* t_0 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113) t_6 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_3 * t_4;
	double t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_4) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -430.0) {
		tmp = t_6;
	} else if (x1 <= 13.2) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_1;
	}
	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 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = t_3 * t_4
    t_6 = x1 + (9.0d0 + (x1 + (t_2 + (t_5 + (t_0 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * t_4) - 6.0d0))))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_1
    else if (x1 <= (-430.0d0)) then
        tmp = t_6
    else if (x1 <= 13.2d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = t_6
    else
        tmp = t_1
    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 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	double t_5 = t_3 * t_4;
	double t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_4) - 6.0))))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_1;
	} else if (x1 <= -430.0) {
		tmp = t_6;
	} else if (x1 <= 13.2) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = t_3 * t_4
	t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_4) - 6.0))))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_1
	elif x1 <= -430.0:
		tmp = t_6
	elif x1 <= 13.2:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = t_6
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_0)
	t_5 = Float64(t_3 * t_4)
	t_6 = Float64(x1 + Float64(9.0 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -430.0)
		tmp = t_6;
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = t_3 * t_4;
	t_6 = x1 + (9.0 + (x1 + (t_2 + (t_5 + (t_0 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * t_4) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_1;
	elseif (x1 <= -430.0)
		tmp = t_6;
	elseif (x1 <= 13.2)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (t_2 + (t_5 + (t_0 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_1;
	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 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$3 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(9.0 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$1, If[LessEqual[x1, -430.0], t$95$6, If[LessEqual[x1, 13.2], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$6, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -430 or 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x1 around 0 81.5%

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

   3. Taylor expanded in x1 around inf 76.8%

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

   4. Taylor expanded in x1 around inf 76.8%

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

   if -430 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -430:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(9 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 18: 82.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_5 := x1 \cdot \left(x1 \cdot x1\right)\\ t_6 := x1 + \left(t_4 + \left(x1 + \left(t_5 + \left(t_3 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -195:\\ \;\;\;\;t_6\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_5 + \left(t_3 + t_2 \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2)))
        (t_4 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_5 (* x1 (* x1 x1)))
        (t_6 (+ x1 (+ t_4 (+ x1 (+ t_5 (+ t_3 (* t_2 (* (* x1 x1) 6.0)))))))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -195.0)
       t_6
       (if (<= x1 13.2)
         (+
          x1
          (+
           t_4
           (+
            x1
            (+ t_5 (+ t_3 (* t_2 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0))))))))))
         (if (<= x1 2.1e+113) t_6 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * ((x1 * x1) * 6.0))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -195.0) {
		tmp = t_6;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_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 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_2)
    t_4 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_5 = x1 * (x1 * x1)
    t_6 = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * ((x1 * x1) * 6.0d0))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-195.0d0)) then
        tmp = t_6
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0)))))))))
    else if (x1 <= 2.1d+113) then
        tmp = t_6
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	double t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_5 = x1 * (x1 * x1);
	double t_6 = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * ((x1 * x1) * 6.0))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -195.0) {
		tmp = t_6;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_6;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_5 = x1 * (x1 * x1)
	t_6 = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * ((x1 * x1) * 6.0))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -195.0:
		tmp = t_6
	elif x1 <= 13.2:
		tmp = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))))
	elif x1 <= 2.1e+113:
		tmp = t_6
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	t_5 = Float64(x1 * Float64(x1 * x1))
	t_6 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_5 + Float64(t_3 + Float64(t_2 * Float64(Float64(x1 * x1) * 6.0)))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -195.0)
		tmp = t_6;
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_5 + Float64(t_3 + Float64(t_2 * Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2);
	t_4 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_5 = x1 * (x1 * x1);
	t_6 = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * ((x1 * x1) * 6.0))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -195.0)
		tmp = t_6;
	elseif (x1 <= 13.2)
		tmp = x1 + (t_4 + (x1 + (t_5 + (t_3 + (t_2 * (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_6;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$5 + N[(t$95$3 + N[(t$95$2 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -195.0], t$95$6, If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$5 + N[(t$95$3 + N[(t$95$2 * N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$6, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -195 or 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x1 around 0 77.4%

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

      1. count-2 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in x1 around inf 64.1%

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

      1. *-commutative 64.1%

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

      2. unpow2 64.1%

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

   7. Simplified 64.1%

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

   if -195 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 98.9%

      \[\leadsto x1 + \left(\left(\left(\left(\color{blue}{\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -195:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 19: 82.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2} + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -480:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2)))))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
              (* t_2 (* (* x1 x1) 6.0)))))))))
   (if (<= x1 -5.6e+102)
     t_0
     (if (<= x1 -480.0)
       t_4
       (if (<= x1 13.2)
         (+ x1 (+ t_3 (+ x1 (* x2 (* 8.0 (* x1 x2))))))
         (if (<= x1 2.1e+113) t_4 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * ((x1 * x1) * 6.0))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -480.0) {
		tmp = t_4;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_3 + (x1 + (x2 * (8.0 * (x1 * x2)))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_4;
	} else {
		tmp = t_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 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_2)) + (t_2 * ((x1 * x1) * 6.0d0))))))
    if (x1 <= (-5.6d+102)) then
        tmp = t_0
    else if (x1 <= (-480.0d0)) then
        tmp = t_4
    else if (x1 <= 13.2d0) then
        tmp = x1 + (t_3 + (x1 + (x2 * (8.0d0 * (x1 * x2)))))
    else if (x1 <= 2.1d+113) then
        tmp = t_4
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * ((x1 * x1) * 6.0))))));
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = t_0;
	} else if (x1 <= -480.0) {
		tmp = t_4;
	} else if (x1 <= 13.2) {
		tmp = x1 + (t_3 + (x1 + (x2 * (8.0 * (x1 * x2)))));
	} else if (x1 <= 2.1e+113) {
		tmp = t_4;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	t_1 = x1 * (x1 * 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * ((x1 * x1) * 6.0))))))
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = t_0
	elif x1 <= -480.0:
		tmp = t_4
	elif x1 <= 13.2:
		tmp = x1 + (t_3 + (x1 + (x2 * (8.0 * (x1 * x2)))))
	elif x1 <= 2.1e+113:
		tmp = t_4
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	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(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)) + Float64(t_2 * Float64(Float64(x1 * x1) * 6.0)))))))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -480.0)
		tmp = t_4;
	elseif (x1 <= 13.2)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(x2 * Float64(8.0 * Float64(x1 * x2))))));
	elseif (x1 <= 2.1e+113)
		tmp = t_4;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	t_1 = x1 * (x1 * 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_2)) + (t_2 * ((x1 * x1) * 6.0))))));
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = t_0;
	elseif (x1 <= -480.0)
		tmp = t_4;
	elseif (x1 <= 13.2)
		tmp = x1 + (t_3 + (x1 + (x2 * (8.0 * (x1 * x2)))));
	elseif (x1 <= 2.1e+113)
		tmp = t_4;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $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[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], t$95$0, If[LessEqual[x1, -480.0], t$95$4, If[LessEqual[x1, 13.2], N[(x1 + N[(t$95$3 + N[(x1 + N[(x2 * N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e+113], t$95$4, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102 or 2.0999999999999999e113 < 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 2.4%

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

   3. Taylor expanded in x1 around 0 64.3%

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

      1. fma-def 68.9%

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

      2. associate-*r* 68.9%

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

      3. fma-neg 68.9%

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

      4. metadata-eval 68.9%

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

      5. *-commutative 68.9%

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

      6. fma-neg 68.9%

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

      7. metadata-eval 68.9%

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

      8. *-commutative 68.9%

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

      9. fma-def 68.9%

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

      10. associate-*r* 68.9%

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

      11. *-commutative 68.9%

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

      12. unpow2 68.9%

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

      13. associate-*r* 68.9%

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

      14. associate-*l* 68.9%

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

      15. *-commutative 68.9%

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

      16. *-commutative 68.9%

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

   5. Simplified 68.9%

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

   6. Taylor expanded in x1 around inf 75.7%

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

      1. associate-*r* 75.7%

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

      2. *-commutative 75.7%

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

      3. unpow2 75.7%

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

      4. associate-*r* 75.7%

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

      5. *-commutative 75.7%

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

      6. associate-*r* 75.7%

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

      7. associate-*l* 75.7%

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

      8. *-commutative 75.7%

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

      9. cancel-sign-sub-inv 75.7%

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

      10. metadata-eval 75.7%

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

      11. *-commutative 75.7%

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

   8. Simplified 75.7%

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

   if -5.60000000000000037e102 < x1 < -480 or 13.199999999999999 < x1 < 2.0999999999999999e113

   1. Initial program 97.2%

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

   2. Taylor expanded in x1 around 0 77.4%

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

      1. count-2 77.4%

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

   4. Simplified 77.4%

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

   5. Taylor expanded in x1 around inf 64.1%

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

      1. *-commutative 64.1%

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

      2. unpow2 64.1%

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

   7. Simplified 64.1%

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

   if -480 < x1 < 13.199999999999999

   1. Initial program 99.6%

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

   2. Taylor expanded in x1 around 0 98.9%

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

      1. count-2 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x2 around inf 87.2%

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

      1. unpow2 87.2%

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

      2. associate-*r* 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-*r* 98.9%

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

      5. *-commutative 98.9%

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

      6. associate-*l* 98.9%

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

      7. *-commutative 98.9%

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

   7. Simplified 98.9%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -480:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 13.2:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{+113}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 20: 75.0% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+60} \lor \neg \left(x1 \leq 1.02 \cdot 10^{+76}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -6e+60) (not (<= x1 1.02e+76)))
   (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))
   (+
    x1
    (+
     (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
     (+ x1 (* x2 (* 8.0 (* x1 x2))))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6e+60) || !(x1 <= 1.02e+76)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x2 * (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-6d+60)) .or. (.not. (x1 <= 1.02d+76))) then
        tmp = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    else
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (x2 * (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -6e+60) || !(x1 <= 1.02e+76)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x2 * (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -6e+60) or not (x1 <= 1.02e+76):
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	else:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x2 * (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -6e+60) || !(x1 <= 1.02e+76))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(x2 * Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -6e+60) || ~((x1 <= 1.02e+76)))
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	else
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (x2 * (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -6e+60], N[Not[LessEqual[x1, 1.02e+76]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x2 * N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.9999999999999997e60 or 1.02000000000000007e76 < x1

   1. Initial program 18.0%

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

   2. Taylor expanded in x1 around 0 3.2%

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

   3. Taylor expanded in x1 around 0 55.6%

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

      1. fma-def 59.4%

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

      2. associate-*r* 59.4%

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

      3. fma-neg 59.4%

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

      4. metadata-eval 59.4%

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

      5. *-commutative 59.4%

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

      6. fma-neg 59.4%

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

      7. metadata-eval 59.4%

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

      8. *-commutative 59.4%

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

      9. fma-def 59.4%

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

      10. associate-*r* 59.4%

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

      11. *-commutative 59.4%

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

      12. unpow2 59.4%

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

      13. associate-*r* 59.4%

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

      14. associate-*l* 59.4%

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

      15. *-commutative 59.4%

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

      16. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in x1 around inf 67.0%

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

      1. associate-*r* 67.0%

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

      2. *-commutative 67.0%

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

      3. unpow2 67.0%

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

      4. associate-*r* 67.0%

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

      5. *-commutative 67.0%

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

      6. associate-*r* 67.0%

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

      7. associate-*l* 67.0%

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

      8. *-commutative 67.0%

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

      9. cancel-sign-sub-inv 67.0%

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

      10. metadata-eval 67.0%

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

      11. *-commutative 67.0%

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

   8. Simplified 67.0%

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

   if -5.9999999999999997e60 < x1 < 1.02000000000000007e76

   1. Initial program 99.5%

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

   2. Taylor expanded in x1 around 0 93.6%

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

      1. count-2 93.6%

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

   4. Simplified 93.6%

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

   5. Taylor expanded in x2 around inf 75.8%

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

      1. unpow2 75.8%

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

      2. associate-*r* 85.3%

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

      3. *-commutative 85.3%

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

      4. associate-*r* 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-*l* 85.3%

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

      7. *-commutative 85.3%

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

   7. Simplified 85.3%

      \[\leadsto x1 + \left(\left(\color{blue}{x2 \cdot \left(8 \cdot \left(x2 \cdot x1\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+60} \lor \neg \left(x1 \leq 1.02 \cdot 10^{+76}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]

Alternative 21: 70.2% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-165}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 1.12 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)))))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))))
   (if (<= x1 -1.85e+61)
     t_1
     (if (<= x1 -3.8e-166)
       t_0
       (if (<= x1 9.5e-165)
         (+ x1 (- (* 8.0 (* x2 (* x1 x2))) (* 6.0 x2)))
         (if (<= x1 1.12e+29) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.85e+61) {
		tmp = t_1;
	} else if (x1 <= -3.8e-166) {
		tmp = t_0;
	} else if (x1 <= 9.5e-165) {
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	} else if (x1 <= 1.12e+29) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    t_1 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    if (x1 <= (-1.85d+61)) then
        tmp = t_1
    else if (x1 <= (-3.8d-166)) then
        tmp = t_0
    else if (x1 <= 9.5d-165) then
        tmp = x1 + ((8.0d0 * (x2 * (x1 * x2))) - (6.0d0 * x2))
    else if (x1 <= 1.12d+29) then
        tmp = t_0
    else
        tmp = t_1
    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 * ((2.0 * x2) - 3.0))) - 2.0)));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.85e+61) {
		tmp = t_1;
	} else if (x1 <= -3.8e-166) {
		tmp = t_0;
	} else if (x1 <= 9.5e-165) {
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	} else if (x1 <= 1.12e+29) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	tmp = 0
	if x1 <= -1.85e+61:
		tmp = t_1
	elif x1 <= -3.8e-166:
		tmp = t_0
	elif x1 <= 9.5e-165:
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2))
	elif x1 <= 1.12e+29:
		tmp = t_0
	else:
		tmp = t_1
	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(2.0 * x2) - 3.0))) - 2.0))))
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	tmp = 0.0
	if (x1 <= -1.85e+61)
		tmp = t_1;
	elseif (x1 <= -3.8e-166)
		tmp = t_0;
	elseif (x1 <= 9.5e-165)
		tmp = Float64(x1 + Float64(Float64(8.0 * Float64(x2 * Float64(x1 * x2))) - Float64(6.0 * x2)));
	elseif (x1 <= 1.12e+29)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	tmp = 0.0;
	if (x1 <= -1.85e+61)
		tmp = t_1;
	elseif (x1 <= -3.8e-166)
		tmp = t_0;
	elseif (x1 <= 9.5e-165)
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	elseif (x1 <= 1.12e+29)
		tmp = t_0;
	else
		tmp = t_1;
	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[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.85e+61], t$95$1, If[LessEqual[x1, -3.8e-166], t$95$0, If[LessEqual[x1, 9.5e-165], N[(x1 + N[(N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.12e+29], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.85000000000000001e61 or 1.1200000000000001e29 < x1

   1. Initial program 22.4%

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

   2. Taylor expanded in x1 around 0 4.3%

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

   3. Taylor expanded in x1 around 0 53.8%

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

      1. fma-def 57.4%

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

      2. associate-*r* 57.4%

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

      3. fma-neg 57.4%

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

      4. metadata-eval 57.4%

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

      5. *-commutative 57.4%

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

      6. fma-neg 57.4%

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

      7. metadata-eval 57.4%

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

      8. *-commutative 57.4%

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

      9. fma-def 57.4%

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

      10. associate-*r* 57.4%

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

      11. *-commutative 57.4%

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

      12. unpow2 57.4%

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

      13. associate-*r* 57.4%

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

      14. associate-*l* 57.4%

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

      15. *-commutative 57.4%

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

      16. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x1 around inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. unpow2 64.5%

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

      4. associate-*r* 64.5%

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

      5. *-commutative 64.5%

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

      6. associate-*r* 64.5%

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

      7. associate-*l* 64.5%

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

      8. *-commutative 64.5%

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

      9. cancel-sign-sub-inv 64.5%

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

      10. metadata-eval 64.5%

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

      11. *-commutative 64.5%

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

   8. Simplified 64.5%

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

   if -1.85000000000000001e61 < x1 < -3.79999999999999982e-166 or 9.49999999999999973e-165 < x1 < 1.1200000000000001e29

   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 80.2%

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

   3. Taylor expanded in x1 around 0 77.9%

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

   if -3.79999999999999982e-166 < x1 < 9.49999999999999973e-165

   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 99.8%

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

   3. Taylor expanded in x1 around 0 99.8%

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

      1. fma-def 99.8%

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

      2. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in x2 around -inf 69.7%

      \[\leadsto x1 + \color{blue}{\left(-1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right) + 8 \cdot \left({x2}^{2} \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 69.7%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) + -1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right)\right)} \]

      2. mul-1-neg 69.7%

         \[\leadsto x1 + \left(8 \cdot \left({x2}^{2} \cdot x1\right) + \color{blue}{\left(-x2 \cdot \left(6 + 12 \cdot x1\right)\right)}\right) \]

      3. unsub-neg 69.7%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]

      4. *-commutative 69.7%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      5. unpow2 69.7%

         \[\leadsto x1 + \left(8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      6. associate-*r* 91.4%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      7. *-commutative 91.4%

         \[\leadsto x1 + \left(8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      8. *-commutative 91.4%

         \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + \color{blue}{x1 \cdot 12}\right)\right) \]

   8. Simplified 91.4%

      \[\leadsto x1 + \color{blue}{\left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + x1 \cdot 12\right)\right)} \]

   9. Taylor expanded in x1 around 0 91.4%

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

       1. *-commutative 91.4%

          \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]

   11. Simplified 91.4%

       \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.85 \cdot 10^{+61}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 9.5 \cdot 10^{-165}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 1.12 \cdot 10^{+29}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 22: 74.4% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+61} \lor \neg \left(x1 \leq 1.12 \cdot 10^{+29}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.7e+61) (not (<= x1 1.12e+29)))
   (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))
   (+
    x1
    (+
     (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))
     (+ (* x1 -3.0) (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.7e+61) || !(x1 <= 1.12e+29)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + ((x1 * -3.0) + (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 <= (-1.7d+61)) .or. (.not. (x1 <= 1.12d+29))) then
        tmp = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    else
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))) + ((x1 * (-3.0d0)) + (x2 * (-6.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.7e+61) || !(x1 <= 1.12e+29)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + ((x1 * -3.0) + (x2 * -6.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.7e+61) or not (x1 <= 1.12e+29):
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	else:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + ((x1 * -3.0) + (x2 * -6.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.7e+61) || !(x1 <= 1.12e+29))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(Float64(x1 * -3.0) + Float64(x2 * -6.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.7e+61) || ~((x1 <= 1.12e+29)))
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	else
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + ((x1 * -3.0) + (x2 * -6.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.7e+61], N[Not[LessEqual[x1, 1.12e+29]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * -3.0), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.70000000000000013e61 or 1.1200000000000001e29 < x1

   1. Initial program 22.4%

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

   2. Taylor expanded in x1 around 0 4.3%

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

   3. Taylor expanded in x1 around 0 53.8%

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

      1. fma-def 57.4%

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

      2. associate-*r* 57.4%

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

      3. fma-neg 57.4%

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

      4. metadata-eval 57.4%

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

      5. *-commutative 57.4%

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

      6. fma-neg 57.4%

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

      7. metadata-eval 57.4%

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

      8. *-commutative 57.4%

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

      9. fma-def 57.4%

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

      10. associate-*r* 57.4%

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

      11. *-commutative 57.4%

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

      12. unpow2 57.4%

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

      13. associate-*r* 57.4%

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

      14. associate-*l* 57.4%

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

      15. *-commutative 57.4%

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

      16. *-commutative 57.4%

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

   5. Simplified 57.4%

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

   6. Taylor expanded in x1 around inf 64.5%

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

      1. associate-*r* 64.5%

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

      2. *-commutative 64.5%

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

      3. unpow2 64.5%

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

      4. associate-*r* 64.5%

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

      5. *-commutative 64.5%

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

      6. associate-*r* 64.5%

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

      7. associate-*l* 64.5%

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

      8. *-commutative 64.5%

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

      9. cancel-sign-sub-inv 64.5%

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

      10. metadata-eval 64.5%

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

      11. *-commutative 64.5%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{x2 \cdot 2}\right)\right)\right) \]

   8. Simplified 64.5%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + x2 \cdot 2\right)\right)\right)} \]

   if -1.70000000000000013e61 < x1 < 1.1200000000000001e29

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 87.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 87.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+61} \lor \neg \left(x1 \leq 1.12 \cdot 10^{+29}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + \left(x1 \cdot -3 + x2 \cdot -6\right)\right)\\ \end{array} \]

Alternative 23: 52.9% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x2 (* x1 x2)))))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))))
   (if (<= x1 -1.55e+61)
     t_1
     (if (<= x1 -8.5e-72)
       t_0
       (if (<= x1 1.45e-59)
         (+ x1 (* x2 -6.0))
         (if (<= x1 5.4e+75) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.55e+61) {
		tmp = t_1;
	} else if (x1 <= -8.5e-72) {
		tmp = t_0;
	} else if (x1 <= 1.45e-59) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 5.4e+75) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_0 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    t_1 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    if (x1 <= (-1.55d+61)) then
        tmp = t_1
    else if (x1 <= (-8.5d-72)) then
        tmp = t_0
    else if (x1 <= 1.45d-59) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x1 <= 5.4d+75) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.55e+61) {
		tmp = t_1;
	} else if (x1 <= -8.5e-72) {
		tmp = t_0;
	} else if (x1 <= 1.45e-59) {
		tmp = x1 + (x2 * -6.0);
	} else if (x1 <= 5.4e+75) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)))
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	tmp = 0
	if x1 <= -1.55e+61:
		tmp = t_1
	elif x1 <= -8.5e-72:
		tmp = t_0
	elif x1 <= 1.45e-59:
		tmp = x1 + (x2 * -6.0)
	elif x1 <= 5.4e+75:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	tmp = 0.0
	if (x1 <= -1.55e+61)
		tmp = t_1;
	elseif (x1 <= -8.5e-72)
		tmp = t_0;
	elseif (x1 <= 1.45e-59)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x1 <= 5.4e+75)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	tmp = 0.0;
	if (x1 <= -1.55e+61)
		tmp = t_1;
	elseif (x1 <= -8.5e-72)
		tmp = t_0;
	elseif (x1 <= 1.45e-59)
		tmp = x1 + (x2 * -6.0);
	elseif (x1 <= 5.4e+75)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.55e+61], t$95$1, If[LessEqual[x1, -8.5e-72], t$95$0, If[LessEqual[x1, 1.45e-59], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.4e+75], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.55e61 or 5.39999999999999996e75 < x1

   1. Initial program 18.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 55.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 59.4%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 59.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x1 around inf 67.0%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)} \]

      2. *-commutative 67.0%

         \[\leadsto x1 + \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      3. unpow2 67.0%

         \[\leadsto x1 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right) \]

      4. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      5. *-commutative 67.0%

         \[\leadsto x1 + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right) \]

      6. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - x2 \cdot -2\right)\right)} \]

      7. associate-*l* 67.0%

         \[\leadsto x1 + x1 \cdot \color{blue}{\left(x1 \cdot \left(3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)} \]

      8. *-commutative 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right)\right) \]

      9. cancel-sign-sub-inv 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right) \]

      10. metadata-eval 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{x2 \cdot 2}\right)\right)\right) \]

   8. Simplified 67.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + x2 \cdot 2\right)\right)\right)} \]

   if -1.55e61 < x1 < -8.50000000000000008e-72 or 1.45000000000000008e-59 < x1 < 5.39999999999999996e75

   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 57.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 54.4%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 54.5%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 54.5%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 54.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 54.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 54.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x2 around inf 37.6%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.6%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]

      2. unpow2 37.6%

         \[\leadsto x1 + 8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \]

      3. associate-*r* 37.6%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} \]

      4. *-commutative 37.6%

         \[\leadsto x1 + 8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) \]

   8. Simplified 37.6%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right)} \]

   if -8.50000000000000008e-72 < x1 < 1.45000000000000008e-59

   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 99.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 67.8%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 67.8%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 67.8%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+61}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -8.5 \cdot 10^{-72}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.45 \cdot 10^{-59}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 5.4 \cdot 10^{+75}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 24: 62.6% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ t_1 := x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-185}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+76}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (- (* 8.0 (* x2 (* x1 x2))) (* 6.0 x2))))
        (t_1 (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))))
   (if (<= x1 -1.9e+61)
     t_1
     (if (<= x1 -6.2e-137)
       t_0
       (if (<= x1 2.6e-185)
         (+ x1 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))
         (if (<= x1 1.32e+76) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.9e+61) {
		tmp = t_1;
	} else if (x1 <= -6.2e-137) {
		tmp = t_0;
	} else if (x1 <= 2.6e-185) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 1.32e+76) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: tmp
    t_0 = x1 + ((8.0d0 * (x2 * (x1 * x2))) - (6.0d0 * x2))
    t_1 = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    if (x1 <= (-1.9d+61)) then
        tmp = t_1
    else if (x1 <= (-6.2d-137)) then
        tmp = t_0
    else if (x1 <= 2.6d-185) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    else if (x1 <= 1.32d+76) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	double t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	double tmp;
	if (x1 <= -1.9e+61) {
		tmp = t_1;
	} else if (x1 <= -6.2e-137) {
		tmp = t_0;
	} else if (x1 <= 2.6e-185) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 1.32e+76) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2))
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	tmp = 0
	if x1 <= -1.9e+61:
		tmp = t_1
	elif x1 <= -6.2e-137:
		tmp = t_0
	elif x1 <= 2.6e-185:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	elif x1 <= 1.32e+76:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(8.0 * Float64(x2 * Float64(x1 * x2))) - Float64(6.0 * x2)))
	t_1 = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))))
	tmp = 0.0
	if (x1 <= -1.9e+61)
		tmp = t_1;
	elseif (x1 <= -6.2e-137)
		tmp = t_0;
	elseif (x1 <= 2.6e-185)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))));
	elseif (x1 <= 1.32e+76)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	t_1 = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	tmp = 0.0;
	if (x1 <= -1.9e+61)
		tmp = t_1;
	elseif (x1 <= -6.2e-137)
		tmp = t_0;
	elseif (x1 <= 2.6e-185)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	elseif (x1 <= 1.32e+76)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.9e+61], t$95$1, If[LessEqual[x1, -6.2e-137], t$95$0, If[LessEqual[x1, 2.6e-185], N[(x1 + N[(N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(x1 * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+76], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.89999999999999998e61 or 1.31999999999999999e76 < x1

   1. Initial program 18.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 55.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 59.4%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 59.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x1 around inf 67.0%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)} \]

      2. *-commutative 67.0%

         \[\leadsto x1 + \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      3. unpow2 67.0%

         \[\leadsto x1 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right) \]

      4. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      5. *-commutative 67.0%

         \[\leadsto x1 + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right) \]

      6. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - x2 \cdot -2\right)\right)} \]

      7. associate-*l* 67.0%

         \[\leadsto x1 + x1 \cdot \color{blue}{\left(x1 \cdot \left(3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)} \]

      8. *-commutative 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right)\right) \]

      9. cancel-sign-sub-inv 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right) \]

      10. metadata-eval 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{x2 \cdot 2}\right)\right)\right) \]

   8. Simplified 67.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + x2 \cdot 2\right)\right)\right)} \]

   if -1.89999999999999998e61 < x1 < -6.19999999999999955e-137 or 2.59999999999999985e-185 < x1 < 1.31999999999999999e76

   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 75.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 75.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 75.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 75.2%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 75.2%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around -inf 52.5%

      \[\leadsto x1 + \color{blue}{\left(-1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right) + 8 \cdot \left({x2}^{2} \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 52.5%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) + -1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right)\right)} \]

      2. mul-1-neg 52.5%

         \[\leadsto x1 + \left(8 \cdot \left({x2}^{2} \cdot x1\right) + \color{blue}{\left(-x2 \cdot \left(6 + 12 \cdot x1\right)\right)}\right) \]

      3. unsub-neg 52.5%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]

      4. *-commutative 52.5%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      5. unpow2 52.5%

         \[\leadsto x1 + \left(8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      6. associate-*r* 57.7%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      7. *-commutative 57.7%

         \[\leadsto x1 + \left(8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      8. *-commutative 57.7%

         \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + \color{blue}{x1 \cdot 12}\right)\right) \]

   8. Simplified 57.7%

      \[\leadsto x1 + \color{blue}{\left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + x1 \cdot 12\right)\right)} \]

   9. Taylor expanded in x1 around 0 59.9%

      \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{6 \cdot x2}\right) \]
   10. Step-by-step derivation

       1. *-commutative 59.9%

          \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]

   11. Simplified 59.9%

       \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]

   if -6.19999999999999955e-137 < x1 < 2.59999999999999985e-185

   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 99.7%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 99.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 99.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 99.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 99.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around 0 92.4%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(-3 \cdot x1 + x1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.9 \cdot 10^{+61}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -6.2 \cdot 10^{-137}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \mathbf{elif}\;x1 \leq 2.6 \cdot 10^{-185}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+76}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \end{array} \]

Alternative 25: 44.3% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ t_1 := x1 + x2 \cdot -6\\ \mathbf{if}\;x2 \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -1.7 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 2.95 \cdot 10^{-176}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 2.45 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x2 (* x1 x2))))) (t_1 (+ x1 (* x2 -6.0))))
   (if (<= x2 -1.3e+170)
     t_0
     (if (<= x2 -1.7e-293)
       t_1
       (if (<= x2 2.95e-176)
         (+ x1 (* x1 -2.0))
         (if (<= x2 2.45e+125) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.3e+170) {
		tmp = t_0;
	} else if (x2 <= -1.7e-293) {
		tmp = t_1;
	} else if (x2 <= 2.95e-176) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 2.45e+125) {
		tmp = t_1;
	} else {
		tmp = t_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) :: tmp
    t_0 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    t_1 = x1 + (x2 * (-6.0d0))
    if (x2 <= (-1.3d+170)) then
        tmp = t_0
    else if (x2 <= (-1.7d-293)) then
        tmp = t_1
    else if (x2 <= 2.95d-176) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 2.45d+125) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x2 * -6.0);
	double tmp;
	if (x2 <= -1.3e+170) {
		tmp = t_0;
	} else if (x2 <= -1.7e-293) {
		tmp = t_1;
	} else if (x2 <= 2.95e-176) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 2.45e+125) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)))
	t_1 = x1 + (x2 * -6.0)
	tmp = 0
	if x2 <= -1.3e+170:
		tmp = t_0
	elif x2 <= -1.7e-293:
		tmp = t_1
	elif x2 <= 2.95e-176:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 2.45e+125:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	t_1 = Float64(x1 + Float64(x2 * -6.0))
	tmp = 0.0
	if (x2 <= -1.3e+170)
		tmp = t_0;
	elseif (x2 <= -1.7e-293)
		tmp = t_1;
	elseif (x2 <= 2.95e-176)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 2.45e+125)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	t_1 = x1 + (x2 * -6.0);
	tmp = 0.0;
	if (x2 <= -1.3e+170)
		tmp = t_0;
	elseif (x2 <= -1.7e-293)
		tmp = t_1;
	elseif (x2 <= 2.95e-176)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 2.45e+125)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.3e+170], t$95$0, If[LessEqual[x2, -1.7e-293], t$95$1, If[LessEqual[x2, 2.95e-176], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 2.45e+125], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.2999999999999999e170 or 2.45000000000000008e125 < x2

   1. Initial program 57.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 56.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 50.9%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 50.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x2 around inf 64.7%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]

      2. unpow2 64.7%

         \[\leadsto x1 + 8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \]

      3. associate-*r* 73.0%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} \]

      4. *-commutative 73.0%

         \[\leadsto x1 + 8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) \]

   8. Simplified 73.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right)} \]

   if -1.2999999999999999e170 < x2 < -1.7e-293 or 2.9499999999999998e-176 < x2 < 2.45000000000000008e125

   1. Initial program 69.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 51.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 42.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 42.0%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 42.0%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if -1.7e-293 < x2 < 2.9499999999999998e-176

   1. Initial program 68.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 42.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around 0 41.9%

      \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 42.3%

         \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

      2. metadata-eval 42.3%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 42.3%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   8. Simplified 42.3%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq -1.7 \cdot 10^{-293}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.95 \cdot 10^{-176}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 2.45 \cdot 10^{+125}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \end{array} \]

Alternative 26: 45.7% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ t_1 := x1 + x2 \cdot \left(-6 - x1 \cdot 12\right)\\ \mathbf{if}\;x2 \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -1.7 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x2 \leq 3.1 \cdot 10^{-176}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 2.35 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x2 (* x1 x2)))))
        (t_1 (+ x1 (* x2 (- -6.0 (* x1 12.0))))))
   (if (<= x2 -1.3e+170)
     t_0
     (if (<= x2 -1.7e-293)
       t_1
       (if (<= x2 3.1e-176)
         (+ x1 (* x1 -2.0))
         (if (<= x2 2.35e+126) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x2 * (-6.0 - (x1 * 12.0)));
	double tmp;
	if (x2 <= -1.3e+170) {
		tmp = t_0;
	} else if (x2 <= -1.7e-293) {
		tmp = t_1;
	} else if (x2 <= 3.1e-176) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 2.35e+126) {
		tmp = t_1;
	} else {
		tmp = t_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) :: tmp
    t_0 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    t_1 = x1 + (x2 * ((-6.0d0) - (x1 * 12.0d0)))
    if (x2 <= (-1.3d+170)) then
        tmp = t_0
    else if (x2 <= (-1.7d-293)) then
        tmp = t_1
    else if (x2 <= 3.1d-176) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 2.35d+126) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double t_1 = x1 + (x2 * (-6.0 - (x1 * 12.0)));
	double tmp;
	if (x2 <= -1.3e+170) {
		tmp = t_0;
	} else if (x2 <= -1.7e-293) {
		tmp = t_1;
	} else if (x2 <= 3.1e-176) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 2.35e+126) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)))
	t_1 = x1 + (x2 * (-6.0 - (x1 * 12.0)))
	tmp = 0
	if x2 <= -1.3e+170:
		tmp = t_0
	elif x2 <= -1.7e-293:
		tmp = t_1
	elif x2 <= 3.1e-176:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 2.35e+126:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	t_1 = Float64(x1 + Float64(x2 * Float64(-6.0 - Float64(x1 * 12.0))))
	tmp = 0.0
	if (x2 <= -1.3e+170)
		tmp = t_0;
	elseif (x2 <= -1.7e-293)
		tmp = t_1;
	elseif (x2 <= 3.1e-176)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 2.35e+126)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	t_1 = x1 + (x2 * (-6.0 - (x1 * 12.0)));
	tmp = 0.0;
	if (x2 <= -1.3e+170)
		tmp = t_0;
	elseif (x2 <= -1.7e-293)
		tmp = t_1;
	elseif (x2 <= 3.1e-176)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 2.35e+126)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * N[(-6.0 - N[(x1 * 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.3e+170], t$95$0, If[LessEqual[x2, -1.7e-293], t$95$1, If[LessEqual[x2, 3.1e-176], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 2.35e+126], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.2999999999999999e170 or 2.3499999999999999e126 < x2

   1. Initial program 57.7%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 56.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 50.9%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 50.9%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 50.9%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 50.9%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 50.9%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x2 around inf 64.7%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   7. Step-by-step derivation

      1. *-commutative 64.7%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \]

      2. unpow2 64.7%

         \[\leadsto x1 + 8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) \]

      3. associate-*r* 73.0%

         \[\leadsto x1 + 8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} \]

      4. *-commutative 73.0%

         \[\leadsto x1 + 8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) \]

   8. Simplified 73.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right)} \]

   if -1.2999999999999999e170 < x2 < -1.7e-293 or 3.09999999999999992e-176 < x2 < 2.3499999999999999e126

   1. Initial program 69.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 51.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 55.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 55.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 55.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 55.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around -inf 44.6%

      \[\leadsto x1 + \color{blue}{\left(-1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right) + 8 \cdot \left({x2}^{2} \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 44.6%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) + -1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right)\right)} \]

      2. mul-1-neg 44.6%

         \[\leadsto x1 + \left(8 \cdot \left({x2}^{2} \cdot x1\right) + \color{blue}{\left(-x2 \cdot \left(6 + 12 \cdot x1\right)\right)}\right) \]

      3. unsub-neg 44.6%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]

      4. *-commutative 44.6%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      5. unpow2 44.6%

         \[\leadsto x1 + \left(8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      6. associate-*r* 47.0%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      7. *-commutative 47.0%

         \[\leadsto x1 + \left(8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      8. *-commutative 47.0%

         \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + \color{blue}{x1 \cdot 12}\right)\right) \]

   8. Simplified 47.0%

      \[\leadsto x1 + \color{blue}{\left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + x1 \cdot 12\right)\right)} \]

   9. Taylor expanded in x2 around 0 44.4%

      \[\leadsto x1 + \color{blue}{-1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 44.4%

          \[\leadsto x1 + \color{blue}{\left(-x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]

       2. *-commutative 44.4%

          \[\leadsto x1 + \left(-x2 \cdot \left(6 + \color{blue}{x1 \cdot 12}\right)\right) \]

       3. distribute-rgt-neg-in 44.4%

          \[\leadsto x1 + \color{blue}{x2 \cdot \left(-\left(6 + x1 \cdot 12\right)\right)} \]

       4. distribute-neg-in 44.4%

          \[\leadsto x1 + x2 \cdot \color{blue}{\left(\left(-6\right) + \left(-x1 \cdot 12\right)\right)} \]

       5. metadata-eval 44.4%

          \[\leadsto x1 + x2 \cdot \left(\color{blue}{-6} + \left(-x1 \cdot 12\right)\right) \]

   11. Simplified 44.4%

       \[\leadsto x1 + \color{blue}{x2 \cdot \left(-6 + \left(-x1 \cdot 12\right)\right)} \]

   if -1.7e-293 < x2 < 3.09999999999999992e-176

   1. Initial program 68.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 42.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around 0 41.9%

      \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 42.3%

         \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

      2. metadata-eval 42.3%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 42.3%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   8. Simplified 42.3%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]
3. Recombined 3 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.3 \cdot 10^{+170}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq -1.7 \cdot 10^{-293}:\\ \;\;\;\;x1 + x2 \cdot \left(-6 - x1 \cdot 12\right)\\ \mathbf{elif}\;x2 \leq 3.1 \cdot 10^{-176}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 2.35 \cdot 10^{+126}:\\ \;\;\;\;x1 + x2 \cdot \left(-6 - x1 \cdot 12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \end{array} \]

Alternative 27: 62.5% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+60} \lor \neg \left(x1 \leq 5.4 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9e+60) (not (<= x1 5.4e+75)))
   (+ x1 (* x1 (* x1 (* 3.0 (+ 3.0 (* 2.0 x2))))))
   (+ x1 (- (* 8.0 (* x2 (* x1 x2))) (* 6.0 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9e+60) || !(x1 <= 5.4e+75)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-9d+60)) .or. (.not. (x1 <= 5.4d+75))) then
        tmp = x1 + (x1 * (x1 * (3.0d0 * (3.0d0 + (2.0d0 * x2)))))
    else
        tmp = x1 + ((8.0d0 * (x2 * (x1 * x2))) - (6.0d0 * x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9e+60) || !(x1 <= 5.4e+75)) {
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	} else {
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9e+60) or not (x1 <= 5.4e+75):
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))))
	else:
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9e+60) || !(x1 <= 5.4e+75))
		tmp = Float64(x1 + Float64(x1 * Float64(x1 * Float64(3.0 * Float64(3.0 + Float64(2.0 * x2))))));
	else
		tmp = Float64(x1 + Float64(Float64(8.0 * Float64(x2 * Float64(x1 * x2))) - Float64(6.0 * x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9e+60) || ~((x1 <= 5.4e+75)))
		tmp = x1 + (x1 * (x1 * (3.0 * (3.0 + (2.0 * x2)))));
	else
		tmp = x1 + ((8.0 * (x2 * (x1 * x2))) - (6.0 * x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9e+60], N[Not[LessEqual[x1, 5.4e+75]], $MachinePrecision]], N[(x1 + N[(x1 * N[(x1 * N[(3.0 * N[(3.0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(6.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.00000000000000026e60 or 5.39999999999999996e75 < x1

   1. Initial program 18.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 3.2%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 55.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(-6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right)} \]
   4. Step-by-step derivation

      1. fma-def 59.4%

         \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)} \]

      2. associate-*r* 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\left(4 \cdot x2\right) \cdot \left(2 \cdot x2 - 3\right)} - 2, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      3. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \color{blue}{\mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, -2\right)}, -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      4. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(4 \cdot x2, 2 \cdot x2 - 3, \color{blue}{-2}\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      5. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(\color{blue}{x2 \cdot 4}, 2 \cdot x2 - 3, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      6. fma-neg 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \color{blue}{\mathsf{fma}\left(2, x2, -3\right)}, -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      7. metadata-eval 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, \color{blue}{-3}\right), -2\right), -6 \cdot x2 + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      8. *-commutative 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{x2 \cdot -6} + 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      9. fma-def 59.4%

         \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \color{blue}{\mathsf{fma}\left(x2, -6, 3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)\right)}\right) \]

      10. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)}\right)\right) \]

      11. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      12. unpow2 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      13. associate-*r* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right) \]

      14. associate-*l* 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right)\right)}\right)\right) \]

      15. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\color{blue}{\left(3 \cdot x1\right)} \cdot \left(3 - -2 \cdot x2\right)\right)\right)\right) \]

      16. *-commutative 59.4%

          \[\leadsto x1 + \mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right)\right)\right)\right) \]

   5. Simplified 59.4%

      \[\leadsto x1 + \color{blue}{\mathsf{fma}\left(x1, \mathsf{fma}\left(x2 \cdot 4, \mathsf{fma}\left(2, x2, -3\right), -2\right), \mathsf{fma}\left(x2, -6, x1 \cdot \left(\left(3 \cdot x1\right) \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)} \]

   6. Taylor expanded in x1 around inf 67.0%

      \[\leadsto x1 + \color{blue}{3 \cdot \left({x1}^{2} \cdot \left(3 - -2 \cdot x2\right)\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(3 \cdot {x1}^{2}\right) \cdot \left(3 - -2 \cdot x2\right)} \]

      2. *-commutative 67.0%

         \[\leadsto x1 + \color{blue}{\left({x1}^{2} \cdot 3\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      3. unpow2 67.0%

         \[\leadsto x1 + \left(\color{blue}{\left(x1 \cdot x1\right)} \cdot 3\right) \cdot \left(3 - -2 \cdot x2\right) \]

      4. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(x1 \cdot 3\right)\right)} \cdot \left(3 - -2 \cdot x2\right) \]

      5. *-commutative 67.0%

         \[\leadsto x1 + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 - \color{blue}{x2 \cdot -2}\right) \]

      6. associate-*r* 67.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x1 \cdot 3\right) \cdot \left(3 - x2 \cdot -2\right)\right)} \]

      7. associate-*l* 67.0%

         \[\leadsto x1 + x1 \cdot \color{blue}{\left(x1 \cdot \left(3 \cdot \left(3 - x2 \cdot -2\right)\right)\right)} \]

      8. *-commutative 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 - \color{blue}{-2 \cdot x2}\right)\right)\right) \]

      9. cancel-sign-sub-inv 67.0%

         \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \color{blue}{\left(3 + \left(--2\right) \cdot x2\right)}\right)\right) \]

      10. metadata-eval 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{2} \cdot x2\right)\right)\right) \]

      11. *-commutative 67.0%

          \[\leadsto x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + \color{blue}{x2 \cdot 2}\right)\right)\right) \]

   8. Simplified 67.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + x2 \cdot 2\right)\right)\right)} \]

   if -9.00000000000000026e60 < x1 < 5.39999999999999996e75

   1. Initial program 99.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 85.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 85.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 85.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 85.0%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 85.0%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around -inf 59.1%

      \[\leadsto x1 + \color{blue}{\left(-1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right) + 8 \cdot \left({x2}^{2} \cdot x1\right)\right)} \]
   7. Step-by-step derivation

      1. +-commutative 59.1%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) + -1 \cdot \left(x2 \cdot \left(6 + 12 \cdot x1\right)\right)\right)} \]

      2. mul-1-neg 59.1%

         \[\leadsto x1 + \left(8 \cdot \left({x2}^{2} \cdot x1\right) + \color{blue}{\left(-x2 \cdot \left(6 + 12 \cdot x1\right)\right)}\right) \]

      3. unsub-neg 59.1%

         \[\leadsto x1 + \color{blue}{\left(8 \cdot \left({x2}^{2} \cdot x1\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right)} \]

      4. *-commutative 59.1%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(x1 \cdot {x2}^{2}\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      5. unpow2 59.1%

         \[\leadsto x1 + \left(8 \cdot \left(x1 \cdot \color{blue}{\left(x2 \cdot x2\right)}\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      6. associate-*r* 68.6%

         \[\leadsto x1 + \left(8 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot x2\right)} - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      7. *-commutative 68.6%

         \[\leadsto x1 + \left(8 \cdot \left(\color{blue}{\left(x2 \cdot x1\right)} \cdot x2\right) - x2 \cdot \left(6 + 12 \cdot x1\right)\right) \]

      8. *-commutative 68.6%

         \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + \color{blue}{x1 \cdot 12}\right)\right) \]

   8. Simplified 68.6%

      \[\leadsto x1 + \color{blue}{\left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - x2 \cdot \left(6 + x1 \cdot 12\right)\right)} \]

   9. Taylor expanded in x1 around 0 69.9%

      \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{6 \cdot x2}\right) \]
   10. Step-by-step derivation

       1. *-commutative 69.9%

          \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]

   11. Simplified 69.9%

       \[\leadsto x1 + \left(8 \cdot \left(\left(x2 \cdot x1\right) \cdot x2\right) - \color{blue}{x2 \cdot 6}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9 \cdot 10^{+60} \lor \neg \left(x1 \leq 5.4 \cdot 10^{+75}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot \left(3 \cdot \left(3 + 2 \cdot x2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right) - 6 \cdot x2\right)\\ \end{array} \]

Alternative 28: 30.5% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.7 \cdot 10^{-293} \lor \neg \left(x2 \leq 1.12 \cdot 10^{-175}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.7e-293) (not (<= x2 1.12e-175)))
   (+ x1 (* x2 -6.0))
   (+ x1 (* x1 -2.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.7e-293) || !(x2 <= 1.12e-175)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.7d-293)) .or. (.not. (x2 <= 1.12d-175))) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = x1 + (x1 * (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.7e-293) || !(x2 <= 1.12e-175)) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = x1 + (x1 * -2.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.7e-293) or not (x2 <= 1.12e-175):
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = x1 + (x1 * -2.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.7e-293) || !(x2 <= 1.12e-175))
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = Float64(x1 + Float64(x1 * -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.7e-293) || ~((x2 <= 1.12e-175)))
		tmp = x1 + (x2 * -6.0);
	else
		tmp = x1 + (x1 * -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.7e-293], N[Not[LessEqual[x2, 1.12e-175]], $MachinePrecision]], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.7e-293 or 1.1200000000000001e-175 < x2

   1. Initial program 65.8%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 52.9%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 32.9%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. *-commutative 32.9%

         \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   5. Simplified 32.9%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

   if -1.7e-293 < x2 < 1.1200000000000001e-175

   1. Initial program 68.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 42.6%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. fma-def 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

      2. *-commutative 43.9%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

   5. Simplified 43.9%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

   6. Taylor expanded in x2 around 0 41.9%

      \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
   7. Step-by-step derivation

      1. distribute-rgt1-in 42.3%

         \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

      2. metadata-eval 42.3%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 42.3%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   8. Simplified 42.3%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.7 \cdot 10^{-293} \lor \neg \left(x2 \leq 1.12 \cdot 10^{-175}\right):\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \end{array} \]

Alternative 29: 14.3% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x1 \cdot -2 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x1 -2.0)))

C

double code(double x1, double x2) {
	return x1 + (x1 * -2.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x1 * (-2.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x1 * -2.0);
}

Python

def code(x1, x2):
	return x1 + (x1 * -2.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x1 * -2.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x1 * -2.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 51.6%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 60.5%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\left(-3 \cdot x1 + -6 \cdot x2\right)}\right) \]
4. Step-by-step derivation

   1. fma-def 60.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, -6 \cdot x2\right)}\right) \]

   2. *-commutative 60.5%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \mathsf{fma}\left(-3, x1, \color{blue}{x2 \cdot -6}\right)\right) \]

5. Simplified 60.5%

   \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + \color{blue}{\mathsf{fma}\left(-3, x1, x2 \cdot -6\right)}\right) \]

6. Taylor expanded in x2 around 0 11.1%

   \[\leadsto x1 + \color{blue}{\left(x1 + -3 \cdot x1\right)} \]
7. Step-by-step derivation

   1. distribute-rgt1-in 11.2%

      \[\leadsto x1 + \color{blue}{\left(-3 + 1\right) \cdot x1} \]

   2. metadata-eval 11.2%

      \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

   3. *-commutative 11.2%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

8. Simplified 11.2%

   \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

9. Final simplification 11.2%

   \[\leadsto x1 + x1 \cdot -2 \]

Alternative 30: 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 66.1%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 51.6%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 29.1%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. *-commutative 29.1%

      \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

5. Simplified 29.1%

   \[\leadsto x1 + \color{blue}{x2 \cdot -6} \]

6. Taylor expanded in x1 around inf 3.3%

   \[\leadsto \color{blue}{x1} \]

7. Final simplification 3.3%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023274 
(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))))))