Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.5% → 99.4%

Time: 32.9s

Alternatives: 17

Speedup: 6.0×

• 47.6% 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: 69.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(x1, x1 \cdot 3, 2 \cdot x2\right)\\ t_1 := -1 - x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := t\_2 + 2 \cdot x2\\ t_4 := \frac{x1 - t\_3}{t\_1}\\ t_5 := \frac{t\_3 - x1}{t\_1}\\ t_6 := \frac{t\_0 - x1}{\mathsf{fma}\left(x1, x1, 1\right)}\\ t_7 := 3 \cdot \left(x1 \cdot x1\right)\\ t_8 := \frac{x1 - t\_0}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t\_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_5\right) + \left(\left(x1 \cdot 2\right) \cdot t\_4\right) \cdot \left(3 + t\_5\right)\right) + t\_2 \cdot t\_4\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 - \left(t\_2 - 2 \cdot x2\right)}{t\_1}\right) \leq \infty:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, \frac{t\_7 - \mathsf{fma}\left(2, x2, x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t\_6, 4, -6\right), \left(x1 \cdot \left(2 \cdot t\_8\right)\right) \cdot \left(t\_8 - -3\right)\right), \mathsf{fma}\left(t\_7, t\_6, {x1}^{3}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (fma x1 (* x1 3.0) (* 2.0 x2)))
        (t_1 (- -1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (+ t_2 (* 2.0 x2)))
        (t_4 (/ (- x1 t_3) t_1))
        (t_5 (/ (- t_3 x1) t_1))
        (t_6 (/ (- t_0 x1) (fma x1 x1 1.0)))
        (t_7 (* 3.0 (* x1 x1)))
        (t_8 (/ (- x1 t_0) (fma x1 x1 1.0))))
   (if (<=
        (+
         x1
         (+
          (+
           x1
           (+
            (+
             (*
              t_1
              (+
               (* (* x1 x1) (+ 6.0 (* 4.0 t_5)))
               (* (* (* x1 2.0) t_4) (+ 3.0 t_5))))
             (* t_2 t_4))
            (* x1 (* x1 x1))))
          (* 3.0 (/ (- x1 (- t_2 (* 2.0 x2))) t_1))))
        INFINITY)
     (+
      x1
      (fma
       3.0
       (/ (- t_7 (fma 2.0 x2 x1)) (fma x1 x1 1.0))
       (+
        x1
        (fma
         (fma x1 x1 1.0)
         (fma x1 (* x1 (fma t_6 4.0 -6.0)) (* (* x1 (* 2.0 t_8)) (- t_8 -3.0)))
         (fma t_7 t_6 (pow x1 3.0))))))
     (* 6.0 (pow x1 4.0)))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), (2.0 * x2));
	double t_1 = -1.0 - (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = t_2 + (2.0 * x2);
	double t_4 = (x1 - t_3) / t_1;
	double t_5 = (t_3 - x1) / t_1;
	double t_6 = (t_0 - x1) / fma(x1, x1, 1.0);
	double t_7 = 3.0 * (x1 * x1);
	double t_8 = (x1 - t_0) / fma(x1, x1, 1.0);
	double tmp;
	if ((x1 + ((x1 + (((t_1 * (((x1 * x1) * (6.0 + (4.0 * t_5))) + (((x1 * 2.0) * t_4) * (3.0 + t_5)))) + (t_2 * t_4)) + (x1 * (x1 * x1)))) + (3.0 * ((x1 - (t_2 - (2.0 * x2))) / t_1)))) <= ((double) INFINITY)) {
		tmp = x1 + fma(3.0, ((t_7 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_6, 4.0, -6.0)), ((x1 * (2.0 * t_8)) * (t_8 - -3.0))), fma(t_7, t_6, pow(x1, 3.0)))));
	} else {
		tmp = 6.0 * pow(x1, 4.0);
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = fma(x1, Float64(x1 * 3.0), Float64(2.0 * x2))
	t_1 = Float64(-1.0 - Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(t_2 + Float64(2.0 * x2))
	t_4 = Float64(Float64(x1 - t_3) / t_1)
	t_5 = Float64(Float64(t_3 - x1) / t_1)
	t_6 = Float64(Float64(t_0 - x1) / fma(x1, x1, 1.0))
	t_7 = Float64(3.0 * Float64(x1 * x1))
	t_8 = Float64(Float64(x1 - t_0) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_5))) + Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(3.0 + t_5)))) + Float64(t_2 * t_4)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(x1 - Float64(t_2 - Float64(2.0 * x2))) / t_1)))) <= Inf)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(t_7 - fma(2.0, x2, x1)) / fma(x1, x1, 1.0)), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_6, 4.0, -6.0)), Float64(Float64(x1 * Float64(2.0 * t_8)) * Float64(t_8 - -3.0))), fma(t_7, t_6, (x1 ^ 3.0))))));
	else
		tmp = Float64(6.0 * (x1 ^ 4.0));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 - t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$6 = N[(N[(t$95$0 - x1), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$7 = N[(3.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$8 = N[(N[(x1 - t$95$0), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(3.0 + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * t$95$4), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x1 - N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x1 + N[(3.0 * N[(N[(t$95$7 - 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$6 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * N[(2.0 * t$95$8), $MachinePrecision]), $MachinePrecision] * N[(t$95$8 - -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$7 * t$95$6 + N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.5%

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

   3. Simplified 99.7%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.8%

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

Alternative 2: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \frac{x1 - t\_1}{t\_2}\\ t_4 := \frac{t\_1 - x1}{t\_2}\\ t_5 := x1 + \left(\left(x1 + \left(\left(t\_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_4\right) + \left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(3 + t\_4\right)\right) + t\_0 \cdot t\_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{x1 - \left(t\_0 - 2 \cdot x2\right)}{t\_2}\right)\\ \mathbf{if}\;t\_5 \leq \infty:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \end{array} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))))) < +inf.0

   1. Initial program 99.5%

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

   if +inf.0 < (+.f64 x1 (+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (+.f64 (*.f64 (*.f64 (*.f64 #s(literal 2 binary64) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) (-.f64 (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) #s(literal 3 binary64))) (*.f64 (*.f64 x1 x1) (-.f64 (*.f64 #s(literal 4 binary64) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64)))) #s(literal 6 binary64)))) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))) (*.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (/.f64 (-.f64 (+.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))) (*.f64 (*.f64 x1 x1) x1)) x1) (*.f64 #s(literal 3 binary64) (/.f64 (-.f64 (-.f64 (*.f64 (*.f64 #s(literal 3 binary64) x1) x1) (*.f64 #s(literal 2 binary64) x2)) x1) (+.f64 (*.f64 x1 x1) #s(literal 1 binary64))))))

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 3: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \frac{t\_1 - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -9.6 \cdot 10^{+26} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+22}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1}}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t\_1}{t\_2}\right) \cdot \left(3 + t\_3\right)\right) - 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (/ (- t_1 x1) t_2)))
   (if (or (<= x1 -9.6e+26) (not (<= x1 2.1e+22)))
     (*
      (pow x1 4.0)
      (- 6.0 (/ (- 3.0 (/ (- 9.0 (* 4.0 (- 3.0 (* 2.0 x2)))) x1)) x1)))
     (+
      x1
      (+
       (+
        x1
        (-
         (* x1 (* x1 x1))
         (-
          (*
           (+ (* x1 x1) 1.0)
           (+
            (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
            (* (* (* x1 2.0) (/ (- x1 t_1) t_2)) (+ 3.0 t_3))))
          (* 3.0 t_0))))
       (* 3.0 (- (* x2 -2.0) x1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 - x1) / t_2;
	double tmp;
	if ((x1 <= -9.6e+26) || !(x1 <= 2.1e+22)) {
		tmp = pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	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 = t_0 + (2.0d0 * x2)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = (t_1 - x1) / t_2
    if ((x1 <= (-9.6d+26)) .or. (.not. (x1 <= 2.1d+22))) then
        tmp = (x1 ** 4.0d0) * (6.0d0 - ((3.0d0 - ((9.0d0 - (4.0d0 * (3.0d0 - (2.0d0 * x2)))) / x1)) / x1))
    else
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + (((x1 * 2.0d0) * ((x1 - t_1) / t_2)) * (3.0d0 + t_3)))) - (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    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 = t_0 + (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 - x1) / t_2;
	double tmp;
	if ((x1 <= -9.6e+26) || !(x1 <= 2.1e+22)) {
		tmp = Math.pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	} else {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = -1.0 - (x1 * x1)
	t_3 = (t_1 - x1) / t_2
	tmp = 0
	if (x1 <= -9.6e+26) or not (x1 <= 2.1e+22):
		tmp = math.pow(x1, 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1))
	else:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(t_1 - x1) / t_2)
	tmp = 0.0
	if ((x1 <= -9.6e+26) || !(x1 <= 2.1e+22))
		tmp = Float64((x1 ^ 4.0) * Float64(6.0 - Float64(Float64(3.0 - Float64(Float64(9.0 - Float64(4.0 * Float64(3.0 - Float64(2.0 * x2)))) / x1)) / x1)));
	else
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2)) * Float64(3.0 + t_3)))) - Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = -1.0 - (x1 * x1);
	t_3 = (t_1 - x1) / t_2;
	tmp = 0.0;
	if ((x1 <= -9.6e+26) || ~((x1 <= 2.1e+22)))
		tmp = (x1 ^ 4.0) * (6.0 - ((3.0 - ((9.0 - (4.0 * (3.0 - (2.0 * x2)))) / x1)) / x1));
	else
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[x1, -9.6e+26], N[Not[LessEqual[x1, 2.1e+22]], $MachinePrecision]], N[(N[Power[x1, 4.0], $MachinePrecision] * N[(6.0 - N[(N[(3.0 - N[(N[(9.0 - N[(4.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision] / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.60000000000000018e26 or 2.0999999999999998e22 < x1

   1. Initial program 38.6%

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

   3. Simplified 38.5%

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

   5. Taylor expanded in x1 around -inf 99.9%

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

   if -9.60000000000000018e26 < x1 < 2.0999999999999998e22

   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

   3. Taylor expanded in x1 around inf 97.6%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.6 \cdot 10^{+26} \lor \neg \left(x1 \leq 2.1 \cdot 10^{+22}\right):\\ \;\;\;\;{x1}^{4} \cdot \left(6 - \frac{3 - \frac{9 - 4 \cdot \left(3 - 2 \cdot x2\right)}{x1}}{x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ t_3 := \frac{t\_2 - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+64}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t\_2}{t\_0}\right) \cdot \left(3 + t\_3\right)\right) - 3 \cdot t\_1\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2)))
        (t_3 (/ (- t_2 x1) t_0)))
   (if (<= x1 -4.3e+64)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 2e+153)
       (+
        x1
        (+
         (+
          x1
          (-
           (* x1 (* x1 x1))
           (-
            (*
             (+ (* x1 x1) 1.0)
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
              (* (* (* x1 2.0) (/ (- x1 t_2) t_0)) (+ 3.0 t_3))))
            (* 3.0 t_1))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (t_2 - x1) / t_0;
	double tmp;
	if (x1 <= -4.3e+64) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + t_3)))) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	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 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    t_3 = (t_2 - x1) / t_0
    if (x1 <= (-4.3d+64)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 2d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + (((x1 * 2.0d0) * ((x1 - t_2) / t_0)) * (3.0d0 + t_3)))) - (3.0d0 * t_1)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double t_3 = (t_2 - x1) / t_0;
	double tmp;
	if (x1 <= -4.3e+64) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + t_3)))) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	t_3 = (t_2 - x1) / t_0
	tmp = 0
	if x1 <= -4.3e+64:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 2e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + t_3)))) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	t_3 = Float64(Float64(t_2 - x1) / t_0)
	tmp = 0.0
	if (x1 <= -4.3e+64)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_2) / t_0)) * Float64(3.0 + t_3)))) - Float64(3.0 * t_1)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	t_3 = (t_2 - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -4.3e+64)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 2e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + t_3)))) - (3.0 * t_1)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -4.3e+64], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.2999999999999998e64

   1. Initial program 15.3%

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

   3. Simplified 15.3%

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

   5. Taylor expanded in x1 around inf 98.0%

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

   if -4.2999999999999998e64 < x1 < 2e153

   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 98.1%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if 2e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.3 \cdot 10^{+64}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := t\_0 + 2 \cdot x2\\ t_2 := -1 - x1 \cdot x1\\ t_3 := \frac{t\_1 - x1}{t\_2}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot t\_3\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t\_1}{t\_2}\right) \cdot \left(3 + t\_3\right)\right) - 3 \cdot t\_0\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ t_0 (* 2.0 x2)))
        (t_2 (- -1.0 (* x1 x1)))
        (t_3 (/ (- t_1 x1) t_2)))
   (if (<= x1 -5.6e+102)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 2e+153)
       (+
        x1
        (+
         (+
          x1
          (-
           (* x1 (* x1 x1))
           (-
            (*
             (+ (* x1 x1) 1.0)
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 t_3)))
              (* (* (* x1 2.0) (/ (- x1 t_1) t_2)) (+ 3.0 t_3))))
            (* 3.0 t_0))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = t_0 + (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 - x1) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	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 = t_0 + (2.0d0 * x2)
    t_2 = (-1.0d0) - (x1 * x1)
    t_3 = (t_1 - x1) / t_2
    if (x1 <= (-5.6d+102)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 2d+153) then
        tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 + (4.0d0 * t_3))) + (((x1 * 2.0d0) * ((x1 - t_1) / t_2)) * (3.0d0 + t_3)))) - (3.0d0 * t_0)))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    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 = t_0 + (2.0 * x2);
	double t_2 = -1.0 - (x1 * x1);
	double t_3 = (t_1 - x1) / t_2;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+153) {
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = t_0 + (2.0 * x2)
	t_2 = -1.0 - (x1 * x1)
	t_3 = (t_1 - x1) / t_2
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 2e+153:
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(t_0 + Float64(2.0 * x2))
	t_2 = Float64(-1.0 - Float64(x1 * x1))
	t_3 = Float64(Float64(t_1 - x1) / t_2)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) - Float64(Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * t_3))) + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_1) / t_2)) * Float64(3.0 + t_3)))) - Float64(3.0 * t_0)))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = t_0 + (2.0 * x2);
	t_2 = -1.0 - (x1 * x1);
	t_3 = (t_1 - x1) / t_2;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 2e+153)
		tmp = x1 + ((x1 + ((x1 * (x1 * x1)) - ((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * t_3))) + (((x1 * 2.0) * ((x1 - t_1) / t_2)) * (3.0 + t_3)))) - (3.0 * t_0)))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	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[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t$95$1 - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] * N[(3.0 + t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 2.2%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in x1 around 0 73.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -5.60000000000000037e102 < x1 < 2e153

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   if 2e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) - \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(t\_1 - 2 \cdot x2\right) - x1}{t\_0} - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - t\_2}{t\_0}\right) \cdot \left(3 + \frac{t\_2 - x1}{t\_0}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - 3 \cdot t\_1\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2))))
   (if (<= x1 -1e+104)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 2e+153)
       (-
        x1
        (-
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_0))
         (-
          x1
          (-
           (-
            (*
             (+ (* x1 x1) 1.0)
             (-
              (* (* (* x1 2.0) (/ (- x1 t_2) t_0)) (+ 3.0 (/ (- t_2 x1) t_0)))
              (* (* x1 x1) 6.0)))
            (* 3.0 t_1))
           (* x1 (* x1 x1))))))
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double tmp;
	if (x1 <= -1e+104) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+153) {
		tmp = x1 - ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) - (x1 - (((((x1 * x1) + 1.0) * ((((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + ((t_2 - x1) / t_0))) - ((x1 * x1) * 6.0))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	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 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    if (x1 <= (-1d+104)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 2d+153) then
        tmp = x1 - ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_0)) - (x1 - (((((x1 * x1) + 1.0d0) * ((((x1 * 2.0d0) * ((x1 - t_2) / t_0)) * (3.0d0 + ((t_2 - x1) / t_0))) - ((x1 * x1) * 6.0d0))) - (3.0d0 * t_1)) - (x1 * (x1 * x1)))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double tmp;
	if (x1 <= -1e+104) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2e+153) {
		tmp = x1 - ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) - (x1 - (((((x1 * x1) + 1.0) * ((((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + ((t_2 - x1) / t_0))) - ((x1 * x1) * 6.0))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	tmp = 0
	if x1 <= -1e+104:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 2e+153:
		tmp = x1 - ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) - (x1 - (((((x1 * x1) + 1.0) * ((((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + ((t_2 - x1) / t_0))) - ((x1 * x1) * 6.0))) - (3.0 * t_1)) - (x1 * (x1 * x1)))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -1e+104)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 2e+153)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_0)) - Float64(x1 - Float64(Float64(Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x1 - t_2) / t_0)) * Float64(3.0 + Float64(Float64(t_2 - x1) / t_0))) - Float64(Float64(x1 * x1) * 6.0))) - Float64(3.0 * t_1)) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -1e+104)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 2e+153)
		tmp = x1 - ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_0)) - (x1 - (((((x1 * x1) + 1.0) * ((((x1 * 2.0) * ((x1 - t_2) / t_0)) * (3.0 + ((t_2 - x1) / t_0))) - ((x1 * x1) * 6.0))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+104], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+153], N[(x1 - N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] * N[(3.0 + N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e104

   1. Initial program 2.2%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in x1 around 0 73.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1e104 < x1 < 2e153

   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 98.2%

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

   4. Taylor expanded in x1 around inf 96.6%

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

   if 2e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1}\right) \cdot \left(3 + \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) - \left(x1 \cdot x1\right) \cdot 6\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -1 - x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := t\_1 + 2 \cdot x2\\ \mathbf{if}\;x1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{t\_2 - x1}{t\_0}\right) + \left(\frac{x1 - t\_2}{t\_0} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right) - 3 \cdot t\_1\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- -1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ t_1 (* 2.0 x2))))
   (if (<= x1 -1e+104)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
     (if (<= x1 4.5e+153)
       (-
        x1
        (-
         (* 3.0 (- x1 (* x2 -2.0)))
         (-
          x1
          (-
           (-
            (*
             (+ (* x1 x1) 1.0)
             (+
              (* (* x1 x1) (+ 6.0 (* 4.0 (/ (- t_2 x1) t_0))))
              (* (- (/ (- x1 t_2) t_0) 3.0) (* (* x1 2.0) (- x1 (* 2.0 x2))))))
            (* 3.0 t_1))
           (* x1 (* x1 x1))))))
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double tmp;
	if (x1 <= -1e+104) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * ((t_2 - x1) / t_0)))) + ((((x1 - t_2) / t_0) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	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 = (-1.0d0) - (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = t_1 + (2.0d0 * x2)
    if (x1 <= (-1d+104)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 4.5d+153) then
        tmp = x1 - ((3.0d0 * (x1 - (x2 * (-2.0d0)))) - (x1 - (((((x1 * x1) + 1.0d0) * (((x1 * x1) * (6.0d0 + (4.0d0 * ((t_2 - x1) / t_0)))) + ((((x1 - t_2) / t_0) - 3.0d0) * ((x1 * 2.0d0) * (x1 - (2.0d0 * x2)))))) - (3.0d0 * t_1)) - (x1 * (x1 * x1)))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = -1.0 - (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = t_1 + (2.0 * x2);
	double tmp;
	if (x1 <= -1e+104) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 4.5e+153) {
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * ((t_2 - x1) / t_0)))) + ((((x1 - t_2) / t_0) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = -1.0 - (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = t_1 + (2.0 * x2)
	tmp = 0
	if x1 <= -1e+104:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 4.5e+153:
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * ((t_2 - x1) / t_0)))) + ((((x1 - t_2) / t_0) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))))) - (3.0 * t_1)) - (x1 * (x1 * x1)))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(-1.0 - Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(t_1 + Float64(2.0 * x2))
	tmp = 0.0
	if (x1 <= -1e+104)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 4.5e+153)
		tmp = Float64(x1 - Float64(Float64(3.0 * Float64(x1 - Float64(x2 * -2.0))) - Float64(x1 - Float64(Float64(Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(Float64(Float64(x1 * x1) * Float64(6.0 + Float64(4.0 * Float64(Float64(t_2 - x1) / t_0)))) + Float64(Float64(Float64(Float64(x1 - t_2) / t_0) - 3.0) * Float64(Float64(x1 * 2.0) * Float64(x1 - Float64(2.0 * x2)))))) - Float64(3.0 * t_1)) - Float64(x1 * Float64(x1 * x1))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = -1.0 - (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = t_1 + (2.0 * x2);
	tmp = 0.0;
	if (x1 <= -1e+104)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 4.5e+153)
		tmp = x1 - ((3.0 * (x1 - (x2 * -2.0))) - (x1 - (((((x1 * x1) + 1.0) * (((x1 * x1) * (6.0 + (4.0 * ((t_2 - x1) / t_0)))) + ((((x1 - t_2) / t_0) - 3.0) * ((x1 * 2.0) * (x1 - (2.0 * x2)))))) - (3.0 * t_1)) - (x1 * (x1 * x1)))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1e+104], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4.5e+153], N[(x1 - N[(N[(3.0 * N[(x1 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(N[(N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(6.0 + N[(4.0 * N[(N[(t$95$2 - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(x1 - t$95$2), $MachinePrecision] / t$95$0), $MachinePrecision] - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(x1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(3.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1e104

   1. Initial program 2.2%

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

   3. Simplified 26.7%

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

   5. Taylor expanded in x1 around 0 73.3%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 97.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -1e104 < x1 < 4.5000000000000001e153

   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 98.2%

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

   4. Taylor expanded in x1 around 0 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. *-commutative 99.4%

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

   6. Simplified 99.4%

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

   7. Taylor expanded in x1 around 0 95.1%

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

   if 4.5000000000000001e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 80.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{+104}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 4.5 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \left(x1 - x2 \cdot -2\right) - \left(x1 - \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(6 + 4 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1}\right) + \left(\frac{x1 - \left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right)}{-1 - x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x1 - 2 \cdot x2\right)\right)\right) - 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right) - x1 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 95.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 - x1 \cdot \left(x1 \cdot \left(3 - \left(x2 \cdot 8 - x1 \cdot \left(3 - x1 \cdot 6\right)\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ t_1 := x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+154}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq -15500000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq 43000000000:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (-
          x1
          (-
           (*
            3.0
            (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (- -1.0 (* x1 x1))))
           (-
            x1
            (*
             x1
             (+
              (* x1 (- 3.0 (- (* x2 8.0) (* x1 (- 3.0 (* x1 6.0))))))
              (* 6.0 (- 3.0 (* 2.0 x2)))))))))
        (t_1 (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))
   (if (<= x1 -5e+154)
     t_1
     (if (<= x1 -15500000000.0)
       t_0
       (if (<= x1 43000000000.0)
         (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
         (if (<= x1 2e+153) t_0 t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 - (x1 * ((x1 * (3.0 - ((x2 * 8.0) - (x1 * (3.0 - (x1 * 6.0)))))) + (6.0 * (3.0 - (2.0 * x2)))))));
	double t_1 = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	double tmp;
	if (x1 <= -5e+154) {
		tmp = t_1;
	} else if (x1 <= -15500000000.0) {
		tmp = t_0;
	} else if (x1 <= 43000000000.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 - ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((-1.0d0) - (x1 * x1)))) - (x1 - (x1 * ((x1 * (3.0d0 - ((x2 * 8.0d0) - (x1 * (3.0d0 - (x1 * 6.0d0)))))) + (6.0d0 * (3.0d0 - (2.0d0 * x2)))))))
    t_1 = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    if (x1 <= (-5d+154)) then
        tmp = t_1
    else if (x1 <= (-15500000000.0d0)) then
        tmp = t_0
    else if (x1 <= 43000000000.0d0) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 2d+153) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 - (x1 * ((x1 * (3.0 - ((x2 * 8.0) - (x1 * (3.0 - (x1 * 6.0)))))) + (6.0 * (3.0 - (2.0 * x2)))))));
	double t_1 = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	double tmp;
	if (x1 <= -5e+154) {
		tmp = t_1;
	} else if (x1 <= -15500000000.0) {
		tmp = t_0;
	} else if (x1 <= 43000000000.0) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 2e+153) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 - (x1 * ((x1 * (3.0 - ((x2 * 8.0) - (x1 * (3.0 - (x1 * 6.0)))))) + (6.0 * (3.0 - (2.0 * x2)))))))
	t_1 = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	tmp = 0
	if x1 <= -5e+154:
		tmp = t_1
	elif x1 <= -15500000000.0:
		tmp = t_0
	elif x1 <= 43000000000.0:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 2e+153:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 - Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(-1.0 - Float64(x1 * x1)))) - Float64(x1 - Float64(x1 * Float64(Float64(x1 * Float64(3.0 - Float64(Float64(x2 * 8.0) - Float64(x1 * Float64(3.0 - Float64(x1 * 6.0)))))) + Float64(6.0 * Float64(3.0 - Float64(2.0 * x2))))))))
	t_1 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))))
	tmp = 0.0
	if (x1 <= -5e+154)
		tmp = t_1;
	elseif (x1 <= -15500000000.0)
		tmp = t_0;
	elseif (x1 <= 43000000000.0)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 2e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 - ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / (-1.0 - (x1 * x1)))) - (x1 - (x1 * ((x1 * (3.0 - ((x2 * 8.0) - (x1 * (3.0 - (x1 * 6.0)))))) + (6.0 * (3.0 - (2.0 * x2)))))));
	t_1 = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	tmp = 0.0;
	if (x1 <= -5e+154)
		tmp = t_1;
	elseif (x1 <= -15500000000.0)
		tmp = t_0;
	elseif (x1 <= 43000000000.0)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 2e+153)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 - N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(-1.0 - N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 - N[(x1 * N[(N[(x1 * N[(3.0 - N[(N[(x2 * 8.0), $MachinePrecision] - N[(x1 * N[(3.0 - N[(x1 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5e+154], t$95$1, If[LessEqual[x1, -15500000000.0], t$95$0, If[LessEqual[x1, 43000000000.0], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 2e+153], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.00000000000000004e154 or 2e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 73.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 100.0%

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

   if -5.00000000000000004e154 < x1 < -1.55e10 or 4.3e10 < x1 < 2e153

   1. Initial program 83.0%

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

   3. Taylor expanded in x1 around inf 83.0%

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

   4. Taylor expanded in x1 around inf 81.4%

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

   5. Taylor expanded in x1 around 0 72.5%

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

   6. Taylor expanded in x2 around 0 98.3%

      \[\leadsto x1 + \left(\left(x1 \cdot \left(6 \cdot \left(2 \cdot x2 - 3\right) + x1 \cdot \left(\left(8 \cdot x2 + \color{blue}{x1 \cdot \left(6 \cdot x1 - 3\right)}\right) - 3\right)\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   if -1.55e10 < x1 < 4.3e10

   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 88.1%

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

   5. Taylor expanded in x1 around 0 85.5%

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

      1. fma-define 85.6%

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

      2. *-commutative 85.6%

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

      3. fmm-def 85.6%

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

      4. metadata-eval 85.6%

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

      5. cancel-sign-sub-inv 85.6%

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

      6. cancel-sign-sub-inv 85.6%

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

      7. metadata-eval 85.6%

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

      8. *-commutative 85.6%

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

      9. metadata-eval 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in x2 around 0 97.1%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+154}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -15500000000:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 - x1 \cdot \left(x1 \cdot \left(3 - \left(x2 \cdot 8 - x1 \cdot \left(3 - x1 \cdot 6\right)\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 43000000000:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+153}:\\ \;\;\;\;x1 - \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{-1 - x1 \cdot x1} - \left(x1 - x1 \cdot \left(x1 \cdot \left(3 - \left(x2 \cdot 8 - x1 \cdot \left(3 - x1 \cdot 6\right)\right)\right) + 6 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 1.56 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4e+17)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 2.9e-55)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (if (<= x1 1.56e+150)
       (+
        x1
        (+
         (* 3.0 (- (* x2 -2.0) x1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (-
            (* 3.0 (* x1 (* x1 3.0)))
            (* (+ (* x1 x1) 1.0) (* 4.0 (* x1 (* x2 (- 3.0 (* 2.0 x2)))))))))))
       (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2.9e-55) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 1.56e+150) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * (x1 * (x1 * 3.0))) - (((x1 * x1) + 1.0) * (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4d+17)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 2.9d-55) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else if (x1 <= 1.56d+150) then
        tmp = x1 + ((3.0d0 * ((x2 * (-2.0d0)) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * (x1 * (x1 * 3.0d0))) - (((x1 * x1) + 1.0d0) * (4.0d0 * (x1 * (x2 * (3.0d0 - (2.0d0 * x2))))))))))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 2.9e-55) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else if (x1 <= 1.56e+150) {
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * (x1 * (x1 * 3.0))) - (((x1 * x1) + 1.0) * (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))))))));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4e+17:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 2.9e-55:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	elif x1 <= 1.56e+150:
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * (x1 * (x1 * 3.0))) - (((x1 * x1) + 1.0) * (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))))))))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4e+17)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 2.9e-55)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	elseif (x1 <= 1.56e+150)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(x2 * -2.0) - x1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * Float64(x1 * Float64(x1 * 3.0))) - Float64(Float64(Float64(x1 * x1) + 1.0) * Float64(4.0 * Float64(x1 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2)))))))))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4e+17)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 2.9e-55)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	elseif (x1 <= 1.56e+150)
		tmp = x1 + ((3.0 * ((x2 * -2.0) - x1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * (x1 * (x1 * 3.0))) - (((x1 * x1) + 1.0) * (4.0 * (x1 * (x2 * (3.0 - (2.0 * x2))))))))));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4e+17], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.9e-55], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], If[LessEqual[x1, 1.56e+150], N[(x1 + N[(N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision] * N[(4.0 * N[(x1 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4e17

   1. Initial program 29.9%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in x1 around 0 56.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -4e17 < x1 < 2.9e-55

   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 87.4%

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

   5. Taylor expanded in x1 around 0 85.1%

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

      1. fma-define 85.3%

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

      2. *-commutative 85.3%

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

      3. fmm-def 85.3%

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

      4. metadata-eval 85.3%

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

      5. cancel-sign-sub-inv 85.3%

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

      6. cancel-sign-sub-inv 85.3%

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

      7. metadata-eval 85.3%

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

      8. *-commutative 85.3%

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

      9. metadata-eval 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in x2 around 0 97.5%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 2.9e-55 < x1 < 1.56e150

   1. Initial program 99.7%

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

   3. Taylor expanded in x1 around inf 95.5%

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

   4. Taylor expanded in x1 around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. *-commutative 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x1 around 0 64.4%

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

   if 1.56e150 < x1

   1. Initial program 2.8%

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

   3. Simplified 2.8%

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

   5. Taylor expanded in x1 around 0 78.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 97.5%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 2.9 \cdot 10^{-55}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{elif}\;x1 \leq 1.56 \cdot 10^{+150}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2 - x1\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) - \left(x1 \cdot x1 + 1\right) \cdot \left(4 \cdot \left(x1 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.1% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-85}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right) - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4e+17)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 1e-85)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (-
      (* x2 -6.0)
      (* x1 (- (- (* x2 (- 12.0 (* x2 8.0))) (* x1 9.0)) -1.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1e-85) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)) - -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 <= (-4d+17)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 1d-85) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) - (x1 * (((x2 * (12.0d0 - (x2 * 8.0d0))) - (x1 * 9.0d0)) - (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1e-85) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)) - -1.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4e+17:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 1e-85:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)) - -1.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4e+17)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 1e-85)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) - Float64(x1 * 9.0)) - -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4e+17)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 1e-85)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) - (x1 * (((x2 * (12.0 - (x2 * 8.0))) - (x1 * 9.0)) - -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4e+17], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-85], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4e17

   1. Initial program 29.9%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in x1 around 0 56.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -4e17 < x1 < 9.9999999999999998e-86

   1. Initial program 99.4%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x1 around 0 84.6%

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

      1. fma-define 84.8%

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

      2. *-commutative 84.8%

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

      3. fmm-def 84.8%

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

      4. metadata-eval 84.8%

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

      5. cancel-sign-sub-inv 84.8%

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

      6. cancel-sign-sub-inv 84.8%

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

      7. metadata-eval 84.8%

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

      8. *-commutative 84.8%

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

      9. metadata-eval 84.8%

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

   7. Simplified 84.8%

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

   8. Taylor expanded in x2 around 0 97.4%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 9.9999999999999998e-86 < x1

   1. Initial program 57.1%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in x1 around 0 56.6%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 61.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{\left(9 \cdot x1 + x2 \cdot \left(\left(8 \cdot x2 + 12 \cdot x1\right) - 12\right)\right)} - 1\right) \]

   7. Taylor expanded in x2 around inf 66.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(9 \cdot x1 + x2 \cdot \left(\color{blue}{8 \cdot x2} - 12\right)\right) - 1\right) \]
   8. Step-by-step derivation

      1. *-commutative 66.8%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(9 \cdot x1 + x2 \cdot \left(\color{blue}{x2 \cdot 8} - 12\right)\right) - 1\right) \]

   9. Simplified 66.8%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\left(9 \cdot x1 + x2 \cdot \left(\color{blue}{x2 \cdot 8} - 12\right)\right) - 1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-85}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(\left(x2 \cdot \left(12 - x2 \cdot 8\right) - x1 \cdot 9\right) - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.6% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -3.5e+17)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 1.15e+144)
     (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-3.5d+17)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 1.15d+144) then
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -3.5e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -3.5e+17:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 1.15e+144:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -3.5e+17)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 1.15e+144)
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -3.5e+17)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 1.15e+144)
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -3.5e+17], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.15e+144], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.5e17

   1. Initial program 29.9%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in x1 around 0 56.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -3.5e17 < x1 < 1.1500000000000001e144

   1. Initial program 99.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x1 around 0 72.8%

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

      1. fma-define 72.9%

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

      2. *-commutative 72.9%

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

      3. fmm-def 72.9%

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

      4. metadata-eval 72.9%

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

      5. cancel-sign-sub-inv 72.9%

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

      6. cancel-sign-sub-inv 72.9%

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

      7. metadata-eval 72.9%

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

      8. *-commutative 72.9%

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

      9. metadata-eval 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in x2 around 0 82.0%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]

   if 1.1500000000000001e144 < x1

   1. Initial program 10.3%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in x1 around 0 72.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 90.8%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.8% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -4e+17)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 1.15e+144)
     (- (* x2 -6.0) (* x1 (- (* x2 (- 12.0 (* x2 8.0))) -1.0)))
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-4d+17)) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 1.15d+144) then
        tmp = (x2 * (-6.0d0)) - (x1 * ((x2 * (12.0d0 - (x2 * 8.0d0))) - (-1.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -4e+17) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -4e+17:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 1.15e+144:
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -4e+17)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 1.15e+144)
		tmp = Float64(Float64(x2 * -6.0) - Float64(x1 * Float64(Float64(x2 * Float64(12.0 - Float64(x2 * 8.0))) - -1.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -4e+17)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 1.15e+144)
		tmp = (x2 * -6.0) - (x1 * ((x2 * (12.0 - (x2 * 8.0))) - -1.0));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -4e+17], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.15e+144], N[(N[(x2 * -6.0), $MachinePrecision] - N[(x1 * N[(N[(x2 * N[(12.0 - N[(x2 * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4e17

   1. Initial program 29.9%

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

   3. Simplified 47.4%

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

   5. Taylor expanded in x1 around 0 56.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 71.9%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if -4e17 < x1 < 1.1500000000000001e144

   1. Initial program 99.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in x1 around 0 72.8%

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

      1. fma-define 72.9%

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

      2. *-commutative 72.9%

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

      3. fmm-def 72.9%

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

      4. metadata-eval 72.9%

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

      5. cancel-sign-sub-inv 72.9%

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

      6. cancel-sign-sub-inv 72.9%

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

      7. metadata-eval 72.9%

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

      8. *-commutative 72.9%

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

      9. metadata-eval 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in x2 around 0 72.9%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)}\right) \]

   9. Taylor expanded in x1 around 0 72.8%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]

   if 1.1500000000000001e144 < x1

   1. Initial program 10.3%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in x1 around 0 72.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 90.8%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+17}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x2 \cdot -6 - x1 \cdot \left(x2 \cdot \left(12 - x2 \cdot 8\right) - -1\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.4% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.7 \cdot 10^{+254} \lor \neg \left(x2 \leq 10^{+171}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -1.7e+254) (not (<= x2 1e+171)))
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.7e+254) || !(x2 <= 1e+171)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-1.7d+254)) .or. (.not. (x2 <= 1d+171))) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -1.7e+254) || !(x2 <= 1e+171)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -1.7e+254) or not (x2 <= 1e+171):
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -1.7e+254) || !(x2 <= 1e+171))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -1.7e+254) || ~((x2 <= 1e+171)))
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -1.7e+254], N[Not[LessEqual[x2, 1e+171]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.7e254 or 9.99999999999999954e170 < x2

   1. Initial program 70.0%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in x1 around 0 68.2%

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

      1. fma-define 68.2%

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

      2. *-commutative 68.2%

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

      3. fmm-def 68.2%

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

      4. metadata-eval 68.2%

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

      5. cancel-sign-sub-inv 68.2%

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

      6. cancel-sign-sub-inv 68.2%

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

      7. metadata-eval 68.2%

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

      8. *-commutative 68.2%

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

      9. metadata-eval 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in x2 around 0 68.2%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)}\right) \]

   9. Taylor expanded in x1 around inf 68.2%

      \[\leadsto \color{blue}{x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]

   if -1.7e254 < x2 < 9.99999999999999954e170

   1. Initial program 68.5%

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

   3. Simplified 69.0%

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

   5. Taylor expanded in x1 around 0 64.2%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 67.6%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.7 \cdot 10^{+254} \lor \neg \left(x2 \leq 10^{+171}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.0% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{-98} \lor \neg \left(x1 \leq 3.7 \cdot 10^{-115}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1e-98) (not (<= x1 3.7e-115)))
   (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1e-98) || !(x1 <= 3.7e-115)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} 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 <= (-1d-98)) .or. (.not. (x1 <= 3.7d-115))) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1e-98) || !(x1 <= 3.7e-115)) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1e-98) or not (x1 <= 3.7e-115):
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1e-98) || !(x1 <= 3.7e-115))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1e-98) || ~((x1 <= 3.7e-115)))
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1e-98], N[Not[LessEqual[x1, 3.7e-115]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -9.99999999999999939e-99 or 3.7e-115 < x1

   1. Initial program 56.7%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in x1 around 0 38.7%

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

      1. fma-define 38.7%

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

      2. *-commutative 38.7%

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

      3. fmm-def 38.7%

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

      4. metadata-eval 38.7%

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

      5. cancel-sign-sub-inv 38.7%

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

      6. cancel-sign-sub-inv 38.7%

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

      7. metadata-eval 38.7%

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

      8. *-commutative 38.7%

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

      9. metadata-eval 38.7%

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

   7. Simplified 38.7%

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

   8. Taylor expanded in x2 around 0 38.7%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)}\right) \]

   9. Taylor expanded in x1 around inf 34.5%

      \[\leadsto \color{blue}{x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]

   if -9.99999999999999939e-99 < x1 < 3.7e-115

   1. Initial program 99.5%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x1 around 0 78.5%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1 \cdot 10^{-98} \lor \neg \left(x1 \leq 3.7 \cdot 10^{-115}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.2% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 2.4e-76)
   (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 (+ 9.0 (* x1 -19.0))))))
   (if (<= x1 1.15e+144)
     (* x1 (+ -1.0 (* x2 (- (* x2 8.0) 12.0))))
     (+ (* x2 -6.0) (* x1 (+ -1.0 (* x1 9.0)))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.4e-76) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= 2.4d-76) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * (9.0d0 + (x1 * (-19.0d0))))))
    else if (x1 <= 1.15d+144) then
        tmp = x1 * ((-1.0d0) + (x2 * ((x2 * 8.0d0) - 12.0d0)))
    else
        tmp = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + (x1 * 9.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= 2.4e-76) {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	} else if (x1 <= 1.15e+144) {
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	} else {
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= 2.4e-76:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))))
	elif x1 <= 1.15e+144:
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)))
	else:
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= 2.4e-76)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * Float64(9.0 + Float64(x1 * -19.0))))));
	elseif (x1 <= 1.15e+144)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * Float64(Float64(x2 * 8.0) - 12.0))));
	else
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(x1 * 9.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= 2.4e-76)
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * (9.0 + (x1 * -19.0)))));
	elseif (x1 <= 1.15e+144)
		tmp = x1 * (-1.0 + (x2 * ((x2 * 8.0) - 12.0)));
	else
		tmp = (x2 * -6.0) + (x1 * (-1.0 + (x1 * 9.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, 2.4e-76], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * N[(9.0 + N[(x1 * -19.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.15e+144], N[(x1 * N[(-1.0 + N[(x2 * N[(N[(x2 * 8.0), $MachinePrecision] - 12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(x1 * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < 2.40000000000000013e-76

   1. Initial program 74.4%

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

   3. Simplified 72.8%

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

   5. Taylor expanded in x1 around 0 67.0%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + \left(8 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + 2 \cdot \left(\left(1 + \left(-3 \cdot \left(3 + -2 \cdot x2\right) + 2 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\right) - -2 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right)\right)\right) - 3\right)\right)\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 74.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + -19 \cdot x1\right)} - 1\right) \]
   7. Step-by-step derivation

      1. *-commutative 74.5%

         \[\leadsto -6 \cdot x2 + x1 \cdot \left(x1 \cdot \left(9 + \color{blue}{x1 \cdot -19}\right) - 1\right) \]

   8. Simplified 74.5%

      \[\leadsto -6 \cdot x2 + x1 \cdot \left(\color{blue}{x1 \cdot \left(9 + x1 \cdot -19\right)} - 1\right) \]

   if 2.40000000000000013e-76 < x1 < 1.1500000000000001e144

   1. Initial program 99.6%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x1 around 0 40.9%

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

      1. fma-define 40.9%

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

      2. *-commutative 40.9%

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

      3. fmm-def 40.9%

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

      4. metadata-eval 40.9%

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

      5. cancel-sign-sub-inv 40.9%

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

      6. cancel-sign-sub-inv 40.9%

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

      7. metadata-eval 40.9%

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

      8. *-commutative 40.9%

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

      9. metadata-eval 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in x2 around 0 40.9%

      \[\leadsto \mathsf{fma}\left(-6, x2, x1 \cdot \color{blue}{\left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)}\right) \]

   9. Taylor expanded in x1 around inf 40.9%

      \[\leadsto \color{blue}{x1 \cdot \left(x2 \cdot \left(8 \cdot x2 - 12\right) - 1\right)} \]

   if 1.1500000000000001e144 < x1

   1. Initial program 10.3%

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

   3. Simplified 10.3%

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

   5. Taylor expanded in x1 around 0 72.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + x1 \cdot \left(\left(-4 \cdot \left(x2 \cdot \left(3 + -2 \cdot x2\right)\right) + x1 \cdot \left(\left(2 \cdot \left(3 + -4 \cdot x2\right) + \left(3 \cdot \left(3 - -2 \cdot x2\right) + \left(6 \cdot x2 + 8 \cdot x2\right)\right)\right) - 6\right)\right) - 1\right)} \]

   6. Taylor expanded in x2 around 0 90.8%

      \[\leadsto -6 \cdot x2 + \color{blue}{x1 \cdot \left(9 \cdot x1 - 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot \left(9 + x1 \cdot -19\right)\right)\\ \mathbf{elif}\;x1 \leq 1.15 \cdot 10^{+144}:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot \left(x2 \cdot 8 - 12\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + x1 \cdot 9\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.1% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.7 \cdot 10^{-234} \lor \neg \left(x2 \leq 1.1 \cdot 10^{-70}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.7e-234) (not (<= x2 1.1e-70))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.7e-234) || !(x2 <= 1.1e-70)) {
		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 <= (-2.7d-234)) .or. (.not. (x2 <= 1.1d-70))) 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 <= -2.7e-234) || !(x2 <= 1.1e-70)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.7e-234) or not (x2 <= 1.1e-70):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.7e-234) || !(x2 <= 1.1e-70))
		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 <= -2.7e-234) || ~((x2 <= 1.1e-70)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.7e-234], N[Not[LessEqual[x2, 1.1e-70]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.7000000000000002e-234 or 1.0999999999999999e-70 < x2

   1. Initial program 68.7%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in x1 around 0 31.3%

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

   if -2.7000000000000002e-234 < x2 < 1.0999999999999999e-70

   1. Initial program 68.8%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in x1 around 0 45.2%

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

      1. fma-define 45.2%

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

      2. *-commutative 45.2%

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

      3. fmm-def 45.2%

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

      4. metadata-eval 45.2%

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

      5. cancel-sign-sub-inv 45.2%

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

      6. cancel-sign-sub-inv 45.2%

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

      7. metadata-eval 45.2%

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

      8. *-commutative 45.2%

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

      9. metadata-eval 45.2%

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

   7. Simplified 45.2%

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

   8. Taylor expanded in x2 around 0 32.6%

      \[\leadsto \color{blue}{-1 \cdot x1} \]
   9. Step-by-step derivation

      1. mul-1-neg 32.6%

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

   10. Simplified 32.6%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.7 \cdot 10^{-234} \lor \neg \left(x2 \leq 1.1 \cdot 10^{-70}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 14.0% 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 68.8%

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

3. Simplified 67.7%

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

5. Taylor expanded in x1 around 0 51.0%

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

   1. fma-define 51.1%

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

   2. *-commutative 51.1%

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

   3. fmm-def 51.1%

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

   4. metadata-eval 51.1%

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

   5. cancel-sign-sub-inv 51.1%

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

   6. cancel-sign-sub-inv 51.1%

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

   7. metadata-eval 51.1%

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

   8. *-commutative 51.1%

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

   9. metadata-eval 51.1%

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

7. Simplified 51.1%

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

8. Taylor expanded in x2 around 0 11.9%

   \[\leadsto \color{blue}{-1 \cdot x1} \]
9. Step-by-step derivation

   1. mul-1-neg 11.9%

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

10. Simplified 11.9%

    \[\leadsto \color{blue}{-x1} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024163 
(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))))))