Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.5%

Time: 42.7s

Alternatives: 24

Speedup: 2.9×

• 46.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.7% 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: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2 + (-x1)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * N[(t$95$0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 + N[(N[(x1 * N[(x1 * -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(N[(x1 * N[(-6.0 + N[(t$95$0 / N[(N[(x1 * x1 + 1.0), $MachinePrecision] / 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $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 99.3%

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

   3. Simplified 99.7%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.2% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_4 (* t_1 t_3))
        (t_5 (* (* (* x1 2.0) t_3) (- t_3 3.0)))
        (t_6 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+ (+ (* t_2 (+ t_5 (* (* x1 x1) (- (* t_3 4.0) 6.0)))) t_4) t_0))
          t_6))
        INFINITY)
     (+
      x1
      (+
       t_6
       (+
        x1
        (+
         t_0
         (+
          t_4
          (*
           t_2
           (+
            t_5
            (*
             (* x1 x1)
             (-
              (*
               4.0
               (*
                (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1)
                (/ 1.0 (fma x1 x1 1.0))))
              6.0)))))))))
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) (* 3.0 (- (* x2 -2.0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_4 = t_1 * t_3;
	double t_5 = ((x1 * 2.0) * t_3) * (t_3 - 3.0);
	double t_6 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if ((x1 + ((x1 + (((t_2 * (t_5 + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= ((double) INFINITY)) {
		tmp = x1 + (t_6 + (x1 + (t_0 + (t_4 + (t_2 * (t_5 + ((x1 * x1) * ((4.0 * ((fma((x1 * 3.0), x1, (2.0 * x2)) - x1) * (1.0 / fma(x1, x1, 1.0)))) - 6.0))))))));
	} else {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(t_1 * t_3)
	t_5 = Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + t_4) + t_0)) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(t_2 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) * Float64(1.0 / fma(x1, x1, 1.0)))) - 6.0)))))))));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$6 + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$2 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $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 99.3%

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

      1. fma-def 99.3%

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

      2. div-inv 99.3%

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

      3. fma-def 99.3%

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

   3. Applied egg-rr 99.3%

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

   if +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 inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.5%

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

Alternative 3: 99.2% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$3 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$0 + N[(N[(t$95$3 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $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 99.3%

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

   2. Taylor expanded in x1 around inf 98.6%

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

   3. Taylor expanded in x1 around 0 99.3%

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

      1. fma-def 99.3%

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

      2. div-inv 99.3%

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

      3. fma-def 99.3%

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

   5. Applied egg-rr 99.3%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.5%

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

Alternative 4: 99.3% accurate, 0.5× speedup

Math

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

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))
        (t_3
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* t_2 4.0) 6.0))))
              (* t_0 t_2))
             (* x1 (* x1 x1))))
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))))
   (if (<= t_3 INFINITY)
     t_3
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) (* 3.0 (- (* x2 -2.0) x1)))))))

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

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 t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	double tmp;
	if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	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
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + (3.0 * ((x2 * -2.0) - x1)))
	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)
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))))
	tmp = 0.0
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	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;
	t_3 = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + (3.0 * ((x2 * -2.0) - x1)));
	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]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $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 99.3%

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

   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 inf 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.5%

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

Alternative 5: 98.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := 3 \cdot t_0\\ \mathbf{if}\;x1 \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + t_2\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(t_1 + \left(t_5 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* 3.0 (- (* x2 -2.0) x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_3))
        (t_5 (* 3.0 t_0)))
   (if (<= x1 -2e+103)
     (+ x1 (+ (+ x1 (* 6.0 (pow x1 4.0))) t_2))
     (if (<= x1 3.1e+71)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+
           t_1
           (+
            (*
             t_3
             (+
              (* (* (* x1 2.0) t_4) (- t_4 3.0))
              (* (* x1 x1) (- (* t_4 4.0) 6.0))))
            t_5)))))
       (+ x1 (+ t_2 (+ x1 (+ t_1 (+ t_5 (* t_3 (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_0;
	double tmp;
	if (x1 <= -2e+103) {
		tmp = x1 + ((x1 + (6.0 * pow(x1, 4.0))) + t_2);
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_2 + (x1 + (t_1 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_2 + (x1 + (t_1 + (t_5 + (t_3 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 * (x1 * x1)
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_3
    t_5 = 3.0d0 * t_0
    if (x1 <= (-2d+103)) then
        tmp = x1 + ((x1 + (6.0d0 * (x1 ** 4.0d0))) + t_2)
    else if (x1 <= 3.1d+71) then
        tmp = x1 + (t_2 + (x1 + (t_1 + ((t_3 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + t_5))))
    else
        tmp = x1 + (t_2 + (x1 + (t_1 + (t_5 + (t_3 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 * (x1 * x1);
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_0;
	double tmp;
	if (x1 <= -2e+103) {
		tmp = x1 + ((x1 + (6.0 * Math.pow(x1, 4.0))) + t_2);
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_2 + (x1 + (t_1 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_2 + (x1 + (t_1 + (t_5 + (t_3 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 * (x1 * x1)
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3
	t_5 = 3.0 * t_0
	tmp = 0
	if x1 <= -2e+103:
		tmp = x1 + ((x1 + (6.0 * math.pow(x1, 4.0))) + t_2)
	elif x1 <= 3.1e+71:
		tmp = x1 + (t_2 + (x1 + (t_1 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))))
	else:
		tmp = x1 + (t_2 + (x1 + (t_1 + (t_5 + (t_3 * ((x1 * x1) * 6.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(3.0 * t_0)
	tmp = 0.0
	if (x1 <= -2e+103)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(6.0 * (x1 ^ 4.0))) + t_2));
	elseif (x1 <= 3.1e+71)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(t_1 + Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_5)))));
	else
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_3 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 * (x1 * x1);
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_3;
	t_5 = 3.0 * t_0;
	tmp = 0.0;
	if (x1 <= -2e+103)
		tmp = x1 + ((x1 + (6.0 * (x1 ^ 4.0))) + t_2);
	elseif (x1 <= 3.1e+71)
		tmp = x1 + (t_2 + (x1 + (t_1 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	else
		tmp = x1 + (t_2 + (x1 + (t_1 + (t_5 + (t_3 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$0), $MachinePrecision]}, If[LessEqual[x1, -2e+103], N[(x1 + N[(N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e+71], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$1 + N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$2 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$3 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2e103

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around inf 2.1%

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

   3. Taylor expanded in x1 around 0 2.1%

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

   4. Taylor expanded in x1 around inf 97.9%

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

      1. *-commutative 97.9%

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

   6. Simplified 97.9%

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

   if -2e103 < x1 < 3.10000000000000018e71

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 97.8%

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

   3. Taylor expanded in x1 around 0 98.6%

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

   if 3.10000000000000018e71 < x1

   1. Initial program 47.3%

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

   2. Taylor expanded in x1 around inf 47.3%

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

   3. Taylor expanded in x1 around 0 47.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(\left(x1 + 6 \cdot {x1}^{4}\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 95.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := 3 \cdot t_1\\ \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_3 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_2 + \left(t_5 + t_3 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5 (* 3.0 t_1)))
   (if (<= x1 -2.4e+129)
     (+ x1 (fma 9.0 (* x1 x1) (* x1 -2.0)))
     (if (<= x1 3.1e+71)
       (+
        x1
        (+
         t_0
         (+
          x1
          (+
           t_2
           (+
            (*
             t_3
             (+
              (* (* (* x1 2.0) t_4) (- t_4 3.0))
              (* (* x1 x1) (- (* t_4 4.0) 6.0))))
            t_5)))))
       (+ x1 (+ t_0 (+ x1 (+ t_2 (+ t_5 (* t_3 (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 * (x1 * x1);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = 3.0 * t_1;
	double tmp;
	if (x1 <= -2.4e+129) {
		tmp = x1 + fma(9.0, (x1 * x1), (x1 * -2.0));
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_0 + (x1 + (t_2 + ((t_3 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + t_5))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_2 + (t_5 + (t_3 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(3.0 * t_1)
	tmp = 0.0
	if (x1 <= -2.4e+129)
		tmp = Float64(x1 + fma(9.0, Float64(x1 * x1), Float64(x1 * -2.0)));
	elseif (x1 <= 3.1e+71)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(Float64(t_3 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + t_5)))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_3 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$1), $MachinePrecision]}, If[LessEqual[x1, -2.4e+129], N[(x1 + N[(9.0 * N[(x1 * x1), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e+71], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(N[(t$95$3 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$3 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.3999999999999999e129

   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 36.9%

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

      1. fma-def 44.2%

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

      2. *-commutative 44.2%

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

      3. associate-*l* 44.2%

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

      4. *-commutative 44.2%

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

      5. fma-neg 44.2%

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

      6. fma-neg 44.2%

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

      7. metadata-eval 44.2%

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

      8. metadata-eval 44.2%

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

      9. *-commutative 44.2%

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

      10. fma-def 44.2%

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

      11. *-commutative 44.2%

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

      12. *-commutative 44.2%

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

      13. associate-*l* 44.2%

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

      14. cancel-sign-sub-inv 44.2%

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

      15. metadata-eval 44.2%

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

      16. +-commutative 44.2%

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

      17. unpow2 44.2%

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

      18. associate-*r* 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in x2 around 0 91.4%

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

      1. fma-def 91.4%

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

      2. unpow2 91.4%

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

      3. *-commutative 91.4%

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

   8. Simplified 91.4%

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

   if -2.3999999999999999e129 < x1 < 3.10000000000000018e71

   1. Initial program 95.9%

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

   2. Taylor expanded in x1 around inf 95.1%

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

   3. Taylor expanded in x1 around 0 95.9%

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

   if 3.10000000000000018e71 < x1

   1. Initial program 47.3%

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

   2. Taylor expanded in x1 around inf 47.3%

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

   3. Taylor expanded in x1 around 0 47.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;x1 + \mathsf{fma}\left(9, x1 \cdot x1, x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 86.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot t_1\\ t_3 := x1 \cdot \left(x1 \cdot x1\right)\\ t_4 := x1 \cdot x1 + 1\\ t_5 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_4}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_3 + \left(t_4 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_5\right) \cdot \left(t_5 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_5 \cdot 4 - 6\right)\right) + t_2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + \left(t_3 + \left(t_2 + t_4 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 t_1))
        (t_3 (* x1 (* x1 x1)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (/ (- (+ t_1 (* 2.0 x2)) x1) t_4)))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_0 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 3.1e+71)
       (+
        x1
        (+
         t_0
         (+
          x1
          (+
           t_3
           (+
            (*
             t_4
             (+
              (* (* (* x1 2.0) t_5) (- t_5 3.0))
              (* (* x1 x1) (- (* t_5 4.0) 6.0))))
            t_2)))))
       (+ x1 (+ t_0 (+ x1 (+ t_3 (+ t_2 (* t_4 (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = x1 * (x1 * x1);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = ((t_1 + (2.0 * x2)) - x1) / t_4;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_0 + (x1 + (t_3 + ((t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_2))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_3 + (t_2 + (t_4 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * t_1
    t_3 = x1 * (x1 * x1)
    t_4 = (x1 * x1) + 1.0d0
    t_5 = ((t_1 + (2.0d0 * x2)) - x1) / t_4
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 3.1d+71) then
        tmp = x1 + (t_0 + (x1 + (t_3 + ((t_4 * ((((x1 * 2.0d0) * t_5) * (t_5 - 3.0d0)) + ((x1 * x1) * ((t_5 * 4.0d0) - 6.0d0)))) + t_2))))
    else
        tmp = x1 + (t_0 + (x1 + (t_3 + (t_2 + (t_4 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * t_1;
	double t_3 = x1 * (x1 * x1);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = ((t_1 + (2.0 * x2)) - x1) / t_4;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_0 + (x1 + (t_3 + ((t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_2))));
	} else {
		tmp = x1 + (t_0 + (x1 + (t_3 + (t_2 + (t_4 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * t_1
	t_3 = x1 * (x1 * x1)
	t_4 = (x1 * x1) + 1.0
	t_5 = ((t_1 + (2.0 * x2)) - x1) / t_4
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 3.1e+71:
		tmp = x1 + (t_0 + (x1 + (t_3 + ((t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_2))))
	else:
		tmp = x1 + (t_0 + (x1 + (t_3 + (t_2 + (t_4 * ((x1 * x1) * 6.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(3.0 * t_1)
	t_3 = Float64(x1 * Float64(x1 * x1))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_4)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 3.1e+71)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_3 + Float64(Float64(t_4 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_5) * Float64(t_5 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_5 * 4.0) - 6.0)))) + t_2)))));
	else
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(t_3 + Float64(t_2 + Float64(t_4 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = 3.0 * t_1;
	t_3 = x1 * (x1 * x1);
	t_4 = (x1 * x1) + 1.0;
	t_5 = ((t_1 + (2.0 * x2)) - x1) / t_4;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 3.1e+71)
		tmp = x1 + (t_0 + (x1 + (t_3 + ((t_4 * ((((x1 * 2.0) * t_5) * (t_5 - 3.0)) + ((x1 * x1) * ((t_5 * 4.0) - 6.0)))) + t_2))));
	else
		tmp = x1 + (t_0 + (x1 + (t_3 + (t_2 + (t_4 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e+71], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$3 + N[(N[(t$95$4 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$5), $MachinePrecision] * N[(t$95$5 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$5 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$0 + N[(x1 + N[(t$95$3 + N[(t$95$2 + N[(t$95$4 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < 3.10000000000000018e71

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 97.8%

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

   3. Taylor expanded in x1 around 0 98.6%

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

   if 3.10000000000000018e71 < x1

   1. Initial program 47.3%

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

   2. Taylor expanded in x1 around inf 47.3%

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

   3. Taylor expanded in x1 around 0 47.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 81.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0}\\ t_4 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_5 := 3 \cdot t_2\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_1 + \left(t_5 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_0} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.75:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_4 + \left(x1 + \left(t_1 + \left(t_5 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0)))
        (t_4 (* 3.0 (- (* x2 -2.0) x1)))
        (t_5 (* 3.0 t_2)))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_4 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 -9.5)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           t_1
           (+
            t_5
            (*
             t_0
             (+
              (* (* x1 x1) (- (* (/ (- (+ t_2 (* 2.0 x2)) x1) t_0) 4.0) 6.0))
              (* (* (* x1 2.0) 3.0) (/ -1.0 x1)))))))))
       (if (<= x1 3.75)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (+ x1 (+ t_4 (+ x1 (+ t_1 (+ t_5 (* t_0 (* (* x1 x1) 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = 3.0 * ((x2 * -2.0) - x1);
	double t_5 = 3.0 * t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -9.5) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	} else if (x1 <= 3.75) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_4 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)
    t_4 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_5 = 3.0d0 * t_2
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_4 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= (-9.5d0)) then
        tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (((x1 * x1) * (((((t_2 + (2.0d0 * x2)) - x1) / t_0) * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * 3.0d0) * ((-1.0d0) / x1))))))))
    else if (x1 <= 3.75d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 + (t_4 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	double t_4 = 3.0 * ((x2 * -2.0) - x1);
	double t_5 = 3.0 * t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_4 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -9.5) {
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	} else if (x1 <= 3.75) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_4 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)
	t_4 = 3.0 * ((x2 * -2.0) - x1)
	t_5 = 3.0 * t_2
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_4 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= -9.5:
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))))
	elif x1 <= 3.75:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 + (t_4 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * x1) * 6.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0))
	t_4 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_5 = Float64(3.0 * t_2)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= -9.5)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(-1.0 / x1)))))))));
	elseif (x1 <= 3.75)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_1 + Float64(t_5 + Float64(t_0 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0);
	t_4 = 3.0 * ((x2 * -2.0) - x1);
	t_5 = 3.0 * t_2;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_4 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= -9.5)
		tmp = x1 + (t_3 + (x1 + (t_1 + (t_5 + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	elseif (x1 <= 3.75)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 + (t_4 + (x1 + (t_1 + (t_5 + (t_0 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -9.5], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.75], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$1 + N[(t$95$5 + N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < -9.5

   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%

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

   3. Taylor expanded in x1 around inf 85.7%

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

   4. Taylor expanded in x1 around inf 85.7%

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

   if -9.5 < x1 < 3.75

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 99.3%

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

   if 3.75 < x1

   1. Initial program 61.9%

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

   2. Taylor expanded in x1 around inf 59.7%

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

   3. Taylor expanded in x1 around 0 61.9%

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

   4. Taylor expanded in x1 around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. unpow2 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -9.5:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 84.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_0}\\ t_5 := 3 \cdot t_3\\ t_6 := \left(x1 \cdot x1\right) \cdot 6\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + t_6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_5 + t_0 \cdot t_6\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (- (* x2 -2.0) x1)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_0))
        (t_5 (* 3.0 t_3))
        (t_6 (* (* x1 x1) 6.0)))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_1 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 3.1e+71)
       (+
        x1
        (+
         t_1
         (+
          x1
          (+ t_2 (+ t_5 (* t_0 (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) t_6)))))))
       (+ x1 (+ t_1 (+ x1 (+ t_2 (+ t_5 (* t_0 t_6))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * ((x2 * -2.0) - x1);
	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 = 3.0 * t_3;
	double t_6 = (x1 * x1) * 6.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + t_6))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * t_6)))));
	}
	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 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_0
    t_5 = 3.0d0 * t_3
    t_6 = (x1 * x1) * 6.0d0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_1 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 3.1d+71) then
        tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + t_6))))))
    else
        tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * t_6)))))
    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 = 3.0 * ((x2 * -2.0) - x1);
	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 = 3.0 * t_3;
	double t_6 = (x1 * x1) * 6.0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 3.1e+71) {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + t_6))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * t_6)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * ((x2 * -2.0) - x1)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0
	t_5 = 3.0 * t_3
	t_6 = (x1 * x1) * 6.0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 3.1e+71:
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + t_6))))))
	else:
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * t_6)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	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(3.0 * t_3)
	t_6 = Float64(Float64(x1 * x1) * 6.0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 3.1e+71)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + t_6)))))));
	else
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(t_5 + Float64(t_0 * t_6))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * ((x2 * -2.0) - x1);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_0;
	t_5 = 3.0 * t_3;
	t_6 = (x1 * x1) * 6.0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 3.1e+71)
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + t_6))))));
	else
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_5 + (t_0 * t_6)))));
	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[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $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[(3.0 * t$95$3), $MachinePrecision]}, Block[{t$95$6 = N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$1 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.1e+71], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(t$95$5 + N[(t$95$0 * t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < 3.10000000000000018e71

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 97.8%

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

   3. Taylor expanded in x1 around 0 98.6%

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

   4. Taylor expanded in x1 around inf 96.9%

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

   if 3.10000000000000018e71 < x1

   1. Initial program 47.3%

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

   2. Taylor expanded in x1 around inf 47.3%

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

   3. Taylor expanded in x1 around 0 47.3%

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

   4. Taylor expanded in x1 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.1 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 10: 80.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -60000 \lor \neg \left(x1 \leq 3.75\right):\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (- (* x2 -2.0) x1))))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_2 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (or (<= x1 -60000.0) (not (<= x1 3.75)))
       (+
        x1
        (+
         t_2
         (+
          x1
          (+ (* x1 (* x1 x1)) (+ (* 3.0 t_0) (* t_1 (* x1 (* x1 6.0))))))))
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if ((x1 <= -60000.0) || !(x1 <= 3.75)) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (x1 * (x1 * 6.0)))))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_2 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if ((x1 <= (-60000.0d0)) .or. (.not. (x1 <= 3.75d0))) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * (x1 * (x1 * 6.0d0)))))))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if ((x1 <= -60000.0) || !(x1 <= 3.75)) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (x1 * (x1 * 6.0)))))));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * ((x2 * -2.0) - x1)
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif (x1 <= -60000.0) or not (x1 <= 3.75):
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (x1 * (x1 * 6.0)))))))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif ((x1 <= -60000.0) || !(x1 <= 3.75))
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(x1 * Float64(x1 * 6.0))))))));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * ((x2 * -2.0) - x1);
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif ((x1 <= -60000.0) || ~((x1 <= 3.75)))
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (x1 * (x1 * 6.0)))))));
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x1, -60000.0], N[Not[LessEqual[x1, 3.75]], $MachinePrecision]], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $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[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < -6e4 or 3.75 < x1

   1. Initial program 69.7%

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

   2. Taylor expanded in x1 around inf 68.0%

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

   3. Taylor expanded in x1 around 0 69.7%

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

   4. Taylor expanded in x1 around inf 84.3%

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

      1. *-commutative 84.3%

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

      2. unpow2 84.3%

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

      3. associate-*l* 84.3%

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

   6. Simplified 84.3%

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

   if -6e4 < x1 < 3.75

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 99.3%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -60000 \lor \neg \left(x1 \leq 3.75\right):\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 11: 80.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ t_2 := x1 \cdot \left(x1 \cdot x1\right)\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := 3 \cdot t_3\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5000:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_4 + t_0 \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(t_1 + \left(x1 + \left(t_2 + \left(t_4 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* 3.0 (- (* x2 -2.0) x1)))
        (t_2 (* x1 (* x1 x1)))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (* 3.0 t_3)))
   (if (<= x1 -5.6e+102)
     (+ x1 (+ t_1 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 -5000.0)
       (+ x1 (+ t_1 (+ x1 (+ t_2 (+ t_4 (* t_0 (* x1 (* x1 6.0))))))))
       (if (<= x1 3.75)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (+ x1 (+ t_1 (+ x1 (+ t_2 (+ t_4 (* t_0 (* (* x1 x1) 6.0))))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * ((x2 * -2.0) - x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -5000.0) {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= 3.75) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    t_2 = x1 * (x1 * x1)
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = 3.0d0 * t_3
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (t_1 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= (-5000.0d0)) then
        tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * (x1 * (x1 * 6.0d0)))))))
    else if (x1 <= 3.75d0) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * x1) * 6.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = 3.0 * ((x2 * -2.0) - x1);
	double t_2 = x1 * (x1 * x1);
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = 3.0 * t_3;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -5000.0) {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * (x1 * (x1 * 6.0)))))));
	} else if (x1 <= 3.75) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = 3.0 * ((x2 * -2.0) - x1)
	t_2 = x1 * (x1 * x1)
	t_3 = x1 * (x1 * 3.0)
	t_4 = 3.0 * t_3
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= -5000.0:
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * (x1 * (x1 * 6.0)))))))
	elif x1 <= 3.75:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * x1) * 6.0))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	t_2 = Float64(x1 * Float64(x1 * x1))
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(3.0 * t_3)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= -5000.0)
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(t_0 * Float64(x1 * Float64(x1 * 6.0))))))));
	elseif (x1 <= 3.75)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(x1 + Float64(t_1 + Float64(x1 + Float64(t_2 + Float64(t_4 + Float64(t_0 * Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = 3.0 * ((x2 * -2.0) - x1);
	t_2 = x1 * (x1 * x1);
	t_3 = x1 * (x1 * 3.0);
	t_4 = 3.0 * t_3;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (t_1 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= -5000.0)
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * (x1 * (x1 * 6.0)))))));
	elseif (x1 <= 3.75)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = x1 + (t_1 + (x1 + (t_2 + (t_4 + (t_0 * ((x1 * x1) * 6.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $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[(3.0 * t$95$3), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(t$95$1 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5000.0], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(t$95$0 * N[(x1 * N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3.75], 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[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(t$95$1 + N[(x1 + N[(t$95$2 + N[(t$95$4 + N[(t$95$0 * N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.1%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 28.5%

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

   if -5.60000000000000037e102 < x1 < -5e3

   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%

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

   3. Taylor expanded in x1 around 0 99.3%

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

   4. Taylor expanded in x1 around inf 76.5%

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

      1. *-commutative 76.5%

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

      2. unpow2 76.5%

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

      3. associate-*l* 76.6%

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

   6. Simplified 76.6%

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

   if -5e3 < x1 < 3.75

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 99.3%

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

   if 3.75 < x1

   1. Initial program 61.9%

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

   2. Taylor expanded in x1 around inf 59.7%

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

   3. Taylor expanded in x1 around 0 61.9%

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

   4. Taylor expanded in x1 around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. unpow2 86.4%

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

   6. Simplified 86.4%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(x1 \cdot \left(x1 \cdot 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 12: 66.9% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -350000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -350000000.0)
   (+ x1 (+ (* 3.0 (- (* x2 -2.0) x1)) (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
   (if (<= x1 1.32e+154)
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
       (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
     (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -350000000.0) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-350000000.0d0)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 1.32d+154) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -350000000.0) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -350000000.0:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 1.32e+154:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -350000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 1.32e+154)
		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(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -350000000.0)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 1.32e+154)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -350000000.0], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+154], 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[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.5e8

   1. Initial program 24.4%

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

   2. Taylor expanded in x1 around 0 2.0%

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

   3. Taylor expanded in x1 around 0 4.8%

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

   4. Taylor expanded in x2 around 0 23.2%

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

   if -3.5e8 < x1 < 1.31999999999999998e154

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 84.4%

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

   if 1.31999999999999998e154 < 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 6.3%

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

      1. *-commutative 6.3%

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

   5. Simplified 6.3%

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

      1. flip-+ 60.0%

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

   7. Applied egg-rr 60.0%

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

      1. swap-sqr 60.0%

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

      2. metadata-eval 60.0%

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

   9. Simplified 60.0%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -350000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 62.3% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -1.85 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \end{array} \]

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 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))))
   (if (<= x1 -5.2e+71)
     t_1
     (if (<= x1 -1.85e-227)
       t_0
       (if (<= x1 3.8e-245)
         t_1
         (if (<= x1 2.2e+169)
           t_0
           (if (<= x1 5.5e+287)
             (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))
             (+ x1 (* 8.0 (* x1 (* x2 x2)))))))))))

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 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	double tmp;
	if (x1 <= -5.2e+71) {
		tmp = t_1;
	} else if (x1 <= -1.85e-227) {
		tmp = t_0;
	} else if (x1 <= 3.8e-245) {
		tmp = t_1;
	} else if (x1 <= 2.2e+169) {
		tmp = t_0;
	} else if (x1 <= 5.5e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (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) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    t_1 = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    if (x1 <= (-5.2d+71)) then
        tmp = t_1
    else if (x1 <= (-1.85d-227)) then
        tmp = t_0
    else if (x1 <= 3.8d-245) then
        tmp = t_1
    else if (x1 <= 2.2d+169) then
        tmp = t_0
    else if (x1 <= 5.5d+287) then
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    else
        tmp = x1 + (8.0d0 * (x1 * (x2 * x2)))
    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 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	double tmp;
	if (x1 <= -5.2e+71) {
		tmp = t_1;
	} else if (x1 <= -1.85e-227) {
		tmp = t_0;
	} else if (x1 <= 3.8e-245) {
		tmp = t_1;
	} else if (x1 <= 2.2e+169) {
		tmp = t_0;
	} else if (x1 <= 5.5e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	}
	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 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	tmp = 0
	if x1 <= -5.2e+71:
		tmp = t_1
	elif x1 <= -1.85e-227:
		tmp = t_0
	elif x1 <= 3.8e-245:
		tmp = t_1
	elif x1 <= 2.2e+169:
		tmp = t_0
	elif x1 <= 5.5e+287:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	else:
		tmp = x1 + (8.0 * (x1 * (x2 * x2)))
	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(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))))
	tmp = 0.0
	if (x1 <= -5.2e+71)
		tmp = t_1;
	elseif (x1 <= -1.85e-227)
		tmp = t_0;
	elseif (x1 <= 3.8e-245)
		tmp = t_1;
	elseif (x1 <= 2.2e+169)
		tmp = t_0;
	elseif (x1 <= 5.5e+287)
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))));
	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 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	tmp = 0.0;
	if (x1 <= -5.2e+71)
		tmp = t_1;
	elseif (x1 <= -1.85e-227)
		tmp = t_0;
	elseif (x1 <= 3.8e-245)
		tmp = t_1;
	elseif (x1 <= 2.2e+169)
		tmp = t_0;
	elseif (x1 <= 5.5e+287)
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	else
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	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[(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, -5.2e+71], t$95$1, If[LessEqual[x1, -1.85e-227], t$95$0, If[LessEqual[x1, 3.8e-245], t$95$1, If[LessEqual[x1, 2.2e+169], t$95$0, If[LessEqual[x1, 5.5e+287], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.19999999999999983e71 or -1.84999999999999989e-227 < x1 < 3.8000000000000001e-245

   1. Initial program 48.2%

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

   2. Taylor expanded in x1 around 0 41.6%

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

   3. Taylor expanded in x1 around 0 43.2%

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

   4. Taylor expanded in x2 around 0 49.4%

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

   if -5.19999999999999983e71 < x1 < -1.84999999999999989e-227 or 3.8000000000000001e-245 < x1 < 2.2e169

   1. Initial program 95.2%

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

   2. Taylor expanded in x1 around 0 73.6%

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

   3. Taylor expanded in x1 around 0 73.0%

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

   if 2.2e169 < x1 < 5.5e287

   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 6.3%

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

      1. *-commutative 6.3%

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

   5. Simplified 6.3%

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

      1. flip-+ 75.0%

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

   7. Applied egg-rr 75.0%

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

      1. swap-sqr 75.0%

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

      2. metadata-eval 75.0%

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

   9. Simplified 75.0%

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

   if 5.5e287 < 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 x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   5. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq -1.85 \cdot 10^{-227}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-245}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+169}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]

Alternative 14: 61.9% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{if}\;x1 \leq -6 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 8.8 \cdot 10^{-245}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 4.3 \cdot 10^{+183}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))))))
   (if (<= x1 -6e+70)
     (+ x1 (+ (* 3.0 (- (* x2 -2.0) x1)) (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 -1.15e-226)
       t_0
       (if (<= x1 8.8e-245)
         (+ x1 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))
         (if (<= x1 4.3e+183)
           t_0
           (if (<= x1 5.5e+287)
             (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))
             (+ x1 (* 8.0 (* x1 (* x2 x2)))))))))))

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 tmp;
	if (x1 <= -6e+70) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -1.15e-226) {
		tmp = t_0;
	} else if (x1 <= 8.8e-245) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 4.3e+183) {
		tmp = t_0;
	} else if (x1 <= 5.5e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (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) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)))
    if (x1 <= (-6d+70)) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= (-1.15d-226)) then
        tmp = t_0
    else if (x1 <= 8.8d-245) then
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    else if (x1 <= 4.3d+183) then
        tmp = t_0
    else if (x1 <= 5.5d+287) then
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    else
        tmp = x1 + (8.0d0 * (x1 * (x2 * x2)))
    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 tmp;
	if (x1 <= -6e+70) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= -1.15e-226) {
		tmp = t_0;
	} else if (x1 <= 8.8e-245) {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	} else if (x1 <= 4.3e+183) {
		tmp = t_0;
	} else if (x1 <= 5.5e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))
	tmp = 0
	if x1 <= -6e+70:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= -1.15e-226:
		tmp = t_0
	elif x1 <= 8.8e-245:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	elif x1 <= 4.3e+183:
		tmp = t_0
	elif x1 <= 5.5e+287:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	else:
		tmp = x1 + (8.0 * (x1 * (x2 * x2)))
	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))))
	tmp = 0.0
	if (x1 <= -6e+70)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= -1.15e-226)
		tmp = t_0;
	elseif (x1 <= 8.8e-245)
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))));
	elseif (x1 <= 4.3e+183)
		tmp = t_0;
	elseif (x1 <= 5.5e+287)
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))));
	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)));
	tmp = 0.0;
	if (x1 <= -6e+70)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= -1.15e-226)
		tmp = t_0;
	elseif (x1 <= 8.8e-245)
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	elseif (x1 <= 4.3e+183)
		tmp = t_0;
	elseif (x1 <= 5.5e+287)
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	else
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	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]}, If[LessEqual[x1, -6e+70], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1.15e-226], t$95$0, If[LessEqual[x1, 8.8e-245], 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, 4.3e+183], t$95$0, If[LessEqual[x1, 5.5e+287], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.99999999999999952e70

   1. Initial program 14.8%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x1 around 0 4.5%

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

   4. Taylor expanded in x2 around 0 25.5%

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

   if -5.99999999999999952e70 < x1 < -1.15e-226 or 8.79999999999999971e-245 < x1 < 4.3000000000000004e183

   1. Initial program 95.2%

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

   2. Taylor expanded in x1 around 0 73.6%

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

   3. Taylor expanded in x1 around 0 73.0%

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

   if -1.15e-226 < x1 < 8.79999999999999971e-245

   1. Initial program 96.9%

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

   2. Taylor expanded in x1 around 0 99.6%

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

   3. Taylor expanded in x1 around 0 99.6%

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

   4. Taylor expanded in x2 around 0 84.8%

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

   if 4.3000000000000004e183 < x1 < 5.5e287

   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 6.3%

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

      1. *-commutative 6.3%

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

   5. Simplified 6.3%

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

      1. flip-+ 75.0%

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

   7. Applied egg-rr 75.0%

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

      1. swap-sqr 75.0%

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

      2. metadata-eval 75.0%

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

   9. Simplified 75.0%

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

   if 5.5e287 < 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 x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   5. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6 \cdot 10^{+70}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.15 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 8.8 \cdot 10^{-245}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \mathbf{elif}\;x1 \leq 4.3 \cdot 10^{+183}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 5.5 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]

Alternative 15: 66.5% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(x2 \cdot -2 - x1\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+169}:\\ \;\;\;\;x1 + \left(t_0 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* 3.0 (- (* x2 -2.0) x1))))
   (if (<= x1 -5e+71)
     (+ x1 (+ t_0 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 2.2e+169)
       (+ x1 (+ t_0 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
       (if (<= x1 5.2e+287)
         (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))
         (+ x1 (* 8.0 (* x1 (* x2 x2)))))))))

C

double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if (x1 <= -5e+71) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.2e+169) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 5.2e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (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) :: tmp
    t_0 = 3.0d0 * ((x2 * (-2.0d0)) - x1)
    if (x1 <= (-5d+71)) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 2.2d+169) then
        tmp = x1 + (t_0 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 5.2d+287) then
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    else
        tmp = x1 + (8.0d0 * (x1 * (x2 * x2)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 3.0 * ((x2 * -2.0) - x1);
	double tmp;
	if (x1 <= -5e+71) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.2e+169) {
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 5.2e+287) {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	} else {
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 3.0 * ((x2 * -2.0) - x1)
	tmp = 0
	if x1 <= -5e+71:
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 2.2e+169:
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 5.2e+287:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	else:
		tmp = x1 + (8.0 * (x1 * (x2 * x2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))
	tmp = 0.0
	if (x1 <= -5e+71)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 2.2e+169)
		tmp = Float64(x1 + Float64(t_0 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 5.2e+287)
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 3.0 * ((x2 * -2.0) - x1);
	tmp = 0.0;
	if (x1 <= -5e+71)
		tmp = x1 + (t_0 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 2.2e+169)
		tmp = x1 + (t_0 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 5.2e+287)
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	else
		tmp = x1 + (8.0 * (x1 * (x2 * x2)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+71], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.2e+169], N[(x1 + N[(t$95$0 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5.2e+287], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.99999999999999972e71

   1. Initial program 14.8%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x1 around 0 4.5%

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

   4. Taylor expanded in x2 around 0 25.5%

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

   if -4.99999999999999972e71 < x1 < 2.2e169

   1. Initial program 95.6%

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

   2. Taylor expanded in x1 around 0 78.7%

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

   3. Taylor expanded in x1 around 0 80.3%

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

   if 2.2e169 < x1 < 5.2000000000000003e287

   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 6.3%

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

      1. *-commutative 6.3%

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

   5. Simplified 6.3%

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

      1. flip-+ 75.0%

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

   7. Applied egg-rr 75.0%

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

      1. swap-sqr 75.0%

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

      2. metadata-eval 75.0%

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

   9. Simplified 75.0%

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

   if 5.2000000000000003e287 < 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 x2 around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. unpow2 100.0%

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

   5. Simplified 100.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+71}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.2 \cdot 10^{+169}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+287}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]

Alternative 16: 60.7% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-63} \lor \neg \left(x2 \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot t_0\right) - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0)))
   (if (or (<= x2 -2.8e-63) (not (<= x2 3.2e-31)))
     (+ x1 (+ (+ x1 (* 4.0 (* x2 (* x1 t_0)))) (* 3.0 (* x2 -2.0))))
     (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 t_0)) 2.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double tmp;
	if ((x2 <= -2.8e-63) || !(x2 <= 3.2e-31)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * t_0)) - 2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    if ((x2 <= (-2.8d-63)) .or. (.not. (x2 <= 3.2d-31))) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * t_0)))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * t_0)) - 2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double tmp;
	if ((x2 <= -2.8e-63) || !(x2 <= 3.2e-31)) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * t_0)) - 2.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	tmp = 0
	if (x2 <= -2.8e-63) or not (x2 <= 3.2e-31):
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * t_0)) - 2.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	tmp = 0.0
	if ((x2 <= -2.8e-63) || !(x2 <= 3.2e-31))
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	tmp = 0.0;
	if ((x2 <= -2.8e-63) || ~((x2 <= 3.2e-31)))
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * t_0)))) + (3.0 * (x2 * -2.0)));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * t_0)) - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, If[Or[LessEqual[x2, -2.8e-63], N[Not[LessEqual[x2, 3.2e-31]], $MachinePrecision]], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.8000000000000002e-63 or 3.20000000000000018e-31 < x2

   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 54.9%

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

   3. Taylor expanded in x1 around 0 62.0%

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

      1. *-commutative 62.0%

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

   5. Simplified 62.0%

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

   if -2.8000000000000002e-63 < x2 < 3.20000000000000018e-31

   1. Initial program 80.8%

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

   2. Taylor expanded in x1 around 0 61.7%

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

   3. Taylor expanded in x1 around 0 62.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-63} \lor \neg \left(x2 \leq 3.2 \cdot 10^{-31}\right):\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \end{array} \]

Alternative 17: 43.2% accurate, 5.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -2.35 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 8.5 \cdot 10^{+202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq 9.5 \cdot 10^{+219}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3.2 \cdot 10^{+236}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x2 (* x1 x2))))))
   (if (<= x2 -1.9e+214)
     t_0
     (if (<= x2 -2.35e-152)
       (* x2 -6.0)
       (if (<= x2 2.5e-130)
         (+ x1 (* x1 -2.0))
         (if (<= x2 7.5e+93)
           (+ x1 (* x2 -6.0))
           (if (<= x2 8.5e+202)
             t_0
             (if (<= x2 9.5e+219)
               (* x2 -6.0)
               (if (<= x2 3.2e+236)
                 (+ 9.0 (* x1 (+ 2.0 (* x2 -12.0))))
                 t_0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	double tmp;
	if (x2 <= -1.9e+214) {
		tmp = t_0;
	} else if (x2 <= -2.35e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-130) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 7.5e+93) {
		tmp = x1 + (x2 * -6.0);
	} else if (x2 <= 8.5e+202) {
		tmp = t_0;
	} else if (x2 <= 9.5e+219) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3.2e+236) {
		tmp = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	} 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) :: tmp
    t_0 = x1 + (8.0d0 * (x2 * (x1 * x2)))
    if (x2 <= (-1.9d+214)) then
        tmp = t_0
    else if (x2 <= (-2.35d-152)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2.5d-130) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 7.5d+93) then
        tmp = x1 + (x2 * (-6.0d0))
    else if (x2 <= 8.5d+202) then
        tmp = t_0
    else if (x2 <= 9.5d+219) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 3.2d+236) then
        tmp = 9.0d0 + (x1 * (2.0d0 + (x2 * (-12.0d0))))
    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 tmp;
	if (x2 <= -1.9e+214) {
		tmp = t_0;
	} else if (x2 <= -2.35e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.5e-130) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 7.5e+93) {
		tmp = x1 + (x2 * -6.0);
	} else if (x2 <= 8.5e+202) {
		tmp = t_0;
	} else if (x2 <= 9.5e+219) {
		tmp = x2 * -6.0;
	} else if (x2 <= 3.2e+236) {
		tmp = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)))
	tmp = 0
	if x2 <= -1.9e+214:
		tmp = t_0
	elif x2 <= -2.35e-152:
		tmp = x2 * -6.0
	elif x2 <= 2.5e-130:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 7.5e+93:
		tmp = x1 + (x2 * -6.0)
	elif x2 <= 8.5e+202:
		tmp = t_0
	elif x2 <= 9.5e+219:
		tmp = x2 * -6.0
	elif x2 <= 3.2e+236:
		tmp = 9.0 + (x1 * (2.0 + (x2 * -12.0)))
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))))
	tmp = 0.0
	if (x2 <= -1.9e+214)
		tmp = t_0;
	elseif (x2 <= -2.35e-152)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2.5e-130)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 7.5e+93)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	elseif (x2 <= 8.5e+202)
		tmp = t_0;
	elseif (x2 <= 9.5e+219)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 3.2e+236)
		tmp = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x2 * -12.0))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x2 * (x1 * x2)));
	tmp = 0.0;
	if (x2 <= -1.9e+214)
		tmp = t_0;
	elseif (x2 <= -2.35e-152)
		tmp = x2 * -6.0;
	elseif (x2 <= 2.5e-130)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 7.5e+93)
		tmp = x1 + (x2 * -6.0);
	elseif (x2 <= 8.5e+202)
		tmp = t_0;
	elseif (x2 <= 9.5e+219)
		tmp = x2 * -6.0;
	elseif (x2 <= 3.2e+236)
		tmp = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	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]}, If[LessEqual[x2, -1.9e+214], t$95$0, If[LessEqual[x2, -2.35e-152], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2.5e-130], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 7.5e+93], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 8.5e+202], t$95$0, If[LessEqual[x2, 9.5e+219], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 3.2e+236], N[(9.0 + N[(x1 * N[(2.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x2 < -1.89999999999999999e214 or 7.5000000000000002e93 < x2 < 8.5000000000000003e202 or 3.2000000000000002e236 < x2

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 58.2%

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

   3. Taylor expanded in x2 around inf 56.0%

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

      1. unpow2 56.0%

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

      2. associate-*l* 63.7%

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

   5. Simplified 63.7%

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

   if -1.89999999999999999e214 < x2 < -2.35000000000000006e-152 or 8.5000000000000003e202 < x2 < 9.49999999999999959e219

   1. Initial program 68.9%

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

   2. Taylor expanded in x1 around 0 52.1%

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

   3. Taylor expanded in x1 around 0 38.7%

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

      1. *-commutative 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in x1 around 0 39.2%

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

      1. *-commutative 39.2%

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

   8. Simplified 39.2%

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

   if -2.35000000000000006e-152 < x2 < 2.4999999999999998e-130

   1. Initial program 79.7%

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

   2. Taylor expanded in x1 around 0 62.2%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x2 around 0 50.7%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 51.4%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   6. Simplified 51.4%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 2.4999999999999998e-130 < x2 < 7.5000000000000002e93

   1. Initial program 92.2%

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

   2. Taylor expanded in x1 around 0 67.7%

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

   3. Taylor expanded in x1 around 0 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   if 9.49999999999999959e219 < x2 < 3.2000000000000002e236

   1. Initial program 25.0%

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

   2. Taylor expanded in x1 around 0 25.0%

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

   3. Taylor expanded in x1 around inf 25.0%

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

   4. Taylor expanded in x2 around 0 75.1%

      \[\leadsto \color{blue}{9 + \left(-12 \cdot \left(x2 \cdot x1\right) + 2 \cdot x1\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 75.1%

         \[\leadsto 9 + \left(\color{blue}{\left(-12 \cdot x2\right) \cdot x1} + 2 \cdot x1\right) \]

      2. distribute-rgt-out 75.1%

         \[\leadsto 9 + \color{blue}{x1 \cdot \left(-12 \cdot x2 + 2\right)} \]

      3. *-commutative 75.1%

         \[\leadsto 9 + x1 \cdot \left(\color{blue}{x2 \cdot -12} + 2\right) \]

   6. Simplified 75.1%

      \[\leadsto \color{blue}{9 + x1 \cdot \left(x2 \cdot -12 + 2\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq -2.35 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.5 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 8.5 \cdot 10^{+202}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq 9.5 \cdot 10^{+219}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 3.2 \cdot 10^{+236}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \end{array} \]

Alternative 18: 49.7% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{+238} \lor \neg \left(x2 \leq 3 \cdot 10^{+253}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -5e+238) (not (<= x2 3e+253)))
   (+ x1 (* 8.0 (* x2 (* x1 x2))))
   (+ x1 (+ (* x2 (- (* x1 -12.0) 6.0)) (+ x1 (* x1 -3.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5e+238) || !(x2 <= 3e+253)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-5d+238)) .or. (.not. (x2 <= 3d+253))) then
        tmp = x1 + (8.0d0 * (x2 * (x1 * x2)))
    else
        tmp = x1 + ((x2 * ((x1 * (-12.0d0)) - 6.0d0)) + (x1 + (x1 * (-3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -5e+238) || !(x2 <= 3e+253)) {
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	} else {
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -5e+238) or not (x2 <= 3e+253):
		tmp = x1 + (8.0 * (x2 * (x1 * x2)))
	else:
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -5e+238) || !(x2 <= 3e+253))
		tmp = Float64(x1 + Float64(8.0 * Float64(x2 * Float64(x1 * x2))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0)) + Float64(x1 + Float64(x1 * -3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -5e+238) || ~((x2 <= 3e+253)))
		tmp = x1 + (8.0 * (x2 * (x1 * x2)));
	else
		tmp = x1 + ((x2 * ((x1 * -12.0) - 6.0)) + (x1 + (x1 * -3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -5e+238], N[Not[LessEqual[x2, 3e+253]], $MachinePrecision]], N[(x1 + N[(8.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]

Derivation

1. Split input into 2 regimes

2. if x2 < -4.99999999999999995e238 or 2.9999999999999998e253 < x2

   1. Initial program 78.5%

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

   2. Taylor expanded in x1 around 0 82.1%

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

   3. Taylor expanded in x2 around inf 76.6%

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

      1. unpow2 76.6%

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

      2. associate-*l* 89.2%

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

   5. Simplified 89.2%

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

   if -4.99999999999999995e238 < x2 < 2.9999999999999998e253

   1. Initial program 72.7%

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

   2. Taylor expanded in x1 around 0 55.3%

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

   3. Taylor expanded in x1 around 0 58.5%

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

   4. Taylor expanded in x2 around 0 53.2%

      \[\leadsto x1 + \color{blue}{\left(x2 \cdot \left(-12 \cdot x1 - 6\right) + \left(-3 \cdot x1 + x1\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -5 \cdot 10^{+238} \lor \neg \left(x2 \leq 3 \cdot 10^{+253}\right):\\ \;\;\;\;x1 + 8 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot \left(x1 \cdot -12 - 6\right) + \left(x1 + x1 \cdot -3\right)\right)\\ \end{array} \]

Alternative 19: 34.9% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 9 + x1 \cdot \left(2 + x2 \cdot -12\right)\\ \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -1.02 \cdot 10^{-150}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 10^{-129}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6 \cdot 10^{+224}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 9.0 (* x1 (+ 2.0 (* x2 -12.0))))))
   (if (<= x2 -2.3e+214)
     t_0
     (if (<= x2 -1.02e-150)
       (* x2 -6.0)
       (if (<= x2 1e-129)
         (+ x1 (* x1 -2.0))
         (if (<= x2 6e+224) (+ x1 (* x2 -6.0)) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	double tmp;
	if (x2 <= -2.3e+214) {
		tmp = t_0;
	} else if (x2 <= -1.02e-150) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1e-129) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6e+224) {
		tmp = x1 + (x2 * -6.0);
	} 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) :: tmp
    t_0 = 9.0d0 + (x1 * (2.0d0 + (x2 * (-12.0d0))))
    if (x2 <= (-2.3d+214)) then
        tmp = t_0
    else if (x2 <= (-1.02d-150)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1d-129) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 6d+224) then
        tmp = x1 + (x2 * (-6.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	double tmp;
	if (x2 <= -2.3e+214) {
		tmp = t_0;
	} else if (x2 <= -1.02e-150) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1e-129) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6e+224) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = 9.0 + (x1 * (2.0 + (x2 * -12.0)))
	tmp = 0
	if x2 <= -2.3e+214:
		tmp = t_0
	elif x2 <= -1.02e-150:
		tmp = x2 * -6.0
	elif x2 <= 1e-129:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 6e+224:
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(9.0 + Float64(x1 * Float64(2.0 + Float64(x2 * -12.0))))
	tmp = 0.0
	if (x2 <= -2.3e+214)
		tmp = t_0;
	elseif (x2 <= -1.02e-150)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1e-129)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 6e+224)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = 9.0 + (x1 * (2.0 + (x2 * -12.0)));
	tmp = 0.0;
	if (x2 <= -2.3e+214)
		tmp = t_0;
	elseif (x2 <= -1.02e-150)
		tmp = x2 * -6.0;
	elseif (x2 <= 1e-129)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 6e+224)
		tmp = x1 + (x2 * -6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(9.0 + N[(x1 * N[(2.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -2.3e+214], t$95$0, If[LessEqual[x2, -1.02e-150], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1e-129], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 6e+224], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -2.2999999999999999e214 or 6.0000000000000002e224 < x2

   1. Initial program 59.4%

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

   2. Taylor expanded in x1 around 0 61.8%

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

   3. Taylor expanded in x1 around inf 60.9%

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

   4. Taylor expanded in x2 around 0 32.0%

      \[\leadsto \color{blue}{9 + \left(-12 \cdot \left(x2 \cdot x1\right) + 2 \cdot x1\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 34.3%

         \[\leadsto 9 + \left(\color{blue}{\left(-12 \cdot x2\right) \cdot x1} + 2 \cdot x1\right) \]

      2. distribute-rgt-out 34.3%

         \[\leadsto 9 + \color{blue}{x1 \cdot \left(-12 \cdot x2 + 2\right)} \]

      3. *-commutative 34.3%

         \[\leadsto 9 + x1 \cdot \left(\color{blue}{x2 \cdot -12} + 2\right) \]

   6. Simplified 34.3%

      \[\leadsto \color{blue}{9 + x1 \cdot \left(x2 \cdot -12 + 2\right)} \]

   if -2.2999999999999999e214 < x2 < -1.0199999999999999e-150

   1. Initial program 66.4%

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

   2. Taylor expanded in x1 around 0 49.5%

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

   3. Taylor expanded in x1 around 0 36.3%

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

      1. *-commutative 36.3%

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

   5. Simplified 36.3%

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

   6. Taylor expanded in x1 around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   if -1.0199999999999999e-150 < x2 < 9.9999999999999993e-130

   1. Initial program 79.7%

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

   2. Taylor expanded in x1 around 0 62.2%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x2 around 0 50.7%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 51.4%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   6. Simplified 51.4%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 9.9999999999999993e-130 < x2 < 6.0000000000000002e224

   1. Initial program 83.0%

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

   2. Taylor expanded in x1 around 0 60.4%

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

   3. Taylor expanded in x1 around 0 41.6%

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

      1. *-commutative 41.6%

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

   5. Simplified 41.6%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.3 \cdot 10^{+214}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x2 \cdot -12\right)\\ \mathbf{elif}\;x2 \leq -1.02 \cdot 10^{-150}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 10^{-129}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6 \cdot 10^{+224}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;9 + x1 \cdot \left(2 + x2 \cdot -12\right)\\ \end{array} \]

Alternative 20: 42.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x2 \leq -8.5 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6.1 \cdot 10^{+91}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* 8.0 (* x1 (* x2 x2))))))
   (if (<= x2 -1.9e+214)
     t_0
     (if (<= x2 -8.5e-152)
       (* x2 -6.0)
       (if (<= x2 1.35e-130)
         (+ x1 (* x1 -2.0))
         (if (<= x2 6.1e+91) (+ x1 (* x2 -6.0)) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (8.0 * (x1 * (x2 * x2)));
	double tmp;
	if (x2 <= -1.9e+214) {
		tmp = t_0;
	} else if (x2 <= -8.5e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.35e-130) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6.1e+91) {
		tmp = x1 + (x2 * -6.0);
	} 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) :: tmp
    t_0 = x1 + (8.0d0 * (x1 * (x2 * x2)))
    if (x2 <= (-1.9d+214)) then
        tmp = t_0
    else if (x2 <= (-8.5d-152)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.35d-130) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x2 <= 6.1d+91) then
        tmp = x1 + (x2 * (-6.0d0))
    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 * (x1 * (x2 * x2)));
	double tmp;
	if (x2 <= -1.9e+214) {
		tmp = t_0;
	} else if (x2 <= -8.5e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.35e-130) {
		tmp = x1 + (x1 * -2.0);
	} else if (x2 <= 6.1e+91) {
		tmp = x1 + (x2 * -6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (8.0 * (x1 * (x2 * x2)))
	tmp = 0
	if x2 <= -1.9e+214:
		tmp = t_0
	elif x2 <= -8.5e-152:
		tmp = x2 * -6.0
	elif x2 <= 1.35e-130:
		tmp = x1 + (x1 * -2.0)
	elif x2 <= 6.1e+91:
		tmp = x1 + (x2 * -6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(8.0 * Float64(x1 * Float64(x2 * x2))))
	tmp = 0.0
	if (x2 <= -1.9e+214)
		tmp = t_0;
	elseif (x2 <= -8.5e-152)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.35e-130)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x2 <= 6.1e+91)
		tmp = Float64(x1 + Float64(x2 * -6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (8.0 * (x1 * (x2 * x2)));
	tmp = 0.0;
	if (x2 <= -1.9e+214)
		tmp = t_0;
	elseif (x2 <= -8.5e-152)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.35e-130)
		tmp = x1 + (x1 * -2.0);
	elseif (x2 <= 6.1e+91)
		tmp = x1 + (x2 * -6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(8.0 * N[(x1 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x2, -1.9e+214], t$95$0, If[LessEqual[x2, -8.5e-152], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.35e-130], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x2, 6.1e+91], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x2 < -1.89999999999999999e214 or 6.1e91 < x2

   1. Initial program 65.0%

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

   2. Taylor expanded in x1 around 0 58.4%

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

   3. Taylor expanded in x2 around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. unpow2 49.5%

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

   5. Simplified 49.5%

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

   if -1.89999999999999999e214 < x2 < -8.5000000000000007e-152

   1. Initial program 66.4%

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

   2. Taylor expanded in x1 around 0 49.5%

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

   3. Taylor expanded in x1 around 0 36.3%

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

      1. *-commutative 36.3%

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

   5. Simplified 36.3%

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

   6. Taylor expanded in x1 around 0 36.9%

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

      1. *-commutative 36.9%

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

   8. Simplified 36.9%

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

   if -8.5000000000000007e-152 < x2 < 1.34999999999999996e-130

   1. Initial program 79.7%

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

   2. Taylor expanded in x1 around 0 62.2%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x2 around 0 50.7%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 51.4%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   6. Simplified 51.4%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 1.34999999999999996e-130 < x2 < 6.1e91

   1. Initial program 92.2%

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

   2. Taylor expanded in x1 around 0 67.7%

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

   3. Taylor expanded in x1 around 0 59.4%

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

      1. *-commutative 59.4%

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

   5. Simplified 59.4%

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

4. Final simplification 47.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.9 \cdot 10^{+214}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \mathbf{elif}\;x2 \leq -8.5 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.35 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x2 \leq 6.1 \cdot 10^{+91}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + 8 \cdot \left(x1 \cdot \left(x2 \cdot x2\right)\right)\\ \end{array} \]

Alternative 21: 32.6% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -6.4 \cdot 10^{-150}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.4 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -6.4e-150)
   (* x2 -6.0)
   (if (<= x2 2.4e-130) (+ x1 (* x1 -2.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6.4e-150) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.4e-130) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-6.4d-150)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 2.4d-130) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -6.4e-150) {
		tmp = x2 * -6.0;
	} else if (x2 <= 2.4e-130) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -6.4e-150:
		tmp = x2 * -6.0
	elif x2 <= 2.4e-130:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -6.4e-150)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 2.4e-130)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -6.4e-150)
		tmp = x2 * -6.0;
	elseif (x2 <= 2.4e-130)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -6.4e-150], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 2.4e-130], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -6.3999999999999996e-150 or 2.39999999999999997e-130 < x2

   1. Initial program 70.0%

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

   2. Taylor expanded in x1 around 0 56.1%

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

   3. Taylor expanded in x1 around 0 31.8%

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

      1. *-commutative 31.8%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in x1 around 0 31.9%

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

      1. *-commutative 31.9%

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

   8. Simplified 31.9%

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

   if -6.3999999999999996e-150 < x2 < 2.39999999999999997e-130

   1. Initial program 79.7%

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

   2. Taylor expanded in x1 around 0 62.2%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x2 around 0 50.7%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 51.4%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   6. Simplified 51.4%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -6.4 \cdot 10^{-150}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 2.4 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 22: 32.9% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -3.9 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.2 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -3.9e-152)
   (* x2 -6.0)
   (if (<= x2 5.2e-130) (+ x1 (* x1 -2.0)) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -3.9e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.2e-130) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-3.9d-152)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 5.2d-130) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -3.9e-152) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.2e-130) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -3.9e-152:
		tmp = x2 * -6.0
	elif x2 <= 5.2e-130:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -3.9e-152)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 5.2e-130)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -3.9e-152)
		tmp = x2 * -6.0;
	elseif (x2 <= 5.2e-130)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -3.9e-152], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 5.2e-130], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -3.9000000000000004e-152

   1. Initial program 64.2%

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

   2. Taylor expanded in x1 around 0 51.8%

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

   3. Taylor expanded in x1 around 0 31.8%

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

      1. *-commutative 31.8%

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

   5. Simplified 31.8%

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

   6. Taylor expanded in x1 around 0 32.4%

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

      1. *-commutative 32.4%

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

   8. Simplified 32.4%

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

   if -3.9000000000000004e-152 < x2 < 5.2000000000000001e-130

   1. Initial program 79.7%

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

   2. Taylor expanded in x1 around 0 62.2%

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

   3. Taylor expanded in x1 around 0 62.9%

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

   4. Taylor expanded in x2 around 0 50.7%

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

      1. distribute-rgt1-in 51.4%

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

      2. metadata-eval 51.4%

         \[\leadsto x1 + \color{blue}{-2} \cdot x1 \]

      3. *-commutative 51.4%

         \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   6. Simplified 51.4%

      \[\leadsto x1 + \color{blue}{x1 \cdot -2} \]

   if 5.2000000000000001e-130 < x2

   1. Initial program 76.6%

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

   2. Taylor expanded in x1 around 0 61.0%

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

   3. Taylor expanded in x1 around 0 31.8%

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

      1. *-commutative 31.8%

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

   5. Simplified 31.8%

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

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -3.9 \cdot 10^{-152}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.2 \cdot 10^{-130}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 23: 26.6% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.3%

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

2. Taylor expanded in x1 around 0 58.2%

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

3. Taylor expanded in x1 around 0 24.7%

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

   1. *-commutative 24.7%

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

5. Simplified 24.7%

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

6. Taylor expanded in x1 around 0 25.0%

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

   1. *-commutative 25.0%

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

8. Simplified 25.0%

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

9. Final simplification 25.0%

   \[\leadsto x2 \cdot -6 \]

Alternative 24: 3.5% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ 9 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 9.0)

C

double code(double x1, double x2) {
	return 9.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = 9.0d0
end function

Java

public static double code(double x1, double x2) {
	return 9.0;
}

Python

def code(x1, x2):
	return 9.0

Julia

function code(x1, x2)
	return 9.0
end

MATLAB

function tmp = code(x1, x2)
	tmp = 9.0;
end

Wolfram

code[x1_, x2_] := 9.0

Derivation

1. Initial program 73.3%

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

2. Taylor expanded in x1 around 0 58.2%

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

3. Taylor expanded in x1 around inf 18.8%

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

4. Taylor expanded in x1 around 0 3.6%

   \[\leadsto \color{blue}{9} \]

5. Final simplification 3.6%

   \[\leadsto 9 \]

Reproduce

herbie shell --seed 2023238 
(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))))))