Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.7% → 99.4%

Time: 1.0min

Alternatives: 16

Speedup: 1.3×

• 46.5% 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: 99.4% accurate, 0.1× speedup

Math

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

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

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 = (fma((x1 * 3.0), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_2 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_1 * t_3)) + t_0)) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2)))) <= ((double) INFINITY)) {
		tmp = x1 + ((t_0 + fma(fma(((x1 * 2.0) * t_4), (t_4 + -3.0), ((x1 * x1) * fma(4.0, t_4, -6.0))), fma(x1, x1, 1.0), (t_1 * t_4))) + (x1 + (3.0 * ((t_1 - (x1 + (2.0 * x2))) / fma(x1, x1, 1.0)))));
	} else {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	}
	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(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_1 * t_3)) + t_0)) + Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2)))) <= Inf)
		tmp = Float64(x1 + Float64(Float64(t_0 + fma(fma(Float64(Float64(x1 * 2.0) * t_4), Float64(t_4 + -3.0), Float64(Float64(x1 * x1) * fma(4.0, t_4, -6.0))), fma(x1, x1, 1.0), Float64(t_1 * t_4))) + Float64(x1 + Float64(3.0 * Float64(Float64(t_1 - Float64(x1 + Float64(2.0 * x2))) / fma(x1, x1, 1.0))))));
	else
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	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[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $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] + t$95$0), $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[(N[(t$95$0 + N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 + -3.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$4 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$1 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

   3. Simplified 99.3%

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

   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 19.5%

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

      1. *-commutative 19.5%

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

   4. Simplified 19.5%

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

   5. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

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

Alternative 2: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	t_3 = x1 + ((x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)))
	tmp = 0
	if t_3 <= math.inf:
		tmp = t_3
	else:
		tmp = x1 + (6.0 * math.pow(x1, 4.0))
	return tmp

Julia

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

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	t_3 = x1 + ((x1 + (((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_1 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)));
	tmp = 0.0;
	if (t_3 <= Inf)
		tmp = t_3;
	else
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

   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 19.5%

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

      1. *-commutative 19.5%

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

   4. Simplified 19.5%

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

   5. Taylor expanded in x1 around inf 97.6%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

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

Alternative 3: 96.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + 6 \cdot {x1}^{4}\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_4 := t_0 \cdot t_3\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\\ t_6 := t_3 \cdot \left(x1 \cdot 2\right)\\ t_7 := x1 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 0.31:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_7 + \left(t_4 + t_2 \cdot \left(t_5 + t_6 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_2 \cdot \left(t_6 \cdot \left(t_3 - 3\right) + t_5\right) + t_4\right) + t_7\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (* 6.0 (pow x1 4.0))))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_4 (* t_0 t_3))
        (t_5 (* (* x1 x1) (- (* t_3 4.0) 6.0)))
        (t_6 (* t_3 (* x1 2.0)))
        (t_7 (* x1 (* x1 x1))))
   (if (<= x1 -1.7e+47)
     t_1
     (if (<= x1 0.31)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2))
         (+ x1 (+ t_7 (+ t_4 (* t_2 (+ t_5 (* t_6 (- (* 2.0 x2) 3.0)))))))))
       (if (<= x1 6e+96)
         (+
          x1
          (+
           (+ x1 (+ (+ (* t_2 (+ (* t_6 (- t_3 3.0)) t_5)) t_4) t_7))
           (* 3.0 (/ 1.0 (/ -0.5 x2)))))
         t_1)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (6.0 * pow(x1, 4.0));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = t_0 * t_3;
	double t_5 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_6 = t_3 * (x1 * 2.0);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.7e+47) {
		tmp = t_1;
	} else if (x1 <= 0.31) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_7 + (t_4 + (t_2 * (t_5 + (t_6 * ((2.0 * x2) - 3.0))))))));
	} else if (x1 <= 6e+96) {
		tmp = x1 + ((x1 + (((t_2 * ((t_6 * (t_3 - 3.0)) + t_5)) + t_4) + t_7)) + (3.0 * (1.0 / (-0.5 / x2))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 + (6.0d0 * (x1 ** 4.0d0))
    t_2 = (x1 * x1) + 1.0d0
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_4 = t_0 * t_3
    t_5 = (x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)
    t_6 = t_3 * (x1 * 2.0d0)
    t_7 = x1 * (x1 * x1)
    if (x1 <= (-1.7d+47)) then
        tmp = t_1
    else if (x1 <= 0.31d0) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (t_7 + (t_4 + (t_2 * (t_5 + (t_6 * ((2.0d0 * x2) - 3.0d0))))))))
    else if (x1 <= 6d+96) then
        tmp = x1 + ((x1 + (((t_2 * ((t_6 * (t_3 - 3.0d0)) + t_5)) + t_4) + t_7)) + (3.0d0 * (1.0d0 / ((-0.5d0) / x2))))
    else
        tmp = t_1
    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 + (6.0 * Math.pow(x1, 4.0));
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_4 = t_0 * t_3;
	double t_5 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	double t_6 = t_3 * (x1 * 2.0);
	double t_7 = x1 * (x1 * x1);
	double tmp;
	if (x1 <= -1.7e+47) {
		tmp = t_1;
	} else if (x1 <= 0.31) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_7 + (t_4 + (t_2 * (t_5 + (t_6 * ((2.0 * x2) - 3.0))))))));
	} else if (x1 <= 6e+96) {
		tmp = x1 + ((x1 + (((t_2 * ((t_6 * (t_3 - 3.0)) + t_5)) + t_4) + t_7)) + (3.0 * (1.0 / (-0.5 / x2))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 + (6.0 * math.pow(x1, 4.0))
	t_2 = (x1 * x1) + 1.0
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_4 = t_0 * t_3
	t_5 = (x1 * x1) * ((t_3 * 4.0) - 6.0)
	t_6 = t_3 * (x1 * 2.0)
	t_7 = x1 * (x1 * x1)
	tmp = 0
	if x1 <= -1.7e+47:
		tmp = t_1
	elif x1 <= 0.31:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_7 + (t_4 + (t_2 * (t_5 + (t_6 * ((2.0 * x2) - 3.0))))))))
	elif x1 <= 6e+96:
		tmp = x1 + ((x1 + (((t_2 * ((t_6 * (t_3 - 3.0)) + t_5)) + t_4) + t_7)) + (3.0 * (1.0 / (-0.5 / x2))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_4 = Float64(t_0 * t_3)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))
	t_6 = Float64(t_3 * Float64(x1 * 2.0))
	t_7 = Float64(x1 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -1.7e+47)
		tmp = t_1;
	elseif (x1 <= 0.31)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_7 + Float64(t_4 + Float64(t_2 * Float64(t_5 + Float64(t_6 * Float64(Float64(2.0 * x2) - 3.0)))))))));
	elseif (x1 <= 6e+96)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_2 * Float64(Float64(t_6 * Float64(t_3 - 3.0)) + t_5)) + t_4) + t_7)) + Float64(3.0 * Float64(1.0 / Float64(-0.5 / x2)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 + (6.0 * (x1 ^ 4.0));
	t_2 = (x1 * x1) + 1.0;
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_4 = t_0 * t_3;
	t_5 = (x1 * x1) * ((t_3 * 4.0) - 6.0);
	t_6 = t_3 * (x1 * 2.0);
	t_7 = x1 * (x1 * x1);
	tmp = 0.0;
	if (x1 <= -1.7e+47)
		tmp = t_1;
	elseif (x1 <= 0.31)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_7 + (t_4 + (t_2 * (t_5 + (t_6 * ((2.0 * x2) - 3.0))))))));
	elseif (x1 <= 6e+96)
		tmp = x1 + ((x1 + (((t_2 * ((t_6 * (t_3 - 3.0)) + t_5)) + t_4) + t_7)) + (3.0 * (1.0 / (-0.5 / x2))));
	else
		tmp = t_1;
	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[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 * t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.7e+47], t$95$1, If[LessEqual[x1, 0.31], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$7 + N[(t$95$4 + N[(t$95$2 * N[(t$95$5 + N[(t$95$6 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e+96], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$2 * N[(N[(t$95$6 * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision] + t$95$4), $MachinePrecision] + t$95$7), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(1.0 / N[(-0.5 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.6999999999999999e47 or 6.0000000000000001e96 < x1

   1. Initial program 22.6%

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

   2. Taylor expanded in x1 around inf 36.8%

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

      1. *-commutative 36.8%

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

   4. Simplified 36.8%

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

   5. Taylor expanded in x1 around inf 97.2%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]

   if -1.6999999999999999e47 < x1 < 0.309999999999999998

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around 0 97.2%

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

   if 0.309999999999999998 < x1 < 6.0000000000000001e96

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

      2. clear-num 99.2%

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

      3. associate--l- 99.2%

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

      4. *-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. inv-pow 99.2%

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

      7. associate-*r* 99.2%

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

      8. *-commutative 99.2%

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

      9. fma-def 99.2%

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

      10. pow2 99.2%

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

   3. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x1 around 0 99.2%

      \[\leadsto x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{1}{\color{blue}{\frac{-0.5}{x2}}}\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 0.31:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{+96}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{1}{\frac{-0.5}{x2}}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \end{array} \]

Alternative 4: 96.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51} \lor \neg \left(x1 \leq 7.2 \cdot 10^{+68}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(t_2 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -1.35e+51) (not (<= x1 7.2e+68)))
     (+ x1 (* 6.0 (pow x1 4.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (* t_2 (* x1 2.0)) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68)) {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((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) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-1.35d+51)) .or. (.not. (x1 <= 7.2d+68))) then
        tmp = x1 + (6.0d0 * (x1 ** 4.0d0))
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 * (x1 * 2.0d0)) * (t_2 - 3.0d0)) + ((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) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68)) {
		tmp = x1 + (6.0 * Math.pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -1.35e+51) or not (x1 <= 7.2e+68):
		tmp = x1 + (6.0 * math.pow(x1, 4.0))
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68))
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + 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) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -1.35e+51) || ~((x1 <= 7.2e+68)))
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((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[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.35e+51], N[Not[LessEqual[x1, 7.2e+68]], $MachinePrecision]], N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.34999999999999996e51 or 7.1999999999999998e68 < x1

   1. Initial program 28.0%

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

   2. Taylor expanded in x1 around inf 40.4%

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

      1. *-commutative 40.4%

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

   4. Simplified 40.4%

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

   5. Taylor expanded in x1 around inf 96.5%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]

   if -1.34999999999999996e51 < x1 < 7.1999999999999998e68

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around inf 95.2%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51} \lor \neg \left(x1 \leq 7.2 \cdot 10^{+68}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 5: 96.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51} \lor \neg \left(x1 \leq 7.2 \cdot 10^{+68}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(t_2 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot t_1\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0)))
   (if (or (<= x1 -1.35e+51) (not (<= x1 7.2e+68)))
     (+ x1 (* 6.0 (pow x1 4.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 (+ (* (* t_2 (* x1 2.0)) (- t_2 3.0)) (* (* x1 x1) 6.0)))
          (* 3.0 t_1)))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68)) {
		tmp = x1 + (6.0 * pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    if ((x1 <= (-1.35d+51)) .or. (.not. (x1 <= 7.2d+68))) then
        tmp = x1 + (6.0d0 * (x1 ** 4.0d0))
    else
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_2 * (x1 * 2.0d0)) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0))) + (3.0d0 * t_1)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68)) {
		tmp = x1 + (6.0 * Math.pow(x1, 4.0));
	} else {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if (x1 <= -1.35e+51) or not (x1 <= 7.2e+68):
		tmp = x1 + (6.0 * math.pow(x1, 4.0))
	else:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if ((x1 <= -1.35e+51) || !(x1 <= 7.2e+68))
		tmp = Float64(x1 + Float64(6.0 * (x1 ^ 4.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(t_2 * Float64(x1 * 2.0)) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))) + Float64(3.0 * t_1))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if ((x1 <= -1.35e+51) || ~((x1 <= 7.2e+68)))
		tmp = x1 + (6.0 * (x1 ^ 4.0));
	else
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_2 * (x1 * 2.0)) * (t_2 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[Or[LessEqual[x1, -1.35e+51], N[Not[LessEqual[x1, 7.2e+68]], $MachinePrecision]], N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(t$95$2 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.34999999999999996e51 or 7.1999999999999998e68 < x1

   1. Initial program 28.0%

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

   2. Taylor expanded in x1 around inf 40.4%

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

      1. *-commutative 40.4%

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

   4. Simplified 40.4%

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

   5. Taylor expanded in x1 around inf 96.5%

      \[\leadsto x1 + \color{blue}{6 \cdot {x1}^{4}} \]

   if -1.34999999999999996e51 < x1 < 7.1999999999999998e68

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around inf 95.2%

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

   3. Taylor expanded in x1 around inf 95.1%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+51} \lor \neg \left(x1 \leq 7.2 \cdot 10^{+68}\right):\\ \;\;\;\;x1 + 6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 6: 73.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ t_3 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(\left(t_3 \cdot \left(x1 \cdot 2\right)\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot t_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0)))
        (t_3 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -8.5e+91)
     (+ x1 (+ t_2 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 2.32e+145)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 (+ (* (* t_3 (* x1 2.0)) (- t_3 3.0)) (* (* x1 x1) 6.0)))
            (* 3.0 t_1))))))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((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) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)
    t_3 = ((t_1 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-8.5d+91)) then
        tmp = x1 + (t_2 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 2.32d+145) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_3 * (x1 * 2.0d0)) * (t_3 - 3.0d0)) + ((x1 * x1) * 6.0d0))) + (3.0d0 * t_1)))))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((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) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double t_3 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -8.5e+91:
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 2.32e+145:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))
	t_3 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -8.5e+91)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 2.32e+145)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(t_3 * Float64(x1 * 2.0)) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))) + Float64(3.0 * t_1))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	t_3 = ((t_1 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -8.5e+91)
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 2.32e+145)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_3 * (x1 * 2.0)) * (t_3 - 3.0)) + ((x1 * x1) * 6.0))) + (3.0 * t_1)))));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -8.5e+91], N[(x1 + N[(t$95$2 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.32e+145], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(t$95$3 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999995e91

   1. Initial program 6.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x2 around 0 10.7%

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

      1. *-commutative 10.7%

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

   5. Simplified 10.7%

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

   if -8.4999999999999995e91 < x1 < 2.31999999999999999e145

   1. Initial program 98.1%

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

   2. Taylor expanded in x1 around inf 94.2%

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

   3. Taylor expanded in x1 around inf 94.2%

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

   if 2.31999999999999999e145 < x1

   1. Initial program 2.8%

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

   2. Taylor expanded in x1 around 0 2.8%

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

   3. Taylor expanded in x1 around inf 50.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 7: 59.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x2 \cdot \left(2 \cdot x2 - 3\right)\\ t_3 := 4 \cdot t_2\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(t_3 - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1} + t_1 \cdot \left(4 \cdot \left(x1 \cdot t_2\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + t_3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x2 (- (* 2.0 x2) 3.0)))
        (t_3 (* 4.0 t_2)))
   (if (<= x1 -2.7e-178)
     (+ x1 (+ (* x2 -6.0) (* x1 (- t_3 2.0))))
     (if (<= x1 1.4e-207)
       (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))
       (if (<= x1 2.32e+145)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
              (* t_1 (* 4.0 (* x1 t_2))))))))
         (+ x1 (* x1 (+ 1.0 t_3))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x2 * ((2.0 * x2) - 3.0);
	double t_3 = 4.0 * t_2;
	double tmp;
	if (x1 <= -2.7e-178) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	} else if (x1 <= 1.4e-207) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + (t_1 * (4.0 * (x1 * t_2)))))));
	} else {
		tmp = x1 + (x1 * (1.0 + t_3));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x2 * ((2.0d0 * x2) - 3.0d0)
    t_3 = 4.0d0 * t_2
    if (x1 <= (-2.7d-178)) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (t_3 - 2.0d0)))
    else if (x1 <= 1.4d-207) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else if (x1 <= 2.32d+145) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (2.0d0 * x2)) - x1) / t_1)) + (t_1 * (4.0d0 * (x1 * t_2)))))))
    else
        tmp = x1 + (x1 * (1.0d0 + t_3))
    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 = x2 * ((2.0 * x2) - 3.0);
	double t_3 = 4.0 * t_2;
	double tmp;
	if (x1 <= -2.7e-178) {
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	} else if (x1 <= 1.4e-207) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + (t_1 * (4.0 * (x1 * t_2)))))));
	} else {
		tmp = x1 + (x1 * (1.0 + t_3));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = x2 * ((2.0 * x2) - 3.0)
	t_3 = 4.0 * t_2
	tmp = 0
	if x1 <= -2.7e-178:
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)))
	elif x1 <= 1.4e-207:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	elif x1 <= 2.32e+145:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + (t_1 * (4.0 * (x1 * t_2)))))))
	else:
		tmp = x1 + (x1 * (1.0 + t_3))
	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(x2 * Float64(Float64(2.0 * x2) - 3.0))
	t_3 = Float64(4.0 * t_2)
	tmp = 0.0
	if (x1 <= -2.7e-178)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(t_3 - 2.0))));
	elseif (x1 <= 1.4e-207)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	elseif (x1 <= 2.32e+145)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)) + Float64(t_1 * Float64(4.0 * Float64(x1 * t_2))))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + t_3)));
	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 = x2 * ((2.0 * x2) - 3.0);
	t_3 = 4.0 * t_2;
	tmp = 0.0;
	if (x1 <= -2.7e-178)
		tmp = x1 + ((x2 * -6.0) + (x1 * (t_3 - 2.0)));
	elseif (x1 <= 1.4e-207)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	elseif (x1 <= 2.32e+145)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (((t_0 + (2.0 * x2)) - x1) / t_1)) + (t_1 * (4.0 * (x1 * t_2)))))));
	else
		tmp = x1 + (x1 * (1.0 + t_3));
	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[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(4.0 * t$95$2), $MachinePrecision]}, If[LessEqual[x1, -2.7e-178], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(t$95$3 - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.4e-207], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.32e+145], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.70000000000000009e-178

   1. Initial program 53.7%

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

   2. Taylor expanded in x1 around 0 35.1%

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

   3. Taylor expanded in x1 around 0 36.1%

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

   if -2.70000000000000009e-178 < x1 < 1.39999999999999996e-207

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 98.5%

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

      1. *-commutative 98.5%

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

   4. Simplified 98.5%

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

   5. Taylor expanded in x1 around 0 98.8%

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

   if 1.39999999999999996e-207 < x1 < 2.31999999999999999e145

   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 71.0%

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

   3. Taylor expanded in x1 around 0 65.2%

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

   if 2.31999999999999999e145 < x1

   1. Initial program 2.8%

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

   2. Taylor expanded in x1 around 0 2.8%

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

   3. Taylor expanded in x1 around inf 50.6%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{-178}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 1.4 \cdot 10^{-207}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 8: 70.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_0} + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(2 \cdot x2\right) \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0)) (t_1 (* x1 (* x1 3.0))))
   (if (<= x1 -8.5e+91)
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
       (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 2.32e+145)
       (+
        x1
        (+
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_1 (/ (- (+ t_1 (* 2.0 x2)) x1) t_0))
            (*
             t_0
             (+
              (* (* x1 x1) 6.0)
              (* (* (* 2.0 x2) (* x1 2.0)) (- (- (* 2.0 x2) x1) 3.0)))))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((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) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    if (x1 <= (-8.5d+91)) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 2.32d+145) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0d0 * x2)) - x1) / t_0)) + (t_0 * (((x1 * x1) * 6.0d0) + (((2.0d0 * x2) * (x1 * 2.0d0)) * (((2.0d0 * x2) - x1) - 3.0d0))))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((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) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	tmp = 0
	if x1 <= -8.5e+91:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 2.32e+145:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	tmp = 0.0
	if (x1 <= -8.5e+91)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 2.32e+145)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_0)) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(2.0 * x2) * Float64(x1 * 2.0)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0))))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	tmp = 0.0;
	if (x1 <= -8.5e+91)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 2.32e+145)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * (((t_1 + (2.0 * x2)) - x1) / t_0)) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+91], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.32e+145], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(2.0 * x2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999995e91

   1. Initial program 6.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x2 around 0 10.7%

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

      1. *-commutative 10.7%

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

   5. Simplified 10.7%

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

   if -8.4999999999999995e91 < x1 < 2.31999999999999999e145

   1. Initial program 98.1%

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

   2. Taylor expanded in x1 around 0 77.9%

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

   3. Taylor expanded in x1 around 0 91.2%

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

   4. Taylor expanded in x1 around inf 91.3%

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

   5. Taylor expanded in x1 around 0 91.3%

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

   if 2.31999999999999999e145 < x1

   1. Initial program 2.8%

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

   2. Taylor expanded in x1 around 0 2.8%

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

   3. Taylor expanded in x1 around inf 50.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(2 \cdot x2\right) \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 9: 70.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_1 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(2 \cdot x2\right) \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))))
   (if (<= x1 -8.5e+91)
     (+ x1 (+ t_2 (+ x1 (* 4.0 (* -3.0 (* x1 x2))))))
     (if (<= x1 2.32e+145)
       (+
        x1
        (+
         t_2
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_1)
            (*
             t_0
             (+
              (* (* x1 x1) 6.0)
              (* (* (* 2.0 x2) (* x1 2.0)) (- (- (* 2.0 x2) x1) 3.0)))))))))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((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) + 1.0d0
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)
    if (x1 <= (-8.5d+91)) then
        tmp = x1 + (t_2 + (x1 + (4.0d0 * ((-3.0d0) * (x1 * x2)))))
    else if (x1 <= 2.32d+145) then
        tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_1) + (t_0 * (((x1 * x1) * 6.0d0) + (((2.0d0 * x2) * (x1 * 2.0d0)) * (((2.0d0 * x2) - x1) - 3.0d0))))))))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((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) + 1.0;
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	double tmp;
	if (x1 <= -8.5e+91) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	} else if (x1 <= 2.32e+145) {
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)
	tmp = 0
	if x1 <= -8.5e+91:
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))))
	elif x1 <= 2.32e+145:
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0))
	tmp = 0.0
	if (x1 <= -8.5e+91)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(4.0 * Float64(-3.0 * Float64(x1 * x2))))));
	elseif (x1 <= 2.32e+145)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_1) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(2.0 * x2) * Float64(x1 * 2.0)) * Float64(Float64(Float64(2.0 * x2) - x1) - 3.0)))))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * (x1 * 3.0);
	t_2 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0);
	tmp = 0.0;
	if (x1 <= -8.5e+91)
		tmp = x1 + (t_2 + (x1 + (4.0 * (-3.0 * (x1 * x2)))));
	elseif (x1 <= 2.32e+145)
		tmp = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_1) + (t_0 * (((x1 * x1) * 6.0) + (((2.0 * x2) * (x1 * 2.0)) * (((2.0 * x2) - x1) - 3.0))))))));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -8.5e+91], N[(x1 + N[(t$95$2 + N[(x1 + N[(4.0 * N[(-3.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.32e+145], N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$1), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(2.0 * x2), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(2.0 * x2), $MachinePrecision] - x1), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -8.4999999999999995e91

   1. Initial program 6.3%

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

   2. Taylor expanded in x1 around 0 2.2%

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

   3. Taylor expanded in x2 around 0 10.7%

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

      1. *-commutative 10.7%

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

   5. Simplified 10.7%

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

   if -8.4999999999999995e91 < x1 < 2.31999999999999999e145

   1. Initial program 98.1%

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

   2. Taylor expanded in x1 around 0 77.9%

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

   3. Taylor expanded in x1 around 0 91.2%

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

   4. Taylor expanded in x1 around inf 91.3%

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

   5. Taylor expanded in x1 around inf 91.2%

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

   if 2.31999999999999999e145 < x1

   1. Initial program 2.8%

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

   2. Taylor expanded in x1 around 0 2.8%

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

   3. Taylor expanded in x1 around inf 50.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.5 \cdot 10^{+91}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(-3 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.32 \cdot 10^{+145}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(2 \cdot x2\right) \cdot \left(x1 \cdot 2\right)\right) \cdot \left(\left(2 \cdot x2 - x1\right) - 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 10: 47.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{-73} \lor \neg \left(x1 \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -9.5e-73) (not (<= x1 1.02e-7)))
   (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))
   (+ x1 (+ (* x2 -6.0) (* x1 -2.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.5e-73) || !(x1 <= 1.02e-7)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-9.5d-73)) .or. (.not. (x1 <= 1.02d-7))) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -9.5e-73) || !(x1 <= 1.02e-7)) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	} else {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -9.5e-73) or not (x1 <= 1.02e-7):
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	else:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -9.5e-73) || !(x1 <= 1.02e-7))
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -9.5e-73) || ~((x1 <= 1.02e-7)))
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	else
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -9.5e-73], N[Not[LessEqual[x1, 1.02e-7]], $MachinePrecision]], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.50000000000000005e-73 or 1.02e-7 < x1

   1. Initial program 46.4%

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

   2. Taylor expanded in x1 around 0 15.2%

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

   3. Taylor expanded in x1 around inf 23.4%

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

   if -9.50000000000000005e-73 < x1 < 1.02e-7

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 82.9%

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

      1. *-commutative 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in x1 around 0 82.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.5 \cdot 10^{-73} \lor \neg \left(x1 \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \end{array} \]

Alternative 11: 47.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.2 \cdot 10^{-81}:\\ \;\;\;\;x1 + \left(t_0 + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0001:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
   (if (<= x1 -2.2e-81)
     (+ x1 (+ t_0 9.0))
     (if (<= x1 0.0001) (+ x1 (+ (* x2 -6.0) (* x1 -2.0))) (+ x1 t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -2.2e-81) {
		tmp = x1 + (t_0 + 9.0);
	} else if (x1 <= 0.0001) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x1 + 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 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))
    if (x1 <= (-2.2d-81)) then
        tmp = x1 + (t_0 + 9.0d0)
    else if (x1 <= 0.0001d0) then
        tmp = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
    else
        tmp = x1 + t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	double tmp;
	if (x1 <= -2.2e-81) {
		tmp = x1 + (t_0 + 9.0);
	} else if (x1 <= 0.0001) {
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	} else {
		tmp = x1 + t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))
	tmp = 0
	if x1 <= -2.2e-81:
		tmp = x1 + (t_0 + 9.0)
	elif x1 <= 0.0001:
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0))
	else:
		tmp = x1 + t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))
	tmp = 0.0
	if (x1 <= -2.2e-81)
		tmp = Float64(x1 + Float64(t_0 + 9.0));
	elseif (x1 <= 0.0001)
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)));
	else
		tmp = Float64(x1 + t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))));
	tmp = 0.0;
	if (x1 <= -2.2e-81)
		tmp = x1 + (t_0 + 9.0);
	elseif (x1 <= 0.0001)
		tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
	else
		tmp = x1 + t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.2e-81], N[(x1 + N[(t$95$0 + 9.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.0001], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.1999999999999999e-81

   1. Initial program 42.0%

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

   2. Taylor expanded in x1 around 0 22.3%

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

   3. Taylor expanded in x1 around inf 15.6%

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

   if -2.1999999999999999e-81 < x1 < 1.00000000000000005e-4

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 83.5%

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

      1. *-commutative 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in x1 around 0 83.3%

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

   if 1.00000000000000005e-4 < x1

   1. Initial program 52.2%

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

   2. Taylor expanded in x1 around 0 10.3%

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

   3. Taylor expanded in x1 around inf 32.3%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{-81}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + 9\right)\\ \mathbf{elif}\;x1 \leq 0.0001:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot -2\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 12: 54.6% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right)\right) \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (+ x1 (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)))))

C

double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
}

Fortran

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

Java

public static double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
}

Python

def code(x1, x2):
	return x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0))))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)));
end

Wolfram

code[x1_, x2_] := 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]

Derivation

1. Initial program 67.5%

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

2. Taylor expanded in x1 around 0 42.3%

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

3. Taylor expanded in x1 around 0 48.5%

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

4. Final simplification 48.5%

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

Alternative 13: 38.7% accurate, 14.1× speedup

Math

\[\begin{array}{l} \\ x1 + \left(x2 \cdot -6 + x1 \cdot -2\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (+ (* x2 -6.0) (* x1 -2.0))))

C

double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * -2.0));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + ((x2 * (-6.0d0)) + (x1 * (-2.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return x1 + ((x2 * -6.0) + (x1 * -2.0));
}

Python

def code(x1, x2):
	return x1 + ((x2 * -6.0) + (x1 * -2.0))

Julia

function code(x1, x2)
	return Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * -2.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + ((x2 * -6.0) + (x1 * -2.0));
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.5%

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

2. Taylor expanded in x1 around inf 58.8%

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

   1. *-commutative 58.8%

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

4. Simplified 58.8%

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

5. Taylor expanded in x1 around 0 35.8%

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

6. Final simplification 35.8%

   \[\leadsto x1 + \left(x2 \cdot -6 + x1 \cdot -2\right) \]

Alternative 14: 26.4% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.5%

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

2. Taylor expanded in x1 around 0 42.3%

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

3. Taylor expanded in x1 around 0 22.1%

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

   1. *-commutative 22.1%

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

5. Simplified 22.1%

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

6. Final simplification 22.1%

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

Alternative 15: 26.3% 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 67.5%

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

2. Taylor expanded in x1 around 0 42.3%

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

3. Taylor expanded in x1 around 0 22.1%

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

   1. *-commutative 22.1%

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

5. Simplified 22.1%

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

6. Taylor expanded in x1 around 0 22.0%

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

7. Final simplification 22.0%

   \[\leadsto x2 \cdot -6 \]

Alternative 16: 3.2% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 67.5%

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

2. Taylor expanded in x1 around 0 42.3%

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

3. Taylor expanded in x1 around 0 22.1%

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

   1. *-commutative 22.1%

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

5. Simplified 22.1%

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

6. Taylor expanded in x1 around inf 3.2%

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

7. Final simplification 3.2%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023333 
(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))))))