Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 71.0% → 95.9%

Time: 1.2min

Alternatives: 18

Speedup: 1.3×

• 46.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(3 \cdot x1\right) \cdot x1\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) \cdot t\_1 + t\_0 \cdot t\_2\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1}\right) \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 71.0% 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: 95.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_1 := 3 \cdot \left(x1 \cdot x1\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_1 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_0, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_0\right)\right) \cdot \left(-3 + t\_0\right)\right), \mathsf{fma}\left(t\_1, t\_0, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (- (fma x1 (* x1 3.0) (* x2 2.0)) x1) (fma x1 x1 1.0)))
        (t_1 (* 3.0 (* x1 x1))))
   (if (<= x1 -3.8e+73)
     (+
      x1
      (+
       (+ x1 (+ (* -3.0 (pow x1 3.0)) (* 6.0 (pow x1 4.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 4.2e+149)
       (+
        x1
        (fma
         3.0
         (/ (- t_1 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
         (+
          x1
          (fma
           (fma x1 x1 1.0)
           (fma
            x1
            (* x1 (fma t_0 4.0 -6.0))
            (* (* x1 (* 2.0 t_0)) (+ -3.0 t_0)))
           (fma t_1 t_0 (pow x1 3.0))))))
       (+
        x1
        (+
         (+
          (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
          (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))
         (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = (fma(x1, (x1 * 3.0), (x2 * 2.0)) - x1) / fma(x1, x1, 1.0);
	double t_1 = 3.0 * (x1 * x1);
	double tmp;
	if (x1 <= -3.8e+73) {
		tmp = x1 + ((x1 + ((-3.0 * pow(x1, 3.0)) + (6.0 * pow(x1, 4.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 4.2e+149) {
		tmp = x1 + fma(3.0, ((t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_0, 4.0, -6.0)), ((x1 * (2.0 * t_0)) * (-3.0 + t_0))), fma(t_1, t_0, pow(x1, 3.0)))));
	} else {
		tmp = x1 + (((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(Float64(fma(x1, Float64(x1 * 3.0), Float64(x2 * 2.0)) - x1) / fma(x1, x1, 1.0))
	t_1 = Float64(3.0 * Float64(x1 * x1))
	tmp = 0.0
	if (x1 <= -3.8e+73)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(-3.0 * (x1 ^ 3.0)) + Float64(6.0 * (x1 ^ 4.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 4.2e+149)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_1 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_0, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_0)) * Float64(-3.0 + t_0))), fma(t_1, t_0, (x1 ^ 3.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))) + Float64(x2 * -6.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+73], N[(x1 + N[(N[(x1 + N[(N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+149], N[(x1 + N[(3.0 * N[(N[(t$95$1 - N[(2.0 * x2 + x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$0), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * t$95$0 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.80000000000000022e73

   1. Initial program 12.2%

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

   3. Taylor expanded in x1 around inf 28.1%

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

   4. Taylor expanded in x1 around 0 96.5%

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

      1. *-commutative 96.5%

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

   6. Simplified 96.5%

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

   if -3.80000000000000022e73 < x1 < 4.2000000000000003e149

   1. Initial program 99.4%

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

   3. Simplified 99.5%

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

   if 4.2000000000000003e149 < x1

   1. Initial program 3.4%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 79.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{3 \cdot \left(x1 \cdot x1\right) - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \left(x1 \cdot \left(2 \cdot \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right), \mathsf{fma}\left(3 \cdot \left(x1 \cdot x1\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := \frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(t\_1 \cdot \left(x1 \cdot 2\right), -3 + t\_1, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, t\_1, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), t\_1 \cdot t\_0\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{t\_0 - \left(x1 + x2 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (/ (- (fma (* x1 3.0) x1 (* x2 2.0)) x1) (fma x1 x1 1.0))))
   (if (<= x1 -3.8e+73)
     (+
      x1
      (+
       (+ x1 (+ (* -3.0 (pow x1 3.0)) (* 6.0 (pow x1 4.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 4.2e+149)
       (+
        x1
        (+
         (+
          (fma
           (fma
            (* t_1 (* x1 2.0))
            (+ -3.0 t_1)
            (* (* x1 x1) (fma 4.0 t_1 -6.0)))
           (fma x1 x1 1.0)
           (* t_1 t_0))
          (* x1 (* x1 x1)))
         (+ x1 (* 3.0 (/ (- t_0 (+ x1 (* x2 2.0))) (fma x1 x1 1.0))))))
       (+
        x1
        (+
         (+
          (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
          (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))
         (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (fma((x1 * 3.0), x1, (x2 * 2.0)) - x1) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -3.8e+73) {
		tmp = x1 + ((x1 + ((-3.0 * pow(x1, 3.0)) + (6.0 * pow(x1, 4.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 4.2e+149) {
		tmp = x1 + ((fma(fma((t_1 * (x1 * 2.0)), (-3.0 + t_1), ((x1 * x1) * fma(4.0, t_1, -6.0))), fma(x1, x1, 1.0), (t_1 * t_0)) + (x1 * (x1 * x1))) + (x1 + (3.0 * ((t_0 - (x1 + (x2 * 2.0))) / fma(x1, x1, 1.0)))));
	} else {
		tmp = x1 + (((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 * 2.0)) - x1) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -3.8e+73)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(-3.0 * (x1 ^ 3.0)) + Float64(6.0 * (x1 ^ 4.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 4.2e+149)
		tmp = Float64(x1 + Float64(Float64(fma(fma(Float64(t_1 * Float64(x1 * 2.0)), Float64(-3.0 + t_1), Float64(Float64(x1 * x1) * fma(4.0, t_1, -6.0))), fma(x1, x1, 1.0), Float64(t_1 * t_0)) + Float64(x1 * Float64(x1 * x1))) + Float64(x1 + Float64(3.0 * Float64(Float64(t_0 - Float64(x1 + Float64(x2 * 2.0))) / fma(x1, x1, 1.0))))));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))) + Float64(x2 * -6.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+73], N[(x1 + N[(N[(x1 + N[(N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+149], N[(x1 + N[(N[(N[(N[(N[(t$95$1 * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision] * N[(-3.0 + t$95$1), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(4.0 * t$95$1 + -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x1 * x1 + 1.0), $MachinePrecision] + N[(t$95$1 * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(3.0 * N[(N[(t$95$0 - N[(x1 + N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.80000000000000022e73

   1. Initial program 12.2%

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

   3. Taylor expanded in x1 around inf 28.1%

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

   4. Taylor expanded in x1 around 0 96.5%

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

      1. *-commutative 96.5%

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

   6. Simplified 96.5%

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

   if -3.80000000000000022e73 < x1 < 4.2000000000000003e149

   1. Initial program 99.4%

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

   3. Simplified 99.4%

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

   if 4.2000000000000003e149 < x1

   1. Initial program 3.4%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 79.3%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(\left(\mathsf{fma}\left(\mathsf{fma}\left(\frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot 2\right), -3 + \frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, \left(x1 \cdot x1\right) \cdot \mathsf{fma}\left(4, \frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}, -6\right)\right), \mathsf{fma}\left(x1, x1, 1\right), \frac{\mathsf{fma}\left(x1 \cdot 3, x1, x2 \cdot 2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) + x1 \cdot \left(x1 \cdot x1\right)\right) + \left(x1 + 3 \cdot \frac{x1 \cdot \left(x1 \cdot 3\right) - \left(x1 + x2 \cdot 2\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_1}\\ t_3 := x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{if}\;t\_3 \leq \infty:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, Infinity], t$95$3, N[(x1 + N[(N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $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 99.4%

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

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 2.6%

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

   4. Taylor expanded in x1 around 0 54.3%

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

4. Final simplification 85.6%

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

Alternative 4: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -3.8e+73)
     (+
      x1
      (+
       (+ x1 (+ (* -3.0 (pow x1 3.0)) (* 6.0 (pow x1 4.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 4.2e+149)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (+
        x1
        (+
         (+
          (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0))))
          (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))
         (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -3.8e+73) {
		tmp = x1 + ((x1 + ((-3.0 * pow(x1, 3.0)) + (6.0 * pow(x1, 4.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 4.2e+149) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (((3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-3.8d+73)) then
        tmp = x1 + ((x1 + (((-3.0d0) * (x1 ** 3.0d0)) + (6.0d0 * (x1 ** 4.0d0)))) + (3.0d0 * (x2 * (-2.0d0))))
    else if (x1 <= 4.2d+149) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)))
    else
        tmp = x1 + (((3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0))))) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0))) + (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -3.8e+73) {
		tmp = x1 + ((x1 + ((-3.0 * Math.pow(x1, 3.0)) + (6.0 * Math.pow(x1, 4.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 4.2e+149) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (((3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -3.8e+73:
		tmp = x1 + ((x1 + ((-3.0 * math.pow(x1, 3.0)) + (6.0 * math.pow(x1, 4.0)))) + (3.0 * (x2 * -2.0)))
	elif x1 <= 4.2e+149:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)))
	else:
		tmp = x1 + (((3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.8e+73)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(-3.0 * (x1 ^ 3.0)) + Float64(6.0 * (x1 ^ 4.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 4.2e+149)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	else
		tmp = Float64(x1 + Float64(Float64(Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))) + Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -3.8e+73)
		tmp = x1 + ((x1 + ((-3.0 * (x1 ^ 3.0)) + (6.0 * (x1 ^ 4.0)))) + (3.0 * (x2 * -2.0)));
	elseif (x1 <= 4.2e+149)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	else
		tmp = x1 + (((3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0)))) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0))) + (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.8e+73], N[(x1 + N[(N[(x1 + N[(N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.2e+149], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.80000000000000022e73

   1. Initial program 12.2%

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

   3. Taylor expanded in x1 around inf 28.1%

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

   4. Taylor expanded in x1 around 0 96.5%

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

      1. *-commutative 96.5%

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

   6. Simplified 96.5%

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

   if -3.80000000000000022e73 < x1 < 4.2000000000000003e149

   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. Add Preprocessing

   if 4.2000000000000003e149 < x1

   1. Initial program 3.4%

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

   3. Taylor expanded in x1 around 0 0.2%

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

   4. Taylor expanded in x1 around 0 79.3%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(-3 \cdot {x1}^{3} + 6 \cdot {x1}^{4}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 4.2 \cdot 10^{+149}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right) + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right) + x2 \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_1}\\ t_3 := 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(t\_3 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t\_3\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1))
        (t_3 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
   (if (<= x1 -1.35e+154)
     (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
     (if (<= x1 -3.8e+73)
       (+ x1 (+ t_3 (+ x1 (* 6.0 (pow x1 4.0)))))
       (if (<= x1 1.32e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
              (* t_0 t_2))
             (* x1 (* x1 x1))))
           t_3))
         (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= -3.8e+73) {
		tmp = x1 + (t_3 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3);
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 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 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    t_3 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)
    if (x1 <= (-1.35d+154)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= (-3.8d+73)) then
        tmp = x1 + (t_3 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else if (x1 <= 1.32d+154) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3)
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= -3.8e+73) {
		tmp = x1 + (t_3 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3);
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= -3.8e+73:
		tmp = x1 + (t_3 + (x1 + (6.0 * math.pow(x1, 4.0))))
	elif x1 <= 1.32e+154:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3)
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= -3.8e+73)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1.32e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + t_3));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= -3.8e+73)
		tmp = x1 + (t_3 + (x1 + (6.0 * (x1 ^ 4.0))));
	elseif (x1 <= 1.32e+154)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3);
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -3.8e+73], N[(x1 + N[(t$95$3 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.35000000000000003e154

   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. Add Preprocessing

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around 0 3.3%

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

      1. fma-def 3.3%

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

      2. fma-neg 3.3%

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

      3. fma-neg 3.3%

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

      4. metadata-eval 3.3%

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

      5. metadata-eval 3.3%

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

   6. Simplified 3.3%

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

   7. Taylor expanded in x2 around 0 32.0%

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

   if -1.35000000000000003e154 < x1 < -3.80000000000000022e73

   1. Initial program 38.8%

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

   3. Taylor expanded in x1 around inf 88.9%

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

      1. *-commutative 88.9%

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

   5. Simplified 88.9%

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

   if -3.80000000000000022e73 < x1 < 1.31999999999999998e154

   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. Add Preprocessing

   if 1.31999999999999998e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 43.1%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t\_2 - 6\right)\right) + t\_0 \cdot t\_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -5.8e+102)
     (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
     (if (<= x1 1.32e+154)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-5.8d+102)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= 1.32d+154) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -5.8e+102:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= 1.32e+154:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= 1.32e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.8e+102)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= 1.32e+154)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.8000000000000005e102

   1. Initial program 2.0%

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

   3. Taylor expanded in x1 around 0 4.0%

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

   4. Taylor expanded in x1 around 0 5.1%

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

      1. fma-def 5.1%

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

      2. fma-neg 5.1%

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

      3. fma-neg 5.1%

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

      4. metadata-eval 5.1%

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

      5. metadata-eval 5.1%

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

   6. Simplified 5.1%

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

   7. Taylor expanded in x2 around 0 27.5%

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

   if -5.8000000000000005e102 < x1 < 1.31999999999999998e154

   1. Initial program 98.8%

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

   if 1.31999999999999998e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 43.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x2 \cdot \left(x2 \cdot 2 - 3\right)\\ t_3 := x1 \cdot x1 + 1\\ t_4 := 3 \cdot \frac{\left(t\_1 - x2 \cdot 2\right) - x1}{t\_3}\\ t_5 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ t_6 := t\_3 \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + t\_1\right) - x1}{t\_3} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\\ t_7 := x1 + \left(t\_4 + \left(x1 + 4 \cdot \left(x1 \cdot t\_2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -850:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_0 + \left(3 \cdot t\_1 + t\_6\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-212}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{-238}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 185:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;x1 + \left(t\_4 + \left(x1 + \left(t\_0 + \left(t\_6 + \left(x2 \cdot 2\right) \cdot t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot t\_2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* x2 (- (* x2 2.0) 3.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_3)))
        (t_5 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0)))))
        (t_6
         (*
          t_3
          (+
           (* 6.0 (* x1 x1))
           (*
            (- (/ (- (+ (* x2 2.0) t_1) x1) t_3) 3.0)
            (* (* x1 2.0) (+ 3.0 (/ -1.0 x1)))))))
        (t_7 (+ x1 (+ t_4 (+ x1 (* 4.0 (* x1 t_2)))))))
   (if (<= x1 -5.8e+102)
     t_5
     (if (<= x1 -850.0)
       (+ x1 (+ t_4 (+ x1 (+ t_0 (+ (* 3.0 t_1) t_6)))))
       (if (<= x1 -2.2e-212)
         t_7
         (if (<= x1 1.95e-238)
           t_5
           (if (<= x1 185.0)
             t_7
             (if (<= x1 5.2e+125)
               (+ x1 (+ t_4 (+ x1 (+ t_0 (+ t_6 (* (* x2 2.0) t_1))))))
               (+ x1 (* x1 (+ 1.0 (* 4.0 t_2))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * ((x2 * 2.0) - 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_6 = t_3 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))));
	double t_7 = x1 + (t_4 + (x1 + (4.0 * (x1 * t_2))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = t_5;
	} else if (x1 <= -850.0) {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((3.0 * t_1) + t_6))));
	} else if (x1 <= -2.2e-212) {
		tmp = t_7;
	} else if (x1 <= 1.95e-238) {
		tmp = t_5;
	} else if (x1 <= 185.0) {
		tmp = t_7;
	} else if (x1 <= 5.2e+125) {
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_6 + ((x2 * 2.0) * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * t_2)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: t_7
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x2 * ((x2 * 2.0d0) - 3.0d0)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = 3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_3)
    t_5 = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    t_6 = t_3 * ((6.0d0 * (x1 * x1)) + ((((((x2 * 2.0d0) + t_1) - x1) / t_3) - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1)))))
    t_7 = x1 + (t_4 + (x1 + (4.0d0 * (x1 * t_2))))
    if (x1 <= (-5.8d+102)) then
        tmp = t_5
    else if (x1 <= (-850.0d0)) then
        tmp = x1 + (t_4 + (x1 + (t_0 + ((3.0d0 * t_1) + t_6))))
    else if (x1 <= (-2.2d-212)) then
        tmp = t_7
    else if (x1 <= 1.95d-238) then
        tmp = t_5
    else if (x1 <= 185.0d0) then
        tmp = t_7
    else if (x1 <= 5.2d+125) then
        tmp = x1 + (t_4 + (x1 + (t_0 + (t_6 + ((x2 * 2.0d0) * t_1)))))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * t_2)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x2 * ((x2 * 2.0) - 3.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	double t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_6 = t_3 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))));
	double t_7 = x1 + (t_4 + (x1 + (4.0 * (x1 * t_2))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = t_5;
	} else if (x1 <= -850.0) {
		tmp = x1 + (t_4 + (x1 + (t_0 + ((3.0 * t_1) + t_6))));
	} else if (x1 <= -2.2e-212) {
		tmp = t_7;
	} else if (x1 <= 1.95e-238) {
		tmp = t_5;
	} else if (x1 <= 185.0) {
		tmp = t_7;
	} else if (x1 <= 5.2e+125) {
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_6 + ((x2 * 2.0) * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * t_2)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x2 * ((x2 * 2.0) - 3.0)
	t_3 = (x1 * x1) + 1.0
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3)
	t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	t_6 = t_3 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))))
	t_7 = x1 + (t_4 + (x1 + (4.0 * (x1 * t_2))))
	tmp = 0
	if x1 <= -5.8e+102:
		tmp = t_5
	elif x1 <= -850.0:
		tmp = x1 + (t_4 + (x1 + (t_0 + ((3.0 * t_1) + t_6))))
	elif x1 <= -2.2e-212:
		tmp = t_7
	elif x1 <= 1.95e-238:
		tmp = t_5
	elif x1 <= 185.0:
		tmp = t_7
	elif x1 <= 5.2e+125:
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_6 + ((x2 * 2.0) * t_1)))))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * t_2)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_3))
	t_5 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	t_6 = Float64(t_3 * Float64(Float64(6.0 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1))))))
	t_7 = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(4.0 * Float64(x1 * t_2)))))
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = t_5;
	elseif (x1 <= -850.0)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(Float64(3.0 * t_1) + t_6)))));
	elseif (x1 <= -2.2e-212)
		tmp = t_7;
	elseif (x1 <= 1.95e-238)
		tmp = t_5;
	elseif (x1 <= 185.0)
		tmp = t_7;
	elseif (x1 <= 5.2e+125)
		tmp = Float64(x1 + Float64(t_4 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(Float64(x2 * 2.0) * t_1))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * t_2))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x2 * ((x2 * 2.0) - 3.0);
	t_3 = (x1 * x1) + 1.0;
	t_4 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_3);
	t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	t_6 = t_3 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_1) - x1) / t_3) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1)))));
	t_7 = x1 + (t_4 + (x1 + (4.0 * (x1 * t_2))));
	tmp = 0.0;
	if (x1 <= -5.8e+102)
		tmp = t_5;
	elseif (x1 <= -850.0)
		tmp = x1 + (t_4 + (x1 + (t_0 + ((3.0 * t_1) + t_6))));
	elseif (x1 <= -2.2e-212)
		tmp = t_7;
	elseif (x1 <= 1.95e-238)
		tmp = t_5;
	elseif (x1 <= 185.0)
		tmp = t_7;
	elseif (x1 <= 5.2e+125)
		tmp = x1 + (t_4 + (x1 + (t_0 + (t_6 + ((x2 * 2.0) * t_1)))));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * t_2)));
	end
	tmp_2 = 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[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$3 * N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(t$95$4 + N[(x1 + N[(4.0 * N[(x1 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], t$95$5, If[LessEqual[x1, -850.0], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(N[(3.0 * t$95$1), $MachinePrecision] + t$95$6), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.2e-212], t$95$7, If[LessEqual[x1, 1.95e-238], t$95$5, If[LessEqual[x1, 185.0], t$95$7, If[LessEqual[x1, 5.2e+125], N[(x1 + N[(t$95$4 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(N[(x2 * 2.0), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.8000000000000005e102 or -2.20000000000000003e-212 < x1 < 1.9499999999999999e-238

   1. Initial program 42.8%

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

   3. Taylor expanded in x1 around 0 34.1%

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

   4. Taylor expanded in x1 around 0 34.7%

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

      1. fma-def 34.8%

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

      2. fma-neg 34.8%

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

      3. fma-neg 34.8%

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

      4. metadata-eval 34.8%

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

      5. metadata-eval 34.8%

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

   6. Simplified 34.8%

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

   7. Taylor expanded in x2 around 0 53.8%

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

   if -5.8000000000000005e102 < x1 < -850

   1. Initial program 93.9%

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

   3. Taylor expanded in x1 around inf 84.5%

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

   4. Taylor expanded in x1 around inf 81.6%

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

   5. Taylor expanded in x1 around inf 86.6%

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

   if -850 < x1 < -2.20000000000000003e-212 or 1.9499999999999999e-238 < x1 < 185

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 85.5%

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

   if 185 < x1 < 5.20000000000000006e125

   1. Initial program 99.5%

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

   3. Taylor expanded in x1 around inf 79.8%

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

   4. Taylor expanded in x1 around inf 70.1%

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

   5. Taylor expanded in x1 around 0 73.4%

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

   if 5.20000000000000006e125 < x1

   1. Initial program 12.5%

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

   3. Taylor expanded in x1 around 0 9.5%

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

   4. Taylor expanded in x1 around inf 47.3%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -850:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-212}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.95 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 185:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right) + \left(x2 \cdot 2\right) \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(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x2 \cdot \left(x2 \cdot 2 - 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t\_0 - x2 \cdot 2\right) - x1}{t\_2}\\ t_4 := x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_2 \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + t\_0\right) - x1}{t\_2} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ t_5 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ t_6 := x1 + \left(t\_3 + \left(x1 + 4 \cdot \left(x1 \cdot t\_1\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq -900:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{-238}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;x1 \leq 460:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot t\_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (* x2 (- (* x2 2.0) 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_2)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_2
               (+
                (* 6.0 (* x1 x1))
                (*
                 (- (/ (- (+ (* x2 2.0) t_0) x1) t_2) 3.0)
                 (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))))))))))))
        (t_5 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0)))))
        (t_6 (+ x1 (+ t_3 (+ x1 (* 4.0 (* x1 t_1)))))))
   (if (<= x1 -5.8e+102)
     t_5
     (if (<= x1 -900.0)
       t_4
       (if (<= x1 -1.35e-209)
         t_6
         (if (<= x1 4.6e-238)
           t_5
           (if (<= x1 460.0)
             t_6
             (if (<= x1 1.32e+154)
               t_4
               (+ x1 (* x1 (+ 1.0 (* 4.0 t_1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x2 * ((x2 * 2.0) - 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_0) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_6 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_1))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = t_5;
	} else if (x1 <= -900.0) {
		tmp = t_4;
	} else if (x1 <= -1.35e-209) {
		tmp = t_6;
	} else if (x1 <= 4.6e-238) {
		tmp = t_5;
	} else if (x1 <= 460.0) {
		tmp = t_6;
	} else if (x1 <= 1.32e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * 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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x2 * ((x2 * 2.0d0) - 3.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_2)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_2 * ((6.0d0 * (x1 * x1)) + ((((((x2 * 2.0d0) + t_0) - x1) / t_2) - 3.0d0) * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1))))))))))
    t_5 = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    t_6 = x1 + (t_3 + (x1 + (4.0d0 * (x1 * t_1))))
    if (x1 <= (-5.8d+102)) then
        tmp = t_5
    else if (x1 <= (-900.0d0)) then
        tmp = t_4
    else if (x1 <= (-1.35d-209)) then
        tmp = t_6
    else if (x1 <= 4.6d-238) then
        tmp = t_5
    else if (x1 <= 460.0d0) then
        tmp = t_6
    else if (x1 <= 1.32d+154) then
        tmp = t_4
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * 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 = x2 * ((x2 * 2.0) - 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_0) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_6 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_1))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = t_5;
	} else if (x1 <= -900.0) {
		tmp = t_4;
	} else if (x1 <= -1.35e-209) {
		tmp = t_6;
	} else if (x1 <= 4.6e-238) {
		tmp = t_5;
	} else if (x1 <= 460.0) {
		tmp = t_6;
	} else if (x1 <= 1.32e+154) {
		tmp = t_4;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * t_1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x2 * ((x2 * 2.0) - 3.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_0) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))))
	t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	t_6 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_1))))
	tmp = 0
	if x1 <= -5.8e+102:
		tmp = t_5
	elif x1 <= -900.0:
		tmp = t_4
	elif x1 <= -1.35e-209:
		tmp = t_6
	elif x1 <= 4.6e-238:
		tmp = t_5
	elif x1 <= 460.0:
		tmp = t_6
	elif x1 <= 1.32e+154:
		tmp = t_4
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * t_1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_2))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_2 * Float64(Float64(6.0 * Float64(x1 * x1)) + Float64(Float64(Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_2) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1)))))))))))
	t_5 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	t_6 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x1 * t_1)))))
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = t_5;
	elseif (x1 <= -900.0)
		tmp = t_4;
	elseif (x1 <= -1.35e-209)
		tmp = t_6;
	elseif (x1 <= 4.6e-238)
		tmp = t_5;
	elseif (x1 <= 460.0)
		tmp = t_6;
	elseif (x1 <= 1.32e+154)
		tmp = t_4;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x2 * ((x2 * 2.0) - 3.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_2);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_2 * ((6.0 * (x1 * x1)) + ((((((x2 * 2.0) + t_0) - x1) / t_2) - 3.0) * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	t_5 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	t_6 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_1))));
	tmp = 0.0;
	if (x1 <= -5.8e+102)
		tmp = t_5;
	elseif (x1 <= -900.0)
		tmp = t_4;
	elseif (x1 <= -1.35e-209)
		tmp = t_6;
	elseif (x1 <= 4.6e-238)
		tmp = t_5;
	elseif (x1 <= 460.0)
		tmp = t_6;
	elseif (x1 <= 1.32e+154)
		tmp = t_4;
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * 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[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$2 * N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], t$95$5, If[LessEqual[x1, -900.0], t$95$4, If[LessEqual[x1, -1.35e-209], t$95$6, If[LessEqual[x1, 4.6e-238], t$95$5, If[LessEqual[x1, 460.0], t$95$6, If[LessEqual[x1, 1.32e+154], t$95$4, N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.8000000000000005e102 or -1.34999999999999999e-209 < x1 < 4.60000000000000009e-238

   1. Initial program 42.8%

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

   3. Taylor expanded in x1 around 0 34.1%

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

   4. Taylor expanded in x1 around 0 34.7%

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

      1. fma-def 34.8%

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

      2. fma-neg 34.8%

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

      3. fma-neg 34.8%

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

      4. metadata-eval 34.8%

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

      5. metadata-eval 34.8%

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

   6. Simplified 34.8%

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

   7. Taylor expanded in x2 around 0 53.8%

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

   if -5.8000000000000005e102 < x1 < -900 or 460 < x1 < 1.31999999999999998e154

   1. Initial program 97.5%

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

   3. Taylor expanded in x1 around inf 83.0%

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

   4. Taylor expanded in x1 around inf 76.6%

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

   5. Taylor expanded in x1 around inf 78.4%

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

   if -900 < x1 < -1.34999999999999999e-209 or 4.60000000000000009e-238 < x1 < 460

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 85.5%

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

   if 1.31999999999999998e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 43.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -900:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-209}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 4.6 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 460:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(x2 \cdot 2 + t\_1\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_1 - x2 \cdot 2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + 6 \cdot \left(x1 \cdot x1\right)\right) + 3 \cdot t\_1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ (* x2 2.0) t_1) x1) t_0)))
   (if (<= x1 -5.8e+102)
     (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
     (if (<= x1 1.32e+154)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_0 (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* 6.0 (* x1 x1))))
            (* 3.0 t_1))))))
       (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 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 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1)))) + (3.0 * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 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 = (((x2 * 2.0d0) + t_1) - x1) / t_0
    if (x1 <= (-5.8d+102)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else if (x1 <= 1.32d+154) then
        tmp = x1 + ((3.0d0 * (((t_1 - (x2 * 2.0d0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + (6.0d0 * (x1 * x1)))) + (3.0d0 * t_1)))))
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 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 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else if (x1 <= 1.32e+154) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1)))) + (3.0 * t_1)))));
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * (x1 * 3.0)
	t_2 = (((x2 * 2.0) + t_1) - x1) / t_0
	tmp = 0
	if x1 <= -5.8e+102:
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	elif x1 <= 1.32e+154:
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1)))) + (3.0 * t_1)))))
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 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(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	elseif (x1 <= 1.32e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(6.0 * Float64(x1 * x1)))) + Float64(3.0 * t_1))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 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 = (((x2 * 2.0) + t_1) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5.8e+102)
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	elseif (x1 <= 1.32e+154)
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + (6.0 * (x1 * x1)))) + (3.0 * t_1)))));
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 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[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.32e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(x1 * x1), $MachinePrecision]), $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[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.8000000000000005e102

   1. Initial program 2.0%

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

   3. Taylor expanded in x1 around 0 4.0%

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

   4. Taylor expanded in x1 around 0 5.1%

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

      1. fma-def 5.1%

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

      2. fma-neg 5.1%

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

      3. fma-neg 5.1%

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

      4. metadata-eval 5.1%

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

      5. metadata-eval 5.1%

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

   6. Simplified 5.1%

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

   7. Taylor expanded in x2 around 0 27.5%

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

   if -5.8000000000000005e102 < x1 < 1.31999999999999998e154

   1. Initial program 98.8%

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

   3. Taylor expanded in x1 around inf 95.6%

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

   4. Taylor expanded in x1 around inf 96.1%

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

   if 1.31999999999999998e154 < x1

   1. Initial program 0.0%

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

   3. Taylor expanded in x1 around 0 0.0%

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

   4. Taylor expanded in x1 around inf 43.1%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{x1 \cdot x1 + 1} - 3\right) + 6 \cdot \left(x1 \cdot x1\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 67.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t\_2 - x2 \cdot 2\right) - x1}{t\_1}\\ t_4 := x2 \cdot 2 - 3\\ t_5 := x2 \cdot t\_4\\ t_6 := x1 + \left(t\_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_2 + t\_1 \cdot \left(6 \cdot \left(x1 \cdot x1\right) + t\_4 \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ t_7 := x1 + \left(t\_3 + \left(x1 + 4 \cdot \left(x1 \cdot t\_5\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -26000000:\\ \;\;\;\;t\_6\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 460:\\ \;\;\;\;t\_7\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;t\_6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot t\_5\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0)))))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* x2 2.0)) x1) t_1)))
        (t_4 (- (* x2 2.0) 3.0))
        (t_5 (* x2 t_4))
        (t_6
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_2)
              (*
               t_1
               (+
                (* 6.0 (* x1 x1))
                (* t_4 (* (* x1 2.0) (+ 3.0 (/ -1.0 x1))))))))))))
        (t_7 (+ x1 (+ t_3 (+ x1 (* 4.0 (* x1 t_5)))))))
   (if (<= x1 -5.1e+95)
     t_0
     (if (<= x1 -26000000.0)
       t_6
       (if (<= x1 -3.4e-207)
         t_7
         (if (<= x1 8.5e-239)
           t_0
           (if (<= x1 460.0)
             t_7
             (if (<= x1 5.2e+125) t_6 (+ x1 (* x1 (+ 1.0 (* 4.0 t_5))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	double t_4 = (x2 * 2.0) - 3.0;
	double t_5 = x2 * t_4;
	double t_6 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * ((6.0 * (x1 * x1)) + (t_4 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_7 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_5))));
	double tmp;
	if (x1 <= -5.1e+95) {
		tmp = t_0;
	} else if (x1 <= -26000000.0) {
		tmp = t_6;
	} else if (x1 <= -3.4e-207) {
		tmp = t_7;
	} else if (x1 <= 8.5e-239) {
		tmp = t_0;
	} else if (x1 <= 460.0) {
		tmp = t_7;
	} else if (x1 <= 5.2e+125) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * t_5)));
	}
	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 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    t_1 = (x1 * x1) + 1.0d0
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (x2 * 2.0d0)) - x1) / t_1)
    t_4 = (x2 * 2.0d0) - 3.0d0
    t_5 = x2 * t_4
    t_6 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + (t_1 * ((6.0d0 * (x1 * x1)) + (t_4 * ((x1 * 2.0d0) * (3.0d0 + ((-1.0d0) / x1))))))))))
    t_7 = x1 + (t_3 + (x1 + (4.0d0 * (x1 * t_5))))
    if (x1 <= (-5.1d+95)) then
        tmp = t_0
    else if (x1 <= (-26000000.0d0)) then
        tmp = t_6
    else if (x1 <= (-3.4d-207)) then
        tmp = t_7
    else if (x1 <= 8.5d-239) then
        tmp = t_0
    else if (x1 <= 460.0d0) then
        tmp = t_7
    else if (x1 <= 5.2d+125) then
        tmp = t_6
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * t_5)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	double t_4 = (x2 * 2.0) - 3.0;
	double t_5 = x2 * t_4;
	double t_6 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * ((6.0 * (x1 * x1)) + (t_4 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	double t_7 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_5))));
	double tmp;
	if (x1 <= -5.1e+95) {
		tmp = t_0;
	} else if (x1 <= -26000000.0) {
		tmp = t_6;
	} else if (x1 <= -3.4e-207) {
		tmp = t_7;
	} else if (x1 <= 8.5e-239) {
		tmp = t_0;
	} else if (x1 <= 460.0) {
		tmp = t_7;
	} else if (x1 <= 5.2e+125) {
		tmp = t_6;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * t_5)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	t_1 = (x1 * x1) + 1.0
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1)
	t_4 = (x2 * 2.0) - 3.0
	t_5 = x2 * t_4
	t_6 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * ((6.0 * (x1 * x1)) + (t_4 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))))
	t_7 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_5))))
	tmp = 0
	if x1 <= -5.1e+95:
		tmp = t_0
	elif x1 <= -26000000.0:
		tmp = t_6
	elif x1 <= -3.4e-207:
		tmp = t_7
	elif x1 <= 8.5e-239:
		tmp = t_0
	elif x1 <= 460.0:
		tmp = t_7
	elif x1 <= 5.2e+125:
		tmp = t_6
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * t_5)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(x2 * 2.0)) - x1) / t_1))
	t_4 = Float64(Float64(x2 * 2.0) - 3.0)
	t_5 = Float64(x2 * t_4)
	t_6 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(t_1 * Float64(Float64(6.0 * Float64(x1 * x1)) + Float64(t_4 * Float64(Float64(x1 * 2.0) * Float64(3.0 + Float64(-1.0 / x1)))))))))))
	t_7 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x1 * t_5)))))
	tmp = 0.0
	if (x1 <= -5.1e+95)
		tmp = t_0;
	elseif (x1 <= -26000000.0)
		tmp = t_6;
	elseif (x1 <= -3.4e-207)
		tmp = t_7;
	elseif (x1 <= 8.5e-239)
		tmp = t_0;
	elseif (x1 <= 460.0)
		tmp = t_7;
	elseif (x1 <= 5.2e+125)
		tmp = t_6;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * t_5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	t_1 = (x1 * x1) + 1.0;
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	t_4 = (x2 * 2.0) - 3.0;
	t_5 = x2 * t_4;
	t_6 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_1 * ((6.0 * (x1 * x1)) + (t_4 * ((x1 * 2.0) * (3.0 + (-1.0 / x1))))))))));
	t_7 = x1 + (t_3 + (x1 + (4.0 * (x1 * t_5))));
	tmp = 0.0;
	if (x1 <= -5.1e+95)
		tmp = t_0;
	elseif (x1 <= -26000000.0)
		tmp = t_6;
	elseif (x1 <= -3.4e-207)
		tmp = t_7;
	elseif (x1 <= 8.5e-239)
		tmp = t_0;
	elseif (x1 <= 460.0)
		tmp = t_7;
	elseif (x1 <= 5.2e+125)
		tmp = t_6;
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * t_5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$5 = N[(x2 * t$95$4), $MachinePrecision]}, Block[{t$95$6 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(t$95$4 * N[(N[(x1 * 2.0), $MachinePrecision] * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x1 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.1e+95], t$95$0, If[LessEqual[x1, -26000000.0], t$95$6, If[LessEqual[x1, -3.4e-207], t$95$7, If[LessEqual[x1, 8.5e-239], t$95$0, If[LessEqual[x1, 460.0], t$95$7, If[LessEqual[x1, 5.2e+125], t$95$6, N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.10000000000000003e95 or -3.39999999999999999e-207 < x1 < 8.49999999999999958e-239

   1. Initial program 43.5%

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

   3. Taylor expanded in x1 around 0 33.7%

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

   4. Taylor expanded in x1 around 0 34.3%

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

      1. fma-def 34.4%

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

      2. fma-neg 34.4%

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

      3. fma-neg 34.4%

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

      4. metadata-eval 34.4%

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

      5. metadata-eval 34.4%

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

   6. Simplified 34.4%

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

   7. Taylor expanded in x2 around 0 53.3%

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

   if -5.10000000000000003e95 < x1 < -2.6e7 or 460 < x1 < 5.20000000000000006e125

   1. Initial program 97.2%

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

   3. Taylor expanded in x1 around inf 81.3%

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

   4. Taylor expanded in x1 around inf 74.2%

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

   5. Taylor expanded in x1 around 0 72.2%

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

   6. Taylor expanded in x1 around inf 74.3%

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

   if -2.6e7 < x1 < -3.39999999999999999e-207 or 8.49999999999999958e-239 < x1 < 460

   1. Initial program 99.3%

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

   3. Taylor expanded in x1 around 0 85.5%

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

   if 5.20000000000000006e125 < x1

   1. Initial program 12.5%

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

   3. Taylor expanded in x1 around 0 9.5%

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

   4. Taylor expanded in x1 around inf 47.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.1 \cdot 10^{+95}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -26000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(x2 \cdot 2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -3.4 \cdot 10^{-207}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq 460:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 5.2 \cdot 10^{+125}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(6 \cdot \left(x1 \cdot x1\right) + \left(x2 \cdot 2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x2 \cdot \left(x2 \cdot 2 - 3\right)\\ t_1 := x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -9 \cdot 10^{-215}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot t\_0\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot t\_0 + -1\right) + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x2 (- (* x2 2.0) 3.0)))
        (t_1 (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))))
   (if (<= x1 -1.35e+154)
     t_1
     (if (<= x1 -9e-215)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (* 4.0 (* x1 t_0)))))
       (if (<= x1 6e-238) t_1 (+ (* x1 (+ (* 4.0 t_0) -1.0)) (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x2 * ((x2 * 2.0) - 3.0);
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = t_1;
	} else if (x1 <= -9e-215) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * t_0))));
	} else if (x1 <= 6e-238) {
		tmp = t_1;
	} else {
		tmp = (x1 * ((4.0 * t_0) + -1.0)) + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x2 * ((x2 * 2.0d0) - 3.0d0)
    t_1 = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    if (x1 <= (-1.35d+154)) then
        tmp = t_1
    else if (x1 <= (-9d-215)) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x1 * t_0))))
    else if (x1 <= 6d-238) then
        tmp = t_1
    else
        tmp = (x1 * ((4.0d0 * t_0) + (-1.0d0))) + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x2 * ((x2 * 2.0) - 3.0);
	double t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	double tmp;
	if (x1 <= -1.35e+154) {
		tmp = t_1;
	} else if (x1 <= -9e-215) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * t_0))));
	} else if (x1 <= 6e-238) {
		tmp = t_1;
	} else {
		tmp = (x1 * ((4.0 * t_0) + -1.0)) + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x2 * ((x2 * 2.0) - 3.0)
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	tmp = 0
	if x1 <= -1.35e+154:
		tmp = t_1
	elif x1 <= -9e-215:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * t_0))))
	elif x1 <= 6e-238:
		tmp = t_1
	else:
		tmp = (x1 * ((4.0 * t_0) + -1.0)) + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))
	t_1 = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))))
	tmp = 0.0
	if (x1 <= -1.35e+154)
		tmp = t_1;
	elseif (x1 <= -9e-215)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x1 * t_0)))));
	elseif (x1 <= 6e-238)
		tmp = t_1;
	else
		tmp = Float64(Float64(x1 * Float64(Float64(4.0 * t_0) + -1.0)) + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x2 * ((x2 * 2.0) - 3.0);
	t_1 = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	tmp = 0.0;
	if (x1 <= -1.35e+154)
		tmp = t_1;
	elseif (x1 <= -9e-215)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x1 * t_0))));
	elseif (x1 <= 6e-238)
		tmp = t_1;
	else
		tmp = (x1 * ((4.0 * t_0) + -1.0)) + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.35e+154], t$95$1, If[LessEqual[x1, -9e-215], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 6e-238], t$95$1, N[(N[(x1 * N[(N[(4.0 * t$95$0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.35000000000000003e154 or -9e-215 < x1 < 5.9999999999999999e-238

   1. Initial program 47.8%

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

   3. Taylor expanded in x1 around 0 36.4%

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

   4. Taylor expanded in x1 around 0 38.1%

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

      1. fma-def 38.2%

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

      2. fma-neg 38.2%

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

      3. fma-neg 38.2%

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

      4. metadata-eval 38.2%

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

      5. metadata-eval 38.2%

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

   6. Simplified 38.2%

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

   7. Taylor expanded in x2 around 0 60.0%

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

   if -1.35000000000000003e154 < x1 < -9e-215

   1. Initial program 83.3%

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

   3. Taylor expanded in x1 around 0 50.1%

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

   if 5.9999999999999999e-238 < x1

   1. Initial program 74.6%

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

   3. Taylor expanded in x1 around 0 50.3%

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

   4. Taylor expanded in x1 around 0 59.3%

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

      1. fma-def 59.3%

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

      2. fma-neg 59.3%

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

      3. fma-neg 59.3%

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

      4. metadata-eval 59.3%

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

      5. metadata-eval 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in x1 around 0 59.3%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{elif}\;x1 \leq -9 \cdot 10^{-215}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x1 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 6 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right) + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.3% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+94} \lor \neg \left(x1 \leq -1.8 \cdot 10^{-217}\right) \land x1 \leq 2.15 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right) + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -7.5e+94) (and (not (<= x1 -1.8e-217)) (<= x1 2.15e-238)))
   (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
   (+ (* x1 (+ (* 4.0 (* x2 (- (* x2 2.0) 3.0))) -1.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.5e+94) || (!(x1 <= -1.8e-217) && (x1 <= 2.15e-238))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)) + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-7.5d+94)) .or. (.not. (x1 <= (-1.8d-217))) .and. (x1 <= 2.15d-238)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else
        tmp = (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) + (-1.0d0))) + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -7.5e+94) || (!(x1 <= -1.8e-217) && (x1 <= 2.15e-238))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)) + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -7.5e+94) or (not (x1 <= -1.8e-217) and (x1 <= 2.15e-238)):
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	else:
		tmp = (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)) + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -7.5e+94) || (!(x1 <= -1.8e-217) && (x1 <= 2.15e-238)))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	else
		tmp = Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) + -1.0)) + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -7.5e+94) || (~((x1 <= -1.8e-217)) && (x1 <= 2.15e-238)))
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	else
		tmp = (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)) + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -7.5e+94], And[N[Not[LessEqual[x1, -1.8e-217]], $MachinePrecision], LessEqual[x1, 2.15e-238]]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -7.49999999999999978e94 or -1.79999999999999991e-217 < x1 < 2.14999999999999984e-238

   1. Initial program 42.9%

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

   3. Taylor expanded in x1 around 0 32.9%

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

   4. Taylor expanded in x1 around 0 33.6%

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

      1. fma-def 33.7%

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

      2. fma-neg 33.7%

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

      3. fma-neg 33.7%

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

      4. metadata-eval 33.7%

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

      5. metadata-eval 33.7%

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

   6. Simplified 33.7%

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

   7. Taylor expanded in x2 around 0 52.7%

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

   if -7.49999999999999978e94 < x1 < -1.79999999999999991e-217 or 2.14999999999999984e-238 < x1

   1. Initial program 82.4%

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

   3. Taylor expanded in x1 around 0 52.9%

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

   4. Taylor expanded in x1 around 0 59.0%

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

      1. fma-def 59.1%

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

      2. fma-neg 59.1%

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

      3. fma-neg 59.1%

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

      4. metadata-eval 59.1%

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

      5. metadata-eval 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in x1 around 0 59.1%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+94} \lor \neg \left(x1 \leq -1.8 \cdot 10^{-217}\right) \land x1 \leq 2.15 \cdot 10^{-238}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right) + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.0% accurate, 4.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{+94} \lor \neg \left(x1 \leq -1.85 \cdot 10^{-110}\right) \land x1 \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.8e+94) (and (not (<= x1 -1.85e-110)) (<= x1 1.8e-63)))
   (+ x1 (+ (* x1 -2.0) (* x2 (- (* x1 -12.0) 6.0))))
   (* x1 (+ (* 4.0 (* x2 (- (* x2 2.0) 3.0))) -1.0))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e+94) || (!(x1 <= -1.85e-110) && (x1 <= 1.8e-63))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.8d+94)) .or. (.not. (x1 <= (-1.85d-110))) .and. (x1 <= 1.8d-63)) then
        tmp = x1 + ((x1 * (-2.0d0)) + (x2 * ((x1 * (-12.0d0)) - 6.0d0)))
    else
        tmp = x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.8e+94) || (!(x1 <= -1.85e-110) && (x1 <= 1.8e-63))) {
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	} else {
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.8e+94) or (not (x1 <= -1.85e-110) and (x1 <= 1.8e-63)):
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)))
	else:
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.8e+94) || (!(x1 <= -1.85e-110) && (x1 <= 1.8e-63)))
		tmp = Float64(x1 + Float64(Float64(x1 * -2.0) + Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0))));
	else
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.8e+94) || (~((x1 <= -1.85e-110)) && (x1 <= 1.8e-63)))
		tmp = x1 + ((x1 * -2.0) + (x2 * ((x1 * -12.0) - 6.0)));
	else
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.8e+94], And[N[Not[LessEqual[x1, -1.85e-110]], $MachinePrecision], LessEqual[x1, 1.8e-63]]], N[(x1 + N[(N[(x1 * -2.0), $MachinePrecision] + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.79999999999999998e94 or -1.85000000000000008e-110 < x1 < 1.80000000000000004e-63

   1. Initial program 64.4%

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

   3. Taylor expanded in x1 around 0 53.6%

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

   4. Taylor expanded in x1 around 0 54.1%

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

      1. fma-def 54.2%

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

      2. fma-neg 54.2%

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

      3. fma-neg 54.2%

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

      4. metadata-eval 54.2%

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

      5. metadata-eval 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in x2 around 0 62.7%

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

   if -2.79999999999999998e94 < x1 < -1.85000000000000008e-110 or 1.80000000000000004e-63 < x1

   1. Initial program 74.6%

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

   3. Taylor expanded in x1 around 0 37.4%

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

   4. Taylor expanded in x1 around 0 46.2%

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

      1. fma-def 46.2%

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

      2. fma-neg 46.2%

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

      3. fma-neg 46.2%

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

      4. metadata-eval 46.2%

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

      5. metadata-eval 46.2%

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

   6. Simplified 46.2%

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

   7. Taylor expanded in x1 around inf 43.1%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.8 \cdot 10^{+94} \lor \neg \left(x1 \leq -1.85 \cdot 10^{-110}\right) \land x1 \leq 1.8 \cdot 10^{-63}:\\ \;\;\;\;x1 + \left(x1 \cdot -2 + x2 \cdot \left(x1 \cdot -12 - 6\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-118} \lor \neg \left(x1 \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.15e-118) (not (<= x1 1.45e-126)))
   (* x1 (+ (* 4.0 (* x2 (- (* x2 2.0) 3.0))) -1.0))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.15e-118) || !(x1 <= 1.45e-126)) {
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.15d-118)) .or. (.not. (x1 <= 1.45d-126))) then
        tmp = x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) + (-1.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.15e-118) || !(x1 <= 1.45e-126)) {
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.15e-118) or not (x1 <= 1.45e-126):
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0)
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.15e-118) || !(x1 <= 1.45e-126))
		tmp = Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) + -1.0));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.15e-118) || ~((x1 <= 1.45e-126)))
		tmp = x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) + -1.0);
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.15e-118], N[Not[LessEqual[x1, 1.45e-126]], $MachinePrecision]], N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.1500000000000001e-118 or 1.44999999999999994e-126 < x1

   1. Initial program 55.7%

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

   3. Taylor expanded in x1 around 0 31.2%

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

   4. Taylor expanded in x1 around 0 37.4%

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

      1. fma-def 37.4%

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

      2. fma-neg 37.4%

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

      3. fma-neg 37.4%

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

      4. metadata-eval 37.4%

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

      5. metadata-eval 37.4%

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

   6. Simplified 37.4%

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

   7. Taylor expanded in x1 around inf 33.2%

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

   if -1.1500000000000001e-118 < x1 < 1.44999999999999994e-126

   1. Initial program 99.6%

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

   3. Taylor expanded in x1 around 0 80.3%

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

   4. Taylor expanded in x1 around 0 72.1%

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

      1. *-commutative 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in x1 around 0 72.3%

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

      1. *-commutative 72.3%

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

   9. Simplified 72.3%

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

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.15 \cdot 10^{-118} \lor \neg \left(x1 \leq 1.45 \cdot 10^{-126}\right):\\ \;\;\;\;x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.6% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 7.1 \cdot 10^{-174}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -2.4e-122)
   (* x2 -6.0)
   (if (<= x2 7.1e-174) (- x1) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.4e-122) {
		tmp = x2 * -6.0;
	} else if (x2 <= 7.1e-174) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-2.4d-122)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 7.1d-174) then
        tmp = -x1
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -2.4e-122) {
		tmp = x2 * -6.0;
	} else if (x2 <= 7.1e-174) {
		tmp = -x1;
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -2.4e-122:
		tmp = x2 * -6.0
	elif x2 <= 7.1e-174:
		tmp = -x1
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -2.4e-122)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 7.1e-174)
		tmp = Float64(-x1);
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -2.4e-122)
		tmp = x2 * -6.0;
	elseif (x2 <= 7.1e-174)
		tmp = -x1;
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -2.4e-122], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 7.1e-174], (-x1), N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -2.39999999999999987e-122

   1. Initial program 68.4%

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

   3. Taylor expanded in x1 around 0 48.9%

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

   4. Taylor expanded in x1 around 0 34.9%

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

      1. *-commutative 34.9%

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

   6. Simplified 34.9%

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

   7. Taylor expanded in x1 around 0 35.3%

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

      1. *-commutative 35.3%

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

   9. Simplified 35.3%

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

   if -2.39999999999999987e-122 < x2 < 7.0999999999999999e-174

   1. Initial program 73.2%

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

   3. Taylor expanded in x1 around 0 41.6%

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

   4. Taylor expanded in x1 around 0 42.6%

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

      1. fma-def 42.6%

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

      2. fma-neg 42.6%

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

      3. fma-neg 42.6%

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

      4. metadata-eval 42.6%

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

      5. metadata-eval 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in x2 around 0 31.8%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 31.8%

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

      2. metadata-eval 31.8%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. neg-mul-1 31.8%

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

   9. Simplified 31.8%

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

   if 7.0999999999999999e-174 < x2

   1. Initial program 67.3%

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

   3. Taylor expanded in x1 around 0 46.7%

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

   4. Taylor expanded in x1 around 0 29.1%

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

      1. *-commutative 29.1%

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

   6. Simplified 29.1%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 7.1 \cdot 10^{-174}:\\ \;\;\;\;-x1\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.3% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-122} \lor \neg \left(x2 \leq 4.3 \cdot 10^{-175}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.8e-122) (not (<= x2 4.3e-175))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.8e-122) || !(x2 <= 4.3e-175)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.8d-122)) .or. (.not. (x2 <= 4.3d-175))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.8e-122) || !(x2 <= 4.3e-175)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.8e-122) or not (x2 <= 4.3e-175):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.8e-122) || !(x2 <= 4.3e-175))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.8e-122) || ~((x2 <= 4.3e-175)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.8e-122], N[Not[LessEqual[x2, 4.3e-175]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.7999999999999999e-122 or 4.29999999999999998e-175 < x2

   1. Initial program 67.8%

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

   3. Taylor expanded in x1 around 0 47.6%

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

   4. Taylor expanded in x1 around 0 31.6%

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

      1. *-commutative 31.6%

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

   6. Simplified 31.6%

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

   7. Taylor expanded in x1 around 0 31.3%

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

      1. *-commutative 31.3%

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

   9. Simplified 31.3%

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

   if -2.7999999999999999e-122 < x2 < 4.29999999999999998e-175

   1. Initial program 73.2%

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

   3. Taylor expanded in x1 around 0 41.6%

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

   4. Taylor expanded in x1 around 0 42.6%

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

      1. fma-def 42.6%

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

      2. fma-neg 42.6%

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

      3. fma-neg 42.6%

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

      4. metadata-eval 42.6%

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

      5. metadata-eval 42.6%

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

   6. Simplified 42.6%

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

   7. Taylor expanded in x2 around 0 31.8%

      \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
   8. Step-by-step derivation

      1. distribute-rgt1-in 31.8%

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

      2. metadata-eval 31.8%

         \[\leadsto \color{blue}{-1} \cdot x1 \]

      3. neg-mul-1 31.8%

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

   9. Simplified 31.8%

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

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.8 \cdot 10^{-122} \lor \neg \left(x2 \leq 4.3 \cdot 10^{-175}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 13.9% accurate, 63.5× 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 Float64(-x1)
end

MATLAB

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

Wolfram

code[x1_, x2_] := (-x1)

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 46.2%

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

4. Taylor expanded in x1 around 0 50.5%

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

   1. fma-def 50.5%

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

   2. fma-neg 50.5%

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

   3. fma-neg 50.5%

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

   4. metadata-eval 50.5%

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

   5. metadata-eval 50.5%

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

6. Simplified 50.5%

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

7. Taylor expanded in x2 around 0 11.2%

   \[\leadsto \color{blue}{x1 + -2 \cdot x1} \]
8. Step-by-step derivation

   1. distribute-rgt1-in 11.2%

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

   2. metadata-eval 11.2%

      \[\leadsto \color{blue}{-1} \cdot x1 \]

   3. neg-mul-1 11.2%

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

9. Simplified 11.2%

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

10. Final simplification 11.2%

    \[\leadsto -x1 \]
11. Add Preprocessing

Alternative 18: 3.3% accurate, 127.0× speedup

Math

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

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

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

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 69.1%

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

3. Taylor expanded in x1 around 0 46.2%

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

4. Taylor expanded in x1 around 0 26.6%

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

   1. *-commutative 26.6%

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

6. Simplified 26.6%

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

7. Taylor expanded in x1 around inf 3.1%

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

8. Final simplification 3.1%

   \[\leadsto x1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(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))))))