Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 70.8% → 99.6%

Time: 57.4s

Alternatives: 29

Speedup: 1.8×

• 45.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.8% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

   3. Simplified 99.6%

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

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

   1. Initial program 0.0%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in x1 around inf 7.2%

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

      1. *-commutative 7.2%

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

      2. fma-def 7.2%

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

      3. *-commutative 7.2%

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

      4. unpow2 7.2%

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

   6. Simplified 7.2%

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

   7. Taylor expanded in x1 around inf 8.7%

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

      1. *-commutative 8.7%

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

   9. Simplified 8.7%

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

   10. Taylor expanded in x1 around 0 100.0%

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

       1. *-commutative 100.0%

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

   12. Simplified 100.0%

       \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x2 \cdot -2}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \mathsf{fma}\left(x1, -4, \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

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

Alternative 2: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 \cdot x1 + 1\\ t_3 := \sqrt[3]{\frac{\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1}{\mathsf{fma}\left(x1, x1, 1\right)}}\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right)\\ t_6 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_2}\\ \mathbf{if}\;x1 + \left(\left(x1 + \left(\left(t_5 + t_1 \cdot t_4\right) + t_0\right)\right) + t_6\right) \leq \infty:\\ \;\;\;\;x1 + \left(t_6 + \left(x1 + \left(t_0 + \left(t_5 + t_1 \cdot \left(t_3 \cdot \left(t_3 \cdot t_3\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x2 \cdot -2, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \mathsf{fma}\left(x1, -4, \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (cbrt (/ (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1) (fma x1 x1 1.0))))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_2))
        (t_5
         (*
          t_2
          (+
           (* (* (* x1 2.0) t_4) (- t_4 3.0))
           (* (* x1 x1) (- (* t_4 4.0) 6.0)))))
        (t_6 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_2))))
   (if (<= (+ x1 (+ (+ x1 (+ (+ t_5 (* t_1 t_4)) t_0)) t_6)) INFINITY)
     (+ x1 (+ t_6 (+ x1 (+ t_0 (+ t_5 (* t_1 (* t_3 (* t_3 t_3))))))))
     (+
      x1
      (fma
       3.0
       (* x2 -2.0)
       (fma
        x1
        (* x1 9.0)
        (* (fma x1 x1 1.0) (+ x1 (fma x1 -4.0 (* (* x1 x1) 6.0))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = cbrt(((fma((x1 * 3.0), x1, (2.0 * x2)) - x1) / fma(x1, x1, 1.0)));
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)));
	double t_6 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_2);
	double tmp;
	if ((x1 + ((x1 + ((t_5 + (t_1 * t_4)) + t_0)) + t_6)) <= ((double) INFINITY)) {
		tmp = x1 + (t_6 + (x1 + (t_0 + (t_5 + (t_1 * (t_3 * (t_3 * t_3)))))));
	} else {
		tmp = x1 + fma(3.0, (x2 * -2.0), fma(x1, (x1 * 9.0), (fma(x1, x1, 1.0) * (x1 + fma(x1, -4.0, ((x1 * x1) * 6.0))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = cbrt(Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) / fma(x1, x1, 1.0)))
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))))
	t_6 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_2))
	tmp = 0.0
	if (Float64(x1 + Float64(Float64(x1 + Float64(Float64(t_5 + Float64(t_1 * t_4)) + t_0)) + t_6)) <= Inf)
		tmp = Float64(x1 + Float64(t_6 + Float64(x1 + Float64(t_0 + Float64(t_5 + Float64(t_1 * Float64(t_3 * Float64(t_3 * t_3))))))));
	else
		tmp = Float64(x1 + fma(3.0, Float64(x2 * -2.0), fma(x1, Float64(x1 * 9.0), Float64(fma(x1, x1, 1.0) * Float64(x1 + fma(x1, -4.0, Float64(Float64(x1 * x1) * 6.0)))))));
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

      2. *-commutative 99.2%

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

      3. fma-def 99.2%

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

      4. add-cube-cbrt 99.3%

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

      5. *-commutative 99.3%

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

      6. *-commutative 99.3%

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

   3. Applied egg-rr 99.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in x1 around inf 7.2%

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

      1. *-commutative 7.2%

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

      2. fma-def 7.2%

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

      3. *-commutative 7.2%

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

      4. unpow2 7.2%

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

   6. Simplified 7.2%

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

   7. Taylor expanded in x1 around inf 8.7%

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

      1. *-commutative 8.7%

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

   9. Simplified 8.7%

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

   10. Taylor expanded in x1 around 0 100.0%

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

       1. *-commutative 100.0%

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

   12. Simplified 100.0%

       \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x2 \cdot -2}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \mathsf{fma}\left(x1, -4, \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 3: 99.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

      2. div-sub 99.2%

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

      3. cancel-sign-sub-inv 99.2%

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

      4. associate-*l* 99.2%

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

      5. metadata-eval 99.2%

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

   3. Applied egg-rr 99.2%

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

      1. fma-def 99.3%

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

      2. *-commutative 99.3%

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

   5. Simplified 99.3%

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

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

   1. Initial program 0.0%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in x1 around inf 7.2%

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

      1. *-commutative 7.2%

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

      2. fma-def 7.2%

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

      3. *-commutative 7.2%

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

      4. unpow2 7.2%

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

   6. Simplified 7.2%

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

   7. Taylor expanded in x1 around inf 8.7%

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

      1. *-commutative 8.7%

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

   9. Simplified 8.7%

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

   10. Taylor expanded in x1 around 0 100.0%

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

       1. *-commutative 100.0%

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

   12. Simplified 100.0%

       \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x2 \cdot -2}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \mathsf{fma}\left(x1, -4, \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 4: 99.4% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

      1. fma-def 99.2%

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

      2. div-inv 99.2%

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

      3. fma-def 99.2%

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

   3. Applied egg-rr 99.2%

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

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

   1. Initial program 0.0%

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

   3. Simplified 7.2%

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

   4. Taylor expanded in x1 around inf 7.2%

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

      1. *-commutative 7.2%

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

      2. fma-def 7.2%

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

      3. *-commutative 7.2%

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

      4. unpow2 7.2%

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

   6. Simplified 7.2%

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

   7. Taylor expanded in x1 around inf 8.7%

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

      1. *-commutative 8.7%

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

   9. Simplified 8.7%

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

   10. Taylor expanded in x1 around 0 100.0%

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

       1. *-commutative 100.0%

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

   12. Simplified 100.0%

       \[\leadsto x1 + \mathsf{fma}\left(3, \color{blue}{x2 \cdot -2}, \mathsf{fma}\left(x1, x1 \cdot 9, \mathsf{fma}\left(x1, x1, 1\right) \cdot \left(x1 + \mathsf{fma}\left(x1, -4, \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

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

Alternative 5: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_3 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ t_4 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)\right)}{t_4}\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + t_0 \cdot \left(\left(\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_4 (+ x1 (* x2 6.0))))
   (if (<= x1 -1.5e+247)
     (/ (fma x1 x1 (log1p (expm1 (* x2 (* x2 -36.0))))) t_4)
     (if (<= x1 -3.5e+157)
       (+
        x1
        (+
         (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
         (+ (* x2 -6.0) (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))))))
       (if (<= x1 -5.8e+102)
         (+ x1 (+ t_3 (+ x1 (* 6.0 (pow x1 4.0)))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+
             t_3
             (+
              x1
              (+
               (* x1 (* x1 x1))
               (+
                (*
                 t_1
                 (+
                  (* (* (* x1 2.0) t_2) (- t_2 3.0))
                  (* (* x1 x1) (- (* t_2 4.0) 6.0))))
                (*
                 t_0
                 (*
                  (- (fma (* x1 3.0) x1 (* 2.0 x2)) x1)
                  (/ 1.0 (fma x1 x1 1.0)))))))))
           (/ (* x1 x1) t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_4 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -1.5e+247) {
		tmp = fma(x1, x1, log1p(expm1((x2 * (x2 * -36.0))))) / t_4;
	} else if (x1 <= -3.5e+157) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0))))));
	} else if (x1 <= -5.8e+102) {
		tmp = x1 + (t_3 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * ((fma((x1 * 3.0), x1, (2.0 * x2)) - x1) * (1.0 / fma(x1, x1, 1.0))))))));
	} else {
		tmp = (x1 * x1) / t_4;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_4 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -1.5e+247)
		tmp = Float64(fma(x1, x1, log1p(expm1(Float64(x2 * Float64(x2 * -36.0))))) / t_4);
	elseif (x1 <= -3.5e+157)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(Float64(x2 * -6.0) + Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))))));
	elseif (x1 <= -5.8e+102)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(2.0 * x2)) - x1) * Float64(1.0 / fma(x1, x1, 1.0)))))))));
	else
		tmp = Float64(Float64(x1 * x1) / t_4);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+247], N[(N[(x1 * x1 + N[Log[1 + N[(Exp[N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[x1, -3.5e+157], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.8e+102], N[(x1 + N[(t$95$3 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$4), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.5e247

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.3%

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

      2. swap-sqr 13.3%

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

      3. unpow2 13.3%

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

      4. distribute-rgt-neg-in 13.3%

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

      5. unpow2 13.3%

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

      6. metadata-eval 13.3%

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

      7. metadata-eval 13.3%

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

      8. sub-neg 13.3%

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

      9. distribute-rgt-neg-in 13.3%

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

      10. metadata-eval 13.3%

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

   7. Simplified 13.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]
   8. Step-by-step derivation

      1. log1p-expm1-u 66.7%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\left(x2 \cdot x2\right) \cdot -36\right)\right)}\right)}{x1 + x2 \cdot 6} \]

      2. associate-*l* 66.7%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}\right)\right)\right)}{x1 + x2 \cdot 6} \]

   9. Applied egg-rr 66.7%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)}\right)}{x1 + x2 \cdot 6} \]

   if -1.5e247 < x1 < -3.50000000000000002e157

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 64.7%

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

   if -3.50000000000000002e157 < x1 < -5.8000000000000005e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 83.3%

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

      1. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -5.8000000000000005e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.7%

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

      1. fma-def 98.7%

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

      2. div-inv 98.7%

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

      3. fma-def 98.7%

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

   3. Applied egg-rr 98.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(\left(\mathsf{fma}\left(x1 \cdot 3, x1, 2 \cdot x2\right) - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 6: 92.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_3 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ t_4 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)\right)}{t_4}\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + t_0 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t_3\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_4 (+ x1 (* x2 6.0))))
   (if (<= x1 -7.2e+252)
     (/ (fma x1 x1 (log1p (expm1 (* x2 (* x2 -36.0))))) t_4)
     (if (<= x1 -3.5e+157)
       (+
        x1
        (+
         (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
         (+ (* x2 -6.0) (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))))))
       (if (<= x1 -1e+103)
         (+ x1 (+ t_3 (+ x1 (* 6.0 (pow x1 4.0)))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+
             (+
              x1
              (+
               (+
                (*
                 t_1
                 (+
                  (* (* (* x1 2.0) t_2) (- t_2 3.0))
                  (* (* x1 x1) (- (* t_2 4.0) 6.0))))
                (* t_0 t_2))
               (* x1 (* x1 x1))))
             t_3))
           (/ (* x1 x1) t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_4 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -7.2e+252) {
		tmp = fma(x1, x1, log1p(expm1((x2 * (x2 * -36.0))))) / t_4;
	} else if (x1 <= -3.5e+157) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0))))));
	} else if (x1 <= -1e+103) {
		tmp = x1 + (t_3 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + t_3);
	} else {
		tmp = (x1 * x1) / t_4;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_4 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -7.2e+252)
		tmp = Float64(fma(x1, x1, log1p(expm1(Float64(x2 * Float64(x2 * -36.0))))) / t_4);
	elseif (x1 <= -3.5e+157)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(Float64(x2 * -6.0) + Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))))));
	elseif (x1 <= -1e+103)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + t_3));
	else
		tmp = Float64(Float64(x1 * x1) / t_4);
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.2e+252], N[(N[(x1 * x1 + N[Log[1 + N[(Exp[N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[x1, -3.5e+157], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -1e+103], N[(x1 + N[(t$95$3 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$4), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -7.1999999999999997e252

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.3%

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

      2. swap-sqr 13.3%

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

      3. unpow2 13.3%

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

      4. distribute-rgt-neg-in 13.3%

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

      5. unpow2 13.3%

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

      6. metadata-eval 13.3%

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

      7. metadata-eval 13.3%

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

      8. sub-neg 13.3%

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

      9. distribute-rgt-neg-in 13.3%

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

      10. metadata-eval 13.3%

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

   7. Simplified 13.3%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]
   8. Step-by-step derivation

      1. log1p-expm1-u 66.7%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\left(x2 \cdot x2\right) \cdot -36\right)\right)}\right)}{x1 + x2 \cdot 6} \]

      2. associate-*l* 66.7%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}\right)\right)\right)}{x1 + x2 \cdot 6} \]

   9. Applied egg-rr 66.7%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)}\right)}{x1 + x2 \cdot 6} \]

   if -7.1999999999999997e252 < x1 < -3.50000000000000002e157

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 64.7%

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

   if -3.50000000000000002e157 < x1 < -1e103

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 83.3%

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

      1. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -1e103 < x1 < 1.35000000000000003e154

   1. Initial program 98.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, \mathsf{log1p}\left(\mathsf{expm1}\left(x2 \cdot \left(x2 \cdot -36\right)\right)\right)\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -1 \cdot 10^{+103}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 7: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\\ t_3 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right) + t_0 \cdot t_3\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + t_2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1)))
        (t_3 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -3.5e+157)
     (+
      x1
      (+
       (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0))
       (+ (* x2 -6.0) (* 3.0 (* (pow x1 2.0) (- 3.0 (* x2 -2.0)))))))
     (if (<= x1 -5.5e+102)
       (+ x1 (+ t_2 (+ x1 (* 6.0 (pow x1 4.0)))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_3) (- t_3 3.0))
                (* (* x1 x1) (- (* t_3 4.0) 6.0))))
              (* t_0 t_3))
             (* x1 (* x1 x1))))
           t_2))
         (/ (* x1 x1) (+ x1 (* x2 6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.5e+157) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (pow(x1, 2.0) * (3.0 - (x2 * -2.0))))));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 + (6.0 * pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + t_2);
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)
    t_3 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-3.5d+157)) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + ((x2 * (-6.0d0)) + (3.0d0 * ((x1 ** 2.0d0) * (3.0d0 - (x2 * (-2.0d0)))))))
    else if (x1 <= (-5.5d+102)) then
        tmp = x1 + (t_2 + (x1 + (6.0d0 * (x1 ** 4.0d0))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * ((t_3 * 4.0d0) - 6.0d0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + t_2)
    else
        tmp = (x1 * x1) / (x1 + (x2 * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	double t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -3.5e+157) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (Math.pow(x1, 2.0) * (3.0 - (x2 * -2.0))))));
	} else if (x1 <= -5.5e+102) {
		tmp = x1 + (t_2 + (x1 + (6.0 * Math.pow(x1, 4.0))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + t_2);
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -3.5e+157:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * (math.pow(x1, 2.0) * (3.0 - (x2 * -2.0))))))
	elif x1 <= -5.5e+102:
		tmp = x1 + (t_2 + (x1 + (6.0 * math.pow(x1, 4.0))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + t_2)
	else:
		tmp = (x1 * x1) / (x1 + (x2 * 6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))
	t_3 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.5e+157)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(Float64(x2 * -6.0) + Float64(3.0 * Float64((x1 ^ 2.0) * Float64(3.0 - Float64(x2 * -2.0)))))));
	elseif (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(6.0 * (x1 ^ 4.0)))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0)))) + Float64(t_0 * t_3)) + Float64(x1 * Float64(x1 * x1)))) + t_2));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 + Float64(x2 * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1);
	t_3 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -3.5e+157)
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + ((x2 * -6.0) + (3.0 * ((x1 ^ 2.0) * (3.0 - (x2 * -2.0))))));
	elseif (x1 <= -5.5e+102)
		tmp = x1 + (t_2 + (x1 + (6.0 * (x1 ^ 4.0))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)))) + (t_0 * t_3)) + (x1 * (x1 * x1)))) + t_2);
	else
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.5e+157], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x2 * -6.0), $MachinePrecision] + N[(3.0 * N[(N[Power[x1, 2.0], $MachinePrecision] * N[(3.0 - N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5.5e+102], N[(x1 + N[(t$95$2 + N[(x1 + N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.50000000000000002e157

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 50.0%

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

   if -3.50000000000000002e157 < x1 < -5.49999999999999981e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 83.3%

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

      1. *-commutative 83.3%

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

   4. Simplified 83.3%

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

   if -5.49999999999999981e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.5 \cdot 10^{+157}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + \left(x2 \cdot -6 + 3 \cdot \left({x1}^{2} \cdot \left(3 - x2 \cdot -2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 6 \cdot {x1}^{4}\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 8: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, -36 \cdot \left(x2 \cdot x2\right)\right)}{x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + t_0 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -6.2e+102)
     (/ (fma x1 x1 (* -36.0 (* x2 x2))) (* x2 6.0))
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))))
       (/ (* x1 x1) (+ x1 (* x2 6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -6.2e+102) {
		tmp = fma(x1, x1, (-36.0 * (x2 * x2))) / (x2 * 6.0);
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)));
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -6.2e+102)
		tmp = Float64(fma(x1, x1, Float64(-36.0 * Float64(x2 * x2))) / Float64(x2 * 6.0));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1))));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 + Float64(x2 * 6.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -6.2e+102], N[(N[(x1 * x1 + N[(-36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -6.19999999999999973e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 42.1%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{6 \cdot x2}} \]
   9. Step-by-step derivation

      1. *-commutative 42.1%

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

   10. Simplified 42.1%

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

   if -6.19999999999999973e102 < x1 < 1.35000000000000003e154

   1. Initial program 98.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, -36 \cdot \left(x2 \cdot x2\right)\right)}{x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 9: 84.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot x1 + 1\\ t_3 := x1 \cdot \left(x1 \cdot 3\right)\\ t_4 := \frac{\left(t_3 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right)\\ \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_3 - 2 \cdot x2\right) - x1}{t_2} + \left(x1 + \left(t_0 + \left(t_5 + 3 \cdot t_3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_5 + t_3 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* x1 (* x1 3.0)))
        (t_4 (/ (- (+ t_3 (* 2.0 x2)) x1) t_2))
        (t_5
         (*
          t_2
          (+
           (* (* (* x1 2.0) t_4) (- t_4 3.0))
           (* (* x1 x1) (- (* t_4 4.0) 6.0))))))
   (if (<= x1 -3.8e+109)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 2e-34)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_3 (* 2.0 x2)) x1) t_2))
         (+ x1 (+ t_0 (+ t_5 (* 3.0 t_3))))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+ x1 (+ t_0 (+ t_5 (* t_3 (+ 3.0 (/ -1.0 x1))))))
           (* 3.0 (* x2 -2.0))))
         (/ (* x1 x1) t_1))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)));
	double tmp;
	if (x1 <= -3.8e+109) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= 2e-34) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + (t_5 + (3.0 * t_3)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + (t_5 + (t_3 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = x1 * (x1 * 3.0d0)
    t_4 = ((t_3 + (2.0d0 * x2)) - x1) / t_2
    t_5 = t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))
    if (x1 <= (-3.8d+109)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= 2d-34) then
        tmp = x1 + ((3.0d0 * (((t_3 - (2.0d0 * x2)) - x1) / t_2)) + (x1 + (t_0 + (t_5 + (3.0d0 * t_3)))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (t_0 + (t_5 + (t_3 * (3.0d0 + ((-1.0d0) / x1)))))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = x1 * (x1 * 3.0);
	double t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2;
	double t_5 = t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)));
	double tmp;
	if (x1 <= -3.8e+109) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= 2e-34) {
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + (t_5 + (3.0 * t_3)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + (t_5 + (t_3 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 + (x2 * 6.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = x1 * (x1 * 3.0)
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2
	t_5 = t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))
	tmp = 0
	if x1 <= -3.8e+109:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= 2e-34:
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + (t_5 + (3.0 * t_3)))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (t_0 + (t_5 + (t_3 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(x1 * Float64(x1 * 3.0))
	t_4 = Float64(Float64(Float64(t_3 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0))))
	tmp = 0.0
	if (x1 <= -3.8e+109)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= 2e-34)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_3 - Float64(2.0 * x2)) - x1) / t_2)) + Float64(x1 + Float64(t_0 + Float64(t_5 + Float64(3.0 * t_3))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_5 + Float64(t_3 * Float64(3.0 + Float64(-1.0 / x1)))))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 + (x2 * 6.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = x1 * (x1 * 3.0);
	t_4 = ((t_3 + (2.0 * x2)) - x1) / t_2;
	t_5 = t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * ((t_4 * 4.0) - 6.0)));
	tmp = 0.0;
	if (x1 <= -3.8e+109)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= 2e-34)
		tmp = x1 + ((3.0 * (((t_3 - (2.0 * x2)) - x1) / t_2)) + (x1 + (t_0 + (t_5 + (3.0 * t_3)))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (t_0 + (t_5 + (t_3 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.8e+109], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, 2e-34], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$3 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$5 + N[(3.0 * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$5 + N[(t$95$3 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.80000000000000039e109

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -3.80000000000000039e109 < x1 < 1.99999999999999986e-34

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 98.6%

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

   if 1.99999999999999986e-34 < x1 < 1.35000000000000003e154

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around inf 82.5%

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

   3. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 33.8%

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

   5. Simplified 99.1%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.8 \cdot 10^{+109}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 10: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_1}\\ t_4 := t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_3\right) \cdot \left(t_3 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_3 \cdot 4 - 6\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, -36 \cdot \left(x2 \cdot x2\right)\right)}{x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + \left(t_0 + \left(t_4 + 3 \cdot t_2\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_4 + t_2 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_1))
        (t_4
         (*
          t_1
          (+
           (* (* (* x1 2.0) t_3) (- t_3 3.0))
           (* (* x1 x1) (- (* t_3 4.0) 6.0))))))
   (if (<= x1 -5.8e+102)
     (/ (fma x1 x1 (* -36.0 (* x2 x2))) (* x2 6.0))
     (if (<= x1 1e-34)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_1))
         (+ x1 (+ t_0 (+ t_4 (* 3.0 t_2))))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+ x1 (+ t_0 (+ t_4 (* t_2 (+ 3.0 (/ -1.0 x1))))))
           (* 3.0 (* x2 -2.0))))
         (/ (* x1 x1) (+ x1 (* x2 6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_1;
	double t_4 = t_1 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * ((t_3 * 4.0) - 6.0)));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = fma(x1, x1, (-36.0 * (x2 * x2))) / (x2 * 6.0);
	} else if (x1 <= 1e-34) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_1)) + (x1 + (t_0 + (t_4 + (3.0 * t_2)))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + (t_4 + (t_2 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_1)
	t_4 = Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_3 * 4.0) - 6.0))))
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = Float64(fma(x1, x1, Float64(-36.0 * Float64(x2 * x2))) / Float64(x2 * 6.0));
	elseif (x1 <= 1e-34)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(3.0 * t_2))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_4 + Float64(t_2 * Float64(3.0 + Float64(-1.0 / x1)))))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 + Float64(x2 * 6.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$3 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], N[(N[(x1 * x1 + N[(-36.0 * N[(x2 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1e-34], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(3.0 * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$4 + N[(t$95$2 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.8000000000000005e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 42.1%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{6 \cdot x2}} \]
   9. Step-by-step derivation

      1. *-commutative 42.1%

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

   10. Simplified 42.1%

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

   if -5.8000000000000005e102 < x1 < 9.99999999999999928e-35

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 98.6%

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

   if 9.99999999999999928e-35 < x1 < 1.35000000000000003e154

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around inf 82.5%

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

   3. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 33.8%

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

   5. Simplified 99.1%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x1, x1, -36 \cdot \left(x2 \cdot x2\right)\right)}{x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 11: 84.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := x1 + x2 \cdot 6\\ t_3 := x1 \cdot x1 + 1\\ t_4 := \frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_3}\\ t_5 := \left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_2}\\ \mathbf{elif}\;x1 \leq 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_3} + \left(x1 + \left(t_0 + \left(t_1 \cdot t_4 + t_3 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_3 \cdot \left(t_5 + \left(x1 \cdot x1\right) \cdot \left(t_4 \cdot 4 - 6\right)\right) + t_1 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ x1 (* x2 6.0)))
        (t_3 (+ (* x1 x1) 1.0))
        (t_4 (/ (- (+ t_1 (* 2.0 x2)) x1) t_3))
        (t_5 (* (* (* x1 2.0) t_4) (- t_4 3.0))))
   (if (<= x1 -5.8e+107)
     (/ (* x2 (* x2 -36.0)) t_2)
     (if (<= x1 1e-34)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_3))
         (+ x1 (+ t_0 (+ (* t_1 t_4) (* t_3 (+ t_5 (* (* x1 x1) 6.0))))))))
       (if (<= x1 1.35e+154)
         (+
          x1
          (+
           (+
            x1
            (+
             t_0
             (+
              (* t_3 (+ t_5 (* (* x1 x1) (- (* t_4 4.0) 6.0))))
              (* t_1 (+ 3.0 (/ -1.0 x1))))))
           (* 3.0 (* x2 -2.0))))
         (/ (* x1 x1) t_2))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 + (x2 * 6.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = ((x1 * 2.0) * t_4) * (t_4 - 3.0);
	double tmp;
	if (x1 <= -5.8e+107) {
		tmp = (x2 * (x2 * -36.0)) / t_2;
	} else if (x1 <= 1e-34) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_0 + ((t_1 * t_4) + (t_3 * (t_5 + ((x1 * x1) * 6.0)))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + ((t_3 * (t_5 + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = (x1 * x1) / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = x1 + (x2 * 6.0d0)
    t_3 = (x1 * x1) + 1.0d0
    t_4 = ((t_1 + (2.0d0 * x2)) - x1) / t_3
    t_5 = ((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)
    if (x1 <= (-5.8d+107)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_2
    else if (x1 <= 1d-34) then
        tmp = x1 + ((3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_3)) + (x1 + (t_0 + ((t_1 * t_4) + (t_3 * (t_5 + ((x1 * x1) * 6.0d0)))))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (t_0 + ((t_3 * (t_5 + ((x1 * x1) * ((t_4 * 4.0d0) - 6.0d0)))) + (t_1 * (3.0d0 + ((-1.0d0) / x1)))))) + (3.0d0 * (x2 * (-2.0d0))))
    else
        tmp = (x1 * x1) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = x1 + (x2 * 6.0);
	double t_3 = (x1 * x1) + 1.0;
	double t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	double t_5 = ((x1 * 2.0) * t_4) * (t_4 - 3.0);
	double tmp;
	if (x1 <= -5.8e+107) {
		tmp = (x2 * (x2 * -36.0)) / t_2;
	} else if (x1 <= 1e-34) {
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_0 + ((t_1 * t_4) + (t_3 * (t_5 + ((x1 * x1) * 6.0)))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + ((t_3 * (t_5 + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	} else {
		tmp = (x1 * x1) / t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = x1 + (x2 * 6.0)
	t_3 = (x1 * x1) + 1.0
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3
	t_5 = ((x1 * 2.0) * t_4) * (t_4 - 3.0)
	tmp = 0
	if x1 <= -5.8e+107:
		tmp = (x2 * (x2 * -36.0)) / t_2
	elif x1 <= 1e-34:
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_0 + ((t_1 * t_4) + (t_3 * (t_5 + ((x1 * x1) * 6.0)))))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (t_0 + ((t_3 * (t_5 + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)))
	else:
		tmp = (x1 * x1) / t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(x1 + Float64(x2 * 6.0))
	t_3 = Float64(Float64(x1 * x1) + 1.0)
	t_4 = Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_3)
	t_5 = Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0))
	tmp = 0.0
	if (x1 <= -5.8e+107)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_2);
	elseif (x1 <= 1e-34)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_3)) + Float64(x1 + Float64(t_0 + Float64(Float64(t_1 * t_4) + Float64(t_3 * Float64(t_5 + Float64(Float64(x1 * x1) * 6.0))))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(Float64(t_3 * Float64(t_5 + Float64(Float64(x1 * x1) * Float64(Float64(t_4 * 4.0) - 6.0)))) + Float64(t_1 * Float64(3.0 + Float64(-1.0 / x1)))))) + Float64(3.0 * Float64(x2 * -2.0))));
	else
		tmp = Float64(Float64(x1 * x1) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = x1 + (x2 * 6.0);
	t_3 = (x1 * x1) + 1.0;
	t_4 = ((t_1 + (2.0 * x2)) - x1) / t_3;
	t_5 = ((x1 * 2.0) * t_4) * (t_4 - 3.0);
	tmp = 0.0;
	if (x1 <= -5.8e+107)
		tmp = (x2 * (x2 * -36.0)) / t_2;
	elseif (x1 <= 1e-34)
		tmp = x1 + ((3.0 * (((t_1 - (2.0 * x2)) - x1) / t_3)) + (x1 + (t_0 + ((t_1 * t_4) + (t_3 * (t_5 + ((x1 * x1) * 6.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (t_0 + ((t_3 * (t_5 + ((x1 * x1) * ((t_4 * 4.0) - 6.0)))) + (t_1 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	else
		tmp = (x1 * x1) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+107], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[x1, 1e-34], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(t$95$0 + N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$3 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(N[(t$95$3 * N[(t$95$5 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$4 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.79999999999999975e107

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -5.79999999999999975e107 < x1 < 9.99999999999999928e-35

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around inf 98.0%

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

   if 9.99999999999999928e-35 < x1 < 1.35000000000000003e154

   1. Initial program 99.1%

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

   2. Taylor expanded in x1 around inf 82.5%

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

   3. Taylor expanded in x1 around 0 99.1%

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

      1. *-commutative 33.8%

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

   5. Simplified 99.1%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+107}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 10^{-34}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 12: 85.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_1}\\ t_3 := x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_2\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t_2 \cdot 4 - 6\right)\right) + t_0 \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ t_4 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_4}\\ \mathbf{elif}\;x1 \leq -3.15 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 10^{-10}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_4}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1))
        (t_3
         (+
          x1
          (+
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (*
               t_1
               (+
                (* (* (* x1 2.0) t_2) (- t_2 3.0))
                (* (* x1 x1) (- (* t_2 4.0) 6.0))))
              (* t_0 (+ 3.0 (/ -1.0 x1))))))
           (* 3.0 (* x2 -2.0)))))
        (t_4 (+ x1 (* x2 6.0))))
   (if (<= x1 -5.2e+105)
     (/ (* x2 (* x2 -36.0)) t_4)
     (if (<= x1 -3.15e-9)
       t_3
       (if (<= x1 1e-10)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154) t_3 (/ (* x1 x1) t_4)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	double t_4 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -5.2e+105) {
		tmp = (x2 * (x2 * -36.0)) / t_4;
	} else if (x1 <= -3.15e-9) {
		tmp = t_3;
	} else if (x1 <= 1e-10) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = (x1 * x1) / t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    t_3 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (t_0 * (3.0d0 + ((-1.0d0) / x1)))))) + (3.0d0 * (x2 * (-2.0d0))))
    t_4 = x1 + (x2 * 6.0d0)
    if (x1 <= (-5.2d+105)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_4
    else if (x1 <= (-3.15d-9)) then
        tmp = t_3
    else if (x1 <= 1d-10) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_3
    else
        tmp = (x1 * x1) / t_4
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double t_3 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	double t_4 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -5.2e+105) {
		tmp = (x2 * (x2 * -36.0)) / t_4;
	} else if (x1 <= -3.15e-9) {
		tmp = t_3;
	} else if (x1 <= 1e-10) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = (x1 * x1) / t_4;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	t_3 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)))
	t_4 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -5.2e+105:
		tmp = (x2 * (x2 * -36.0)) / t_4
	elif x1 <= -3.15e-9:
		tmp = t_3
	elif x1 <= 1e-10:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_3
	else:
		tmp = (x1 * x1) / t_4
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	t_3 = Float64(x1 + Float64(Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1)))))) + Float64(3.0 * Float64(x2 * -2.0))))
	t_4 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -5.2e+105)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_4);
	elseif (x1 <= -3.15e-9)
		tmp = t_3;
	elseif (x1 <= 1e-10)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = Float64(Float64(x1 * x1) / t_4);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	t_3 = x1 + ((x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (t_0 * (3.0 + (-1.0 / x1)))))) + (3.0 * (x2 * -2.0)));
	t_4 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -5.2e+105)
		tmp = (x2 * (x2 * -36.0)) / t_4;
	elseif (x1 <= -3.15e-9)
		tmp = t_3;
	elseif (x1 <= 1e-10)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = (x1 * x1) / t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.2e+105], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision], If[LessEqual[x1, -3.15e-9], t$95$3, If[LessEqual[x1, 1e-10], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$3, N[(N[(x1 * x1), $MachinePrecision] / t$95$4), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.2000000000000004e105

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -5.2000000000000004e105 < x1 < -3.1500000000000001e-9 or 1.00000000000000004e-10 < x1 < 1.35000000000000003e154

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 92.9%

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

   3. Taylor expanded in x1 around 0 99.2%

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

      1. *-commutative 21.5%

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

   5. Simplified 99.2%

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

   if -3.1500000000000001e-9 < x1 < 1.00000000000000004e-10

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 99.3%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -3.15 \cdot 10^{-9}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 10^{-10}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 13: 83.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := \frac{\left(t_0 + 2 \cdot x2\right) - x1}{t_2}\\ t_5 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(3 + \frac{-1}{x1}\right) + t_2 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t_4\right) \cdot \left(t_4 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -4 \cdot 10^{+106}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -7.3 \cdot 10^{-6}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x1 \leq 1.75:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4 (/ (- (+ t_0 (* 2.0 x2)) x1) t_2))
        (t_5
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (+ 3.0 (/ -1.0 x1)))
              (*
               t_2
               (+ (* (* (* x1 2.0) t_4) (- t_4 3.0)) (* (* x1 x1) 6.0))))))))))
   (if (<= x1 -4e+106)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -7.3e-6)
       t_5
       (if (<= x1 1.75)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154) t_5 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -4e+106) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -7.3e-6) {
		tmp = t_5;
	} else if (x1 <= 1.75) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = ((t_0 + (2.0d0 * x2)) - x1) / t_2
    t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0d0 + ((-1.0d0) / x1))) + (t_2 * ((((x1 * 2.0d0) * t_4) * (t_4 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    if (x1 <= (-4d+106)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-7.3d-6)) then
        tmp = t_5
    else if (x1 <= 1.75d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_5
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	double t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	double tmp;
	if (x1 <= -4e+106) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -7.3e-6) {
		tmp = t_5;
	} else if (x1 <= 1.75) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_5;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 + (x2 * 6.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))))
	tmp = 0
	if x1 <= -4e+106:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -7.3e-6:
		tmp = t_5
	elif x1 <= 1.75:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_5
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_2)
	t_5 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1))) + Float64(t_2 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_4) * Float64(t_4 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))))
	tmp = 0.0
	if (x1 <= -4e+106)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -7.3e-6)
		tmp = t_5;
	elseif (x1 <= 1.75)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 + (x2 * 6.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = ((t_0 + (2.0 * x2)) - x1) / t_2;
	t_5 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * ((((x1 * 2.0) * t_4) * (t_4 - 3.0)) + ((x1 * x1) * 6.0)))))));
	tmp = 0.0;
	if (x1 <= -4e+106)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -7.3e-6)
		tmp = t_5;
	elseif (x1 <= 1.75)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_5;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, Block[{t$95$5 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision] * N[(t$95$4 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4e+106], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -7.3e-6], t$95$5, If[LessEqual[x1, 1.75], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$5, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.00000000000000036e106

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -4.00000000000000036e106 < x1 < -7.30000000000000041e-6 or 1.75 < x1 < 1.35000000000000003e154

   1. Initial program 99.4%

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

   2. Taylor expanded in x1 around inf 99.4%

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

   3. Taylor expanded in x1 around inf 90.8%

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

   if -7.30000000000000041e-6 < x1 < 1.75

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 96.4%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4 \cdot 10^{+106}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -7.3 \cdot 10^{-6}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.75:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 14: 81.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\\ t_3 := x1 + x2 \cdot 6\\ t_4 := x1 \cdot x1 + 1\\ t_5 := 3 \cdot \frac{\left(t_1 - 2 \cdot x2\right) - x1}{t_4}\\ t_6 := t_1 \cdot \left(3 + \frac{-1}{x1}\right)\\ \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_3}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + \left(t_0 + \left(t_6 + t_4 \cdot \left(t_2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(t_5 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(t_0 + \left(t_6 + t_4 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_1 + 2 \cdot x2\right) - x1}{t_4} \cdot 4 - 6\right) + t_2\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (* (* (* x1 2.0) 3.0) (/ -1.0 x1)))
        (t_3 (+ x1 (* x2 6.0)))
        (t_4 (+ (* x1 x1) 1.0))
        (t_5 (* 3.0 (/ (- (- t_1 (* 2.0 x2)) x1) t_4)))
        (t_6 (* t_1 (+ 3.0 (/ -1.0 x1)))))
   (if (<= x1 -1.55e+103)
     (/ (* x2 (* x2 -36.0)) t_3)
     (if (<= x1 -52000000.0)
       (+
        x1
        (+
         t_5
         (+
          x1
          (+
           t_0
           (+
            t_6
            (*
             t_4
             (+
              t_2
              (*
               (* x1 x1)
               (-
                (*
                 4.0
                 (+
                  3.0
                  (+
                   (* 2.0 (/ x2 (* x1 x1)))
                   (- (/ -1.0 x1) (/ 3.0 (* x1 x1))))))
                6.0)))))))))
       (if (<= x1 0.48)
         (+ x1 (+ t_5 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+
             (+
              x1
              (+
               t_0
               (+
                t_6
                (*
                 t_4
                 (+
                  (*
                   (* x1 x1)
                   (- (* (/ (- (+ t_1 (* 2.0 x2)) x1) t_4) 4.0) 6.0))
                  t_2)))))
             (* 3.0 (- (* x2 -2.0) x1))))
           (/ (* x1 x1) t_3)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((x1 * 2.0) * 3.0) * (-1.0 / x1);
	double t_3 = x1 + (x2 * 6.0);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_4);
	double t_6 = t_1 * (3.0 + (-1.0 / x1));
	double tmp;
	if (x1 <= -1.55e+103) {
		tmp = (x2 * (x2 * -36.0)) / t_3;
	} else if (x1 <= -52000000.0) {
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_6 + (t_4 * (t_2 + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	} else if (x1 <= 0.48) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + (t_6 + (t_4 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_4) * 4.0) - 6.0)) + t_2))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: t_6
    real(8) :: tmp
    t_0 = x1 * (x1 * x1)
    t_1 = x1 * (x1 * 3.0d0)
    t_2 = ((x1 * 2.0d0) * 3.0d0) * ((-1.0d0) / x1)
    t_3 = x1 + (x2 * 6.0d0)
    t_4 = (x1 * x1) + 1.0d0
    t_5 = 3.0d0 * (((t_1 - (2.0d0 * x2)) - x1) / t_4)
    t_6 = t_1 * (3.0d0 + ((-1.0d0) / x1))
    if (x1 <= (-1.55d+103)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_3
    else if (x1 <= (-52000000.0d0)) then
        tmp = x1 + (t_5 + (x1 + (t_0 + (t_6 + (t_4 * (t_2 + ((x1 * x1) * ((4.0d0 * (3.0d0 + ((2.0d0 * (x2 / (x1 * x1))) + (((-1.0d0) / x1) - (3.0d0 / (x1 * x1)))))) - 6.0d0))))))))
    else if (x1 <= 0.48d0) then
        tmp = x1 + (t_5 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (t_0 + (t_6 + (t_4 * (((x1 * x1) * (((((t_1 + (2.0d0 * x2)) - x1) / t_4) * 4.0d0) - 6.0d0)) + t_2))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x1 * x1) / t_3
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = ((x1 * 2.0) * 3.0) * (-1.0 / x1);
	double t_3 = x1 + (x2 * 6.0);
	double t_4 = (x1 * x1) + 1.0;
	double t_5 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_4);
	double t_6 = t_1 * (3.0 + (-1.0 / x1));
	double tmp;
	if (x1 <= -1.55e+103) {
		tmp = (x2 * (x2 * -36.0)) / t_3;
	} else if (x1 <= -52000000.0) {
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_6 + (t_4 * (t_2 + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	} else if (x1 <= 0.48) {
		tmp = x1 + (t_5 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (t_0 + (t_6 + (t_4 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_4) * 4.0) - 6.0)) + t_2))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_3;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = x1 * (x1 * 3.0)
	t_2 = ((x1 * 2.0) * 3.0) * (-1.0 / x1)
	t_3 = x1 + (x2 * 6.0)
	t_4 = (x1 * x1) + 1.0
	t_5 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_4)
	t_6 = t_1 * (3.0 + (-1.0 / x1))
	tmp = 0
	if x1 <= -1.55e+103:
		tmp = (x2 * (x2 * -36.0)) / t_3
	elif x1 <= -52000000.0:
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_6 + (t_4 * (t_2 + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))))
	elif x1 <= 0.48:
		tmp = x1 + (t_5 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (t_0 + (t_6 + (t_4 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_4) * 4.0) - 6.0)) + t_2))))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x1 * x1) / t_3
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(-1.0 / x1))
	t_3 = Float64(x1 + Float64(x2 * 6.0))
	t_4 = Float64(Float64(x1 * x1) + 1.0)
	t_5 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(2.0 * x2)) - x1) / t_4))
	t_6 = Float64(t_1 * Float64(3.0 + Float64(-1.0 / x1)))
	tmp = 0.0
	if (x1 <= -1.55e+103)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_3);
	elseif (x1 <= -52000000.0)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_4 * Float64(t_2 + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(3.0 + Float64(Float64(2.0 * Float64(x2 / Float64(x1 * x1))) + Float64(Float64(-1.0 / x1) - Float64(3.0 / Float64(x1 * x1)))))) - 6.0)))))))));
	elseif (x1 <= 0.48)
		tmp = Float64(x1 + Float64(t_5 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(t_0 + Float64(t_6 + Float64(t_4 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_1 + Float64(2.0 * x2)) - x1) / t_4) * 4.0) - 6.0)) + t_2))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x1 * x1) / t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = x1 * (x1 * 3.0);
	t_2 = ((x1 * 2.0) * 3.0) * (-1.0 / x1);
	t_3 = x1 + (x2 * 6.0);
	t_4 = (x1 * x1) + 1.0;
	t_5 = 3.0 * (((t_1 - (2.0 * x2)) - x1) / t_4);
	t_6 = t_1 * (3.0 + (-1.0 / x1));
	tmp = 0.0;
	if (x1 <= -1.55e+103)
		tmp = (x2 * (x2 * -36.0)) / t_3;
	elseif (x1 <= -52000000.0)
		tmp = x1 + (t_5 + (x1 + (t_0 + (t_6 + (t_4 * (t_2 + ((x1 * x1) * ((4.0 * (3.0 + ((2.0 * (x2 / (x1 * x1))) + ((-1.0 / x1) - (3.0 / (x1 * x1)))))) - 6.0))))))));
	elseif (x1 <= 0.48)
		tmp = x1 + (t_5 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (t_0 + (t_6 + (t_4 * (((x1 * x1) * (((((t_1 + (2.0 * x2)) - x1) / t_4) * 4.0) - 6.0)) + t_2))))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x1 * x1) / t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$5 = N[(3.0 * N[(N[(N[(t$95$1 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$6 = N[(t$95$1 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.55e+103], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[x1, -52000000.0], N[(x1 + N[(t$95$5 + N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$4 * N[(t$95$2 + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(3.0 + N[(N[(2.0 * N[(x2 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / x1), $MachinePrecision] - N[(3.0 / N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.48], N[(x1 + N[(t$95$5 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(t$95$0 + N[(t$95$6 + N[(t$95$4 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$1 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$4), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$3), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -1.5500000000000001e103

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -1.5500000000000001e103 < x1 < -5.2e7

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 99.3%

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

   3. Taylor expanded in x1 around inf 92.3%

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

   4. Taylor expanded in x1 around inf 92.3%

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

   5. Taylor expanded in x1 around inf 92.5%

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

      1. associate--l+ 92.5%

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

      2. unpow2 92.5%

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

      3. +-commutative 92.5%

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

      4. associate-*r/ 92.5%

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

      5. metadata-eval 92.5%

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

      6. unpow2 92.5%

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

   7. Simplified 92.5%

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

   if -5.2e7 < x1 < 0.47999999999999998

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 96.8%

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

   if 0.47999999999999998 < x1 < 1.35000000000000003e154

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 91.7%

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

   3. Taylor expanded in x1 around inf 75.9%

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

   4. Taylor expanded in x1 around inf 76.2%

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

   5. Taylor expanded in x1 around 0 76.7%

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

      1. +-commutative 26.9%

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

      2. neg-mul-1 26.9%

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

      3. unsub-neg 26.9%

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

      4. *-commutative 26.9%

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

   7. Simplified 76.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+103}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1} + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \left(3 + \left(2 \cdot \frac{x2}{x1 \cdot x1} + \left(\frac{-1}{x1} - \frac{3}{x1 \cdot x1}\right)\right)\right) - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 15: 81.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_2 \cdot \left(3 + \frac{-1}{x1}\right) + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_0} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\\ \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + t_3\right)\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_2 (+ 3.0 (/ -1.0 x1)))
            (*
             t_0
             (+
              (* (* x1 x1) (- (* (/ (- (+ t_2 (* 2.0 x2)) x1) t_0) 4.0) 6.0))
              (* (* (* x1 2.0) 3.0) (/ -1.0 x1)))))))))
   (if (<= x1 -2.7e+107)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -52000000.0)
       (+ x1 (+ (* 3.0 (* x2 -2.0)) t_3))
       (if (<= x1 0.48)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154)
           (+ x1 (+ t_3 (* 3.0 (- (* x2 -2.0) x1))))
           (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))));
	double tmp;
	if (x1 <= -2.7e+107) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -52000000.0) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + t_3);
	} else if (x1 <= 0.48) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0d0 + ((-1.0d0) / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0d0 * x2)) - x1) / t_0) * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * 3.0d0) * ((-1.0d0) / x1))))))
    if (x1 <= (-2.7d+107)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-52000000.0d0)) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + t_3)
    else if (x1 <= 0.48d0) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_3 + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))));
	double tmp;
	if (x1 <= -2.7e+107) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -52000000.0) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + t_3);
	} else if (x1 <= 0.48) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x2 * 6.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))
	tmp = 0
	if x1 <= -2.7e+107:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -52000000.0:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + t_3)
	elif x1 <= 0.48:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(3.0 + Float64(-1.0 / x1))) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(-1.0 / x1)))))))
	tmp = 0.0
	if (x1 <= -2.7e+107)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -52000000.0)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + t_3));
	elseif (x1 <= 0.48)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x2 * 6.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))));
	tmp = 0.0;
	if (x1 <= -2.7e+107)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -52000000.0)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + t_3);
	elseif (x1 <= 0.48)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_3 + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.7e+107], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -52000000.0], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 0.48], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -2.7000000000000001e107

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -2.7000000000000001e107 < x1 < -5.2e7

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 99.3%

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

   3. Taylor expanded in x1 around inf 92.3%

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

   4. Taylor expanded in x1 around inf 92.3%

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

   5. Taylor expanded in x1 around 0 92.3%

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

      1. *-commutative 12.0%

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

   7. Simplified 92.3%

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

   if -5.2e7 < x1 < 0.47999999999999998

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 96.8%

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

   if 0.47999999999999998 < x1 < 1.35000000000000003e154

   1. Initial program 99.2%

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

   2. Taylor expanded in x1 around inf 91.7%

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

   3. Taylor expanded in x1 around inf 75.9%

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

   4. Taylor expanded in x1 around inf 76.2%

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

   5. Taylor expanded in x1 around 0 76.7%

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

      1. +-commutative 26.9%

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

      2. neg-mul-1 26.9%

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

      3. unsub-neg 26.9%

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

      4. *-commutative 26.9%

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

   7. Simplified 76.7%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.7 \cdot 10^{+107}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 16: 81.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_2 \cdot \left(3 + \frac{-1}{x1}\right) + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(t_2 + 2 \cdot x2\right) - x1}{t_0} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_2 - 2 \cdot x2\right) - x1}{t_0} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3
         (+
          x1
          (+
           (* 3.0 (* x2 -2.0))
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_2 (+ 3.0 (/ -1.0 x1)))
              (*
               t_0
               (+
                (* (* x1 x1) (- (* (/ (- (+ t_2 (* 2.0 x2)) x1) t_0) 4.0) 6.0))
                (* (* (* x1 2.0) 3.0) (/ -1.0 x1)))))))))))
   (if (<= x1 -6.8e+108)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -52000000.0)
       t_3
       (if (<= x1 0.48)
         (+
          x1
          (+
           (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
           (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154) t_3 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -6.8e+108) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -52000000.0) {
		tmp = t_3;
	} else if (x1 <= 0.48) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0d0 + ((-1.0d0) / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0d0 * x2)) - x1) / t_0) * 4.0d0) - 6.0d0)) + (((x1 * 2.0d0) * 3.0d0) * ((-1.0d0) / x1))))))))
    if (x1 <= (-6.8d+108)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-52000000.0d0)) then
        tmp = t_3
    else if (x1 <= 0.48d0) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_3
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -6.8e+108) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -52000000.0) {
		tmp = t_3;
	} else if (x1 <= 0.48) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 + (x2 * 6.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))))
	tmp = 0
	if x1 <= -6.8e+108:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -52000000.0:
		tmp = t_3
	elif x1 <= 0.48:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_3
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_2 * Float64(3.0 + Float64(-1.0 / x1))) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(-1.0 / x1)))))))))
	tmp = 0.0
	if (x1 <= -6.8e+108)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -52000000.0)
		tmp = t_3;
	elseif (x1 <= 0.48)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 + (x2 * 6.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = x1 + ((3.0 * (x2 * -2.0)) + (x1 + ((x1 * (x1 * x1)) + ((t_2 * (3.0 + (-1.0 / x1))) + (t_0 * (((x1 * x1) * (((((t_2 + (2.0 * x2)) - x1) / t_0) * 4.0) - 6.0)) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	tmp = 0.0;
	if (x1 <= -6.8e+108)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -52000000.0)
		tmp = t_3;
	elseif (x1 <= 0.48)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision] * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -6.8e+108], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -52000000.0], t$95$3, If[LessEqual[x1, 0.48], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$3, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -6.79999999999999992e108

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -6.79999999999999992e108 < x1 < -5.2e7 or 0.47999999999999998 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 95.1%

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

   3. Taylor expanded in x1 around inf 83.3%

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

   4. Taylor expanded in x1 around inf 83.5%

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

   5. Taylor expanded in x1 around 0 83.5%

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

      1. *-commutative 21.7%

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

   7. Simplified 83.5%

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

   if -5.2e7 < x1 < 0.47999999999999998

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 96.8%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -6.8 \cdot 10^{+108}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -52000000:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.48:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} \cdot 4 - 6\right) + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 17: 79.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 + x2 \cdot 6\\ t_2 := x1 \cdot x1 + 1\\ t_3 := 3 \cdot \frac{\left(t_0 - 2 \cdot x2\right) - x1}{t_2}\\ t_4 := x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \left(3 + \frac{-1}{x1}\right) + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -8.6 \cdot 10^{+16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x1 \leq 0.47:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ x1 (* x2 6.0)))
        (t_2 (+ (* x1 x1) 1.0))
        (t_3 (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_2)))
        (t_4
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (+ 3.0 (/ -1.0 x1)))
              (*
               t_2
               (+ (* (* x1 x1) 6.0) (* (* (* x1 2.0) 3.0) (/ -1.0 x1)))))))))))
   (if (<= x1 -5.8e+102)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -8.6e+16)
       t_4
       (if (<= x1 0.47)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
         (if (<= x1 1.35e+154) t_4 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -8.6e+16) {
		tmp = t_4;
	} else if (x1 <= 0.47) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = x1 + (x2 * 6.0d0)
    t_2 = (x1 * x1) + 1.0d0
    t_3 = 3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_2)
    t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0d0 + ((-1.0d0) / x1))) + (t_2 * (((x1 * x1) * 6.0d0) + (((x1 * 2.0d0) * 3.0d0) * ((-1.0d0) / x1))))))))
    if (x1 <= (-5.8d+102)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-8.6d+16)) then
        tmp = t_4
    else if (x1 <= 0.47d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_4
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = x1 + (x2 * 6.0);
	double t_2 = (x1 * x1) + 1.0;
	double t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	double t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	double tmp;
	if (x1 <= -5.8e+102) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -8.6e+16) {
		tmp = t_4;
	} else if (x1 <= 0.47) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_4;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = x1 + (x2 * 6.0)
	t_2 = (x1 * x1) + 1.0
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2)
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))))
	tmp = 0
	if x1 <= -5.8e+102:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -8.6e+16:
		tmp = t_4
	elif x1 <= 0.47:
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	elif x1 <= 1.35e+154:
		tmp = t_4
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	t_2 = Float64(Float64(x1 * x1) + 1.0)
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_2))
	t_4 = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(3.0 + Float64(-1.0 / x1))) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * 6.0) + Float64(Float64(Float64(x1 * 2.0) * 3.0) * Float64(-1.0 / x1)))))))))
	tmp = 0.0
	if (x1 <= -5.8e+102)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -8.6e+16)
		tmp = t_4;
	elseif (x1 <= 0.47)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = x1 + (x2 * 6.0);
	t_2 = (x1 * x1) + 1.0;
	t_3 = 3.0 * (((t_0 - (2.0 * x2)) - x1) / t_2);
	t_4 = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * (3.0 + (-1.0 / x1))) + (t_2 * (((x1 * x1) * 6.0) + (((x1 * 2.0) * 3.0) * (-1.0 / x1))))))));
	tmp = 0.0;
	if (x1 <= -5.8e+102)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -8.6e+16)
		tmp = t_4;
	elseif (x1 <= 0.47)
		tmp = x1 + (t_3 + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_4;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(3.0 + N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision] + N[(N[(N[(x1 * 2.0), $MachinePrecision] * 3.0), $MachinePrecision] * N[(-1.0 / x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.8e+102], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -8.6e+16], t$95$4, If[LessEqual[x1, 0.47], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$4, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.8000000000000005e102

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 0.9%

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

      1. flip-+ 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   5. Applied egg-rr 0.0%

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

      1. fma-neg 13.2%

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

      2. swap-sqr 13.2%

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

      3. unpow2 13.2%

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

      4. distribute-rgt-neg-in 13.2%

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

      5. unpow2 13.2%

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

      6. metadata-eval 13.2%

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

      7. metadata-eval 13.2%

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

      8. sub-neg 13.2%

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

      9. distribute-rgt-neg-in 13.2%

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

      10. metadata-eval 13.2%

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

   7. Simplified 13.2%

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

   8. Taylor expanded in x1 around 0 14.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 14.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 14.8%

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

      3. associate-*r* 14.8%

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

   10. Simplified 14.8%

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

   if -5.8000000000000005e102 < x1 < -8.6e16 or 0.46999999999999997 < x1 < 1.35000000000000003e154

   1. Initial program 99.3%

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

   2. Taylor expanded in x1 around inf 95.0%

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

   3. Taylor expanded in x1 around inf 84.3%

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

   4. Taylor expanded in x1 around inf 84.5%

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

   5. Taylor expanded in x1 around inf 76.0%

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

   if -8.6e16 < x1 < 0.46999999999999997

   1. Initial program 98.4%

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

   2. Taylor expanded in x1 around 0 96.1%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

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

   10. Simplified 93.3%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+102}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -8.6 \cdot 10^{+16}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 0.47:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \left(3 + \frac{-1}{x1}\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 6 + \left(\left(x1 \cdot 2\right) \cdot 3\right) \cdot \frac{-1}{x1}\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 18: 68.6% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_0}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0))))
   (if (<= x1 -4.8e+30)
     (/ (* x2 (* x2 -36.0)) t_0)
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))
         (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))))
       (/ (* x1 x1) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    if (x1 <= (-4.8d+30)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_0
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (2.0d0 * x2)) - x1) / ((x1 * x1) + 1.0d0))) + (x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))))
    else
        tmp = (x1 * x1) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -4.8e+30:
		tmp = (x2 * (x2 * -36.0)) / t_0
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))))
	else:
		tmp = (x1 * x1) / t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -4.8e+30)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_0);
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(2.0 * x2)) - x1) / Float64(Float64(x1 * x1) + 1.0))) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0)))))));
	else
		tmp = Float64(Float64(x1 * x1) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -4.8e+30)
		tmp = (x2 * (x2 * -36.0)) / t_0;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (2.0 * x2)) - x1) / ((x1 * x1) + 1.0))) + (x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))));
	else
		tmp = (x1 * x1) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+30], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(3.0 * N[(N[(N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.7999999999999999e30

   1. Initial program 32.1%

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

   2. Taylor expanded in x1 around 0 2.1%

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

   3. Taylor expanded in x1 around 0 1.0%

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

      1. flip-+ 2.0%

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

      2. *-commutative 2.0%

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

      3. *-commutative 2.0%

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

      4. *-commutative 2.0%

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

   5. Applied egg-rr 2.0%

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

      1. fma-neg 11.0%

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

      2. swap-sqr 11.0%

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

      3. unpow2 11.0%

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

      4. distribute-rgt-neg-in 11.0%

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

      5. unpow2 11.0%

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

      6. metadata-eval 11.0%

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

      7. metadata-eval 11.0%

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

      8. sub-neg 11.0%

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

      9. distribute-rgt-neg-in 11.0%

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

      10. metadata-eval 11.0%

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

   7. Simplified 11.0%

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

   8. Taylor expanded in x1 around 0 12.4%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 12.4%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 12.4%

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

      3. associate-*r* 12.4%

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

   10. Simplified 12.4%

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

   if -4.7999999999999999e30 < x1 < 1.35000000000000003e154

   1. Initial program 98.6%

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

   2. Taylor expanded in x1 around 0 79.9%

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

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x1 around 0 6.3%

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

      1. flip-+ 83.3%

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

      2. *-commutative 83.3%

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

      3. *-commutative 83.3%

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

      4. *-commutative 83.3%

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

   5. Applied egg-rr 83.3%

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

      1. fma-neg 90.0%

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

      2. swap-sqr 90.0%

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

      3. unpow2 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

      5. unpow2 90.0%

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

      6. metadata-eval 90.0%

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

      7. metadata-eval 90.0%

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

      8. sub-neg 90.0%

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

      9. distribute-rgt-neg-in 90.0%

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

      10. metadata-eval 90.0%

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

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 19: 63.7% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot x2 - 3\\ t_1 := x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot t_0\right) - 2\right) + x2 \cdot -6\right)\\ t_2 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -1.02 \cdot 10^{+154}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_2}\\ \mathbf{elif}\;x1 \leq -1.42 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot t_0\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (- (* 2.0 x2) 3.0))
        (t_1 (+ x1 (+ (* x1 (- (* 4.0 (* x2 t_0)) 2.0)) (* x2 -6.0))))
        (t_2 (+ x1 (* x2 6.0))))
   (if (<= x1 -1.02e+154)
     (/ (* x2 (* x2 -36.0)) t_2)
     (if (<= x1 -1.42e-153)
       t_1
       (if (<= x1 1.3e-271)
         (+ x1 (+ (* 3.0 (* x2 -2.0)) (+ x1 (* 4.0 (* x2 (* x1 t_0))))))
         (if (<= x1 1.35e+154) t_1 (/ (* x1 x1) t_2)))))))

C

double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	double t_2 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -1.02e+154) {
		tmp = (x2 * (x2 * -36.0)) / t_2;
	} else if (x1 <= -1.42e-153) {
		tmp = t_1;
	} else if (x1 <= 1.3e-271) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_1;
	} else {
		tmp = (x1 * x1) / t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (2.0d0 * x2) - 3.0d0
    t_1 = x1 + ((x1 * ((4.0d0 * (x2 * t_0)) - 2.0d0)) + (x2 * (-6.0d0)))
    t_2 = x1 + (x2 * 6.0d0)
    if (x1 <= (-1.02d+154)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_2
    else if (x1 <= (-1.42d-153)) then
        tmp = t_1
    else if (x1 <= 1.3d-271) then
        tmp = x1 + ((3.0d0 * (x2 * (-2.0d0))) + (x1 + (4.0d0 * (x2 * (x1 * t_0)))))
    else if (x1 <= 1.35d+154) then
        tmp = t_1
    else
        tmp = (x1 * x1) / t_2
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (2.0 * x2) - 3.0;
	double t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	double t_2 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -1.02e+154) {
		tmp = (x2 * (x2 * -36.0)) / t_2;
	} else if (x1 <= -1.42e-153) {
		tmp = t_1;
	} else if (x1 <= 1.3e-271) {
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_1;
	} else {
		tmp = (x1 * x1) / t_2;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (2.0 * x2) - 3.0
	t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0))
	t_2 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -1.02e+154:
		tmp = (x2 * (x2 * -36.0)) / t_2
	elif x1 <= -1.42e-153:
		tmp = t_1
	elif x1 <= 1.3e-271:
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))))
	elif x1 <= 1.35e+154:
		tmp = t_1
	else:
		tmp = (x1 * x1) / t_2
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(2.0 * x2) - 3.0)
	t_1 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * t_0)) - 2.0)) + Float64(x2 * -6.0)))
	t_2 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -1.02e+154)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_2);
	elseif (x1 <= -1.42e-153)
		tmp = t_1;
	elseif (x1 <= 1.3e-271)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(x2 * -2.0)) + Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * t_0))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_1;
	else
		tmp = Float64(Float64(x1 * x1) / t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (2.0 * x2) - 3.0;
	t_1 = x1 + ((x1 * ((4.0 * (x2 * t_0)) - 2.0)) + (x2 * -6.0));
	t_2 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -1.02e+154)
		tmp = (x2 * (x2 * -36.0)) / t_2;
	elseif (x1 <= -1.42e-153)
		tmp = t_1;
	elseif (x1 <= 1.3e-271)
		tmp = x1 + ((3.0 * (x2 * -2.0)) + (x1 + (4.0 * (x2 * (x1 * t_0)))));
	elseif (x1 <= 1.35e+154)
		tmp = t_1;
	else
		tmp = (x1 * x1) / t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * t$95$0), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.02e+154], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[x1, -1.42e-153], t$95$1, If[LessEqual[x1, 1.3e-271], N[(x1 + N[(N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(x2 * N[(x1 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$1, N[(N[(x1 * x1), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.02000000000000007e154

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 0.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 15.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 15.2%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 15.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 16.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 16.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 16.8%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 16.8%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 16.8%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -1.02000000000000007e154 < x1 < -1.42000000000000007e-153 or 1.3e-271 < x1 < 1.35000000000000003e154

   1. Initial program 95.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 63.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 61.2%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   if -1.42000000000000007e-153 < x1 < 1.3e-271

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 87.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. *-commutative 87.7%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   5. Simplified 87.7%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2\right)}\right) \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.02 \cdot 10^{+154}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -1.42 \cdot 10^{-153}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.3 \cdot 10^{-271}:\\ \;\;\;\;x1 + \left(3 \cdot \left(x2 \cdot -2\right) + \left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 20: 68.5% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_0}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0))))
   (if (<= x1 -7.5e+153)
     (/ (* x2 (* x2 -36.0)) t_0)
     (if (<= x1 1.35e+154)
       (+
        x1
        (+
         (+ x1 (* 4.0 (* x2 (* x1 (- (* 2.0 x2) 3.0)))))
         (* 3.0 (- (* x2 -2.0) x1))))
       (/ (* x1 x1) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -7.5e+153) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    if (x1 <= (-7.5d+153)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_0
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 + (4.0d0 * (x2 * (x1 * ((2.0d0 * x2) - 3.0d0))))) + (3.0d0 * ((x2 * (-2.0d0)) - x1)))
    else
        tmp = (x1 * x1) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -7.5e+153) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -7.5e+153:
		tmp = (x2 * (x2 * -36.0)) / t_0
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)))
	else:
		tmp = (x1 * x1) / t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -7.5e+153)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_0);
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(4.0 * Float64(x2 * Float64(x1 * Float64(Float64(2.0 * x2) - 3.0))))) + Float64(3.0 * Float64(Float64(x2 * -2.0) - x1))));
	else
		tmp = Float64(Float64(x1 * x1) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -7.5e+153)
		tmp = (x2 * (x2 * -36.0)) / t_0;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 + (4.0 * (x2 * (x1 * ((2.0 * x2) - 3.0))))) + (3.0 * ((x2 * -2.0) - x1)));
	else
		tmp = (x1 * x1) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -7.5e+153], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 + N[(4.0 * N[(x2 * N[(x1 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -7.50000000000000065e153

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 0.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 15.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 15.2%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 15.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 16.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 16.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 16.8%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 16.8%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 16.8%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -7.50000000000000065e153 < x1 < 1.35000000000000003e154

   1. Initial program 96.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 71.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-1 \cdot x1 + -2 \cdot x2\right)}\right) \]
   4. Step-by-step derivation

      1. +-commutative 70.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 + -1 \cdot x1\right)}\right) \]

      2. neg-mul-1 70.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(-2 \cdot x2 + \color{blue}{\left(-x1\right)}\right)\right) \]

      3. unsub-neg 70.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(-2 \cdot x2 - x1\right)}\right) \]

      4. *-commutative 70.6%

         \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \left(\color{blue}{x2 \cdot -2} - x1\right)\right) \]

   5. Simplified 70.6%

      \[\leadsto x1 + \left(\left(4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right) + x1\right) + 3 \cdot \color{blue}{\left(x2 \cdot -2 - x1\right)}\right) \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -7.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(\left(x1 + 4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right) + 3 \cdot \left(x2 \cdot -2 - x1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 21: 47.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -4 \cdot 10^{-105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ 9.0 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0))))))))
        (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -4.8e+30)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -4e-105)
       t_0
       (if (<= x1 3.7e-122)
         (* x2 -6.0)
         (if (<= x1 1.35e+154) t_0 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (9.0 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -4e-105) {
		tmp = t_0;
	} else if (x1 <= 3.7e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / 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 + (9.0d0 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))))))
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-4.8d+30)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-4d-105)) then
        tmp = t_0
    else if (x1 <= 3.7d-122) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.35d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (9.0 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -4e-105) {
		tmp = t_0;
	} else if (x1 <= 3.7e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (9.0 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))))
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -4.8e+30:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -4e-105:
		tmp = t_0
	elif x1 <= 3.7e-122:
		tmp = x2 * -6.0
	elif x1 <= 1.35e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(9.0 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0)))))))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -4.8e+30)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -4e-105)
		tmp = t_0;
	elseif (x1 <= 3.7e-122)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (9.0 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0))))));
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -4.8e+30)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -4e-105)
		tmp = t_0;
	elseif (x1 <= 3.7e-122)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(9.0 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+30], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -4e-105], t$95$0, If[LessEqual[x1, 3.7e-122], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.7999999999999999e30

   1. Initial program 32.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 2.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 2.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 2.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 11.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 11.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 11.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 12.4%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 12.4%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 12.4%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 12.4%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 12.4%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -4.7999999999999999e30 < x1 < -3.99999999999999986e-105 or 3.6999999999999997e-122 < x1 < 1.35000000000000003e154

   1. Initial program 98.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 39.3%

      \[\leadsto x1 + \color{blue}{\left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)} \]

   if -3.99999999999999986e-105 < x1 < 3.6999999999999997e-122

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

   4. Taylor expanded in x1 around 0 59.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -4 \cdot 10^{-105}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(9 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 22: 47.6% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* 2.0 x2) 3.0)))))))
        (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -4.8e+30)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -5.5e-106)
       t_0
       (if (<= x1 3.8e-122)
         (* x2 -6.0)
         (if (<= x1 1.35e+154) t_0 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -5.5e-106) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / 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 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0)))))
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-4.8d+30)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-5.5d-106)) then
        tmp = t_0
    else if (x1 <= 3.8d-122) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.35d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.8e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -5.5e-106) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))))
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -4.8e+30:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -5.5e-106:
		tmp = t_0
	elif x1 <= 3.8e-122:
		tmp = x2 * -6.0
	elif x1 <= 1.35e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))))))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -4.8e+30)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -5.5e-106)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * (1.0 + (4.0 * (x2 * ((2.0 * x2) - 3.0)))));
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -4.8e+30)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -5.5e-106)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.8e+30], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -5.5e-106], t$95$0, If[LessEqual[x1, 3.8e-122], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -4.7999999999999999e30

   1. Initial program 32.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 2.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 2.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 2.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 11.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 11.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 11.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 12.4%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 12.4%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 12.4%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 12.4%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 12.4%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -4.7999999999999999e30 < x1 < -5.5000000000000001e-106 or 3.8000000000000001e-122 < x1 < 1.35000000000000003e154

   1. Initial program 98.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around inf 39.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} \]

   if -5.5000000000000001e-106 < x1 < 3.8000000000000001e-122

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

   4. Taylor expanded in x1 around 0 59.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -5.5 \cdot 10^{-106}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 23: 63.0% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_0}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x2 6.0))))
   (if (<= x1 -4.5e+153)
     (/ (* x2 (* x2 -36.0)) t_0)
     (if (<= x1 1.35e+154)
       (+ x1 (+ (* x1 (- (* 4.0 (* x2 (- (* 2.0 x2) 3.0))) 2.0)) (* x2 -6.0)))
       (/ (* x1 x1) t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x2 * 6.0d0)
    if (x1 <= (-4.5d+153)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_0
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((x1 * ((4.0d0 * (x2 * ((2.0d0 * x2) - 3.0d0))) - 2.0d0)) + (x2 * (-6.0d0)))
    else
        tmp = (x1 * x1) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -4.5e+153) {
		tmp = (x2 * (x2 * -36.0)) / t_0;
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = (x1 * x1) / t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -4.5e+153:
		tmp = (x2 * (x2 * -36.0)) / t_0
	elif x1 <= 1.35e+154:
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0))
	else:
		tmp = (x1 * x1) / t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -4.5e+153)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_0);
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(2.0 * x2) - 3.0))) - 2.0)) + Float64(x2 * -6.0)));
	else
		tmp = Float64(Float64(x1 * x1) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -4.5e+153)
		tmp = (x2 * (x2 * -36.0)) / t_0;
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((x1 * ((4.0 * (x2 * ((2.0 * x2) - 3.0))) - 2.0)) + (x2 * -6.0));
	else
		tmp = (x1 * x1) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -4.5e+153], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(2.0 * x2), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x1 * x1), $MachinePrecision] / t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -4.5000000000000001e153

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 0.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 0.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 15.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 15.2%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 15.2%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 15.2%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 16.8%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 16.8%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 16.8%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 16.8%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 16.8%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -4.5000000000000001e153 < x1 < 1.35000000000000003e154

   1. Initial program 96.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 71.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 62.7%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + -6 \cdot x2\right)} \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(4 \cdot \left(x2 \cdot \left(2 \cdot x2 - 3\right)\right) - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 24: 47.6% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ t_1 := x1 + x2 \cdot 6\\ \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{t_1}\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* (* x2 x2) 8.0)))) (t_1 (+ x1 (* x2 6.0))))
   (if (<= x1 -2.05e+30)
     (/ (* x2 (* x2 -36.0)) t_1)
     (if (<= x1 -1.35e-104)
       t_0
       (if (<= x1 3.8e-122)
         (* x2 -6.0)
         (if (<= x1 1.35e+154) t_0 (/ (* x1 x1) t_1)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -2.05e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -1.35e-104) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / 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 + (x1 * ((x2 * x2) * 8.0d0))
    t_1 = x1 + (x2 * 6.0d0)
    if (x1 <= (-2.05d+30)) then
        tmp = (x2 * (x2 * (-36.0d0))) / t_1
    else if (x1 <= (-1.35d-104)) then
        tmp = t_0
    else if (x1 <= 3.8d-122) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.35d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double t_1 = x1 + (x2 * 6.0);
	double tmp;
	if (x1 <= -2.05e+30) {
		tmp = (x2 * (x2 * -36.0)) / t_1;
	} else if (x1 <= -1.35e-104) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((x2 * x2) * 8.0))
	t_1 = x1 + (x2 * 6.0)
	tmp = 0
	if x1 <= -2.05e+30:
		tmp = (x2 * (x2 * -36.0)) / t_1
	elif x1 <= -1.35e-104:
		tmp = t_0
	elif x1 <= 3.8e-122:
		tmp = x2 * -6.0
	elif x1 <= 1.35e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)))
	t_1 = Float64(x1 + Float64(x2 * 6.0))
	tmp = 0.0
	if (x1 <= -2.05e+30)
		tmp = Float64(Float64(x2 * Float64(x2 * -36.0)) / t_1);
	elseif (x1 <= -1.35e-104)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	t_1 = x1 + (x2 * 6.0);
	tmp = 0.0;
	if (x1 <= -2.05e+30)
		tmp = (x2 * (x2 * -36.0)) / t_1;
	elseif (x1 <= -1.35e-104)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.05e+30], N[(N[(x2 * N[(x2 * -36.0), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[x1, -1.35e-104], t$95$0, If[LessEqual[x1, 3.8e-122], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -2.05000000000000003e30

   1. Initial program 32.1%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 2.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 1.0%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 2.0%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 2.0%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 2.0%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 11.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 11.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 11.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 11.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around 0 12.4%

      \[\leadsto \frac{\color{blue}{-36 \cdot {x2}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. *-commutative 12.4%

         \[\leadsto \frac{\color{blue}{{x2}^{2} \cdot -36}}{x1 + x2 \cdot 6} \]

      2. unpow2 12.4%

         \[\leadsto \frac{\color{blue}{\left(x2 \cdot x2\right)} \cdot -36}{x1 + x2 \cdot 6} \]

      3. associate-*r* 12.4%

         \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   10. Simplified 12.4%

       \[\leadsto \frac{\color{blue}{x2 \cdot \left(x2 \cdot -36\right)}}{x1 + x2 \cdot 6} \]

   if -2.05000000000000003e30 < x1 < -1.3499999999999999e-104 or 3.8000000000000001e-122 < x1 < 1.35000000000000003e154

   1. Initial program 98.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 63.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 39.0%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 39.0%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 39.0%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. associate-*l* 39.0%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left({x2}^{2} \cdot 8\right)} \]

      4. unpow2 39.0%

         \[\leadsto x1 + x1 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot 8\right) \]

   5. Simplified 39.0%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)} \]

   if -1.3499999999999999e-104 < x1 < 3.8000000000000001e-122

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

   4. Taylor expanded in x1 around 0 59.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.05 \cdot 10^{+30}:\\ \;\;\;\;\frac{x2 \cdot \left(x2 \cdot -36\right)}{x1 + x2 \cdot 6}\\ \mathbf{elif}\;x1 \leq -1.35 \cdot 10^{-104}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 25: 45.4% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{if}\;x1 \leq -2.75 \cdot 10^{-106}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* (* x2 x2) 8.0)))))
   (if (<= x1 -2.75e-106)
     t_0
     (if (<= x1 3.8e-122)
       (* x2 -6.0)
       (if (<= x1 1.35e+154) t_0 (/ (* x1 x1) (+ x1 (* x2 6.0))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double tmp;
	if (x1 <= -2.75e-106) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 * ((x2 * x2) * 8.0d0))
    if (x1 <= (-2.75d-106)) then
        tmp = t_0
    else if (x1 <= 3.8d-122) then
        tmp = x2 * (-6.0d0)
    else if (x1 <= 1.35d+154) then
        tmp = t_0
    else
        tmp = (x1 * x1) / (x1 + (x2 * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double tmp;
	if (x1 <= -2.75e-106) {
		tmp = t_0;
	} else if (x1 <= 3.8e-122) {
		tmp = x2 * -6.0;
	} else if (x1 <= 1.35e+154) {
		tmp = t_0;
	} else {
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((x2 * x2) * 8.0))
	tmp = 0
	if x1 <= -2.75e-106:
		tmp = t_0
	elif x1 <= 3.8e-122:
		tmp = x2 * -6.0
	elif x1 <= 1.35e+154:
		tmp = t_0
	else:
		tmp = (x1 * x1) / (x1 + (x2 * 6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)))
	tmp = 0.0
	if (x1 <= -2.75e-106)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = Float64(x2 * -6.0);
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = Float64(Float64(x1 * x1) / Float64(x1 + Float64(x2 * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	tmp = 0.0;
	if (x1 <= -2.75e-106)
		tmp = t_0;
	elseif (x1 <= 3.8e-122)
		tmp = x2 * -6.0;
	elseif (x1 <= 1.35e+154)
		tmp = t_0;
	else
		tmp = (x1 * x1) / (x1 + (x2 * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -2.75e-106], t$95$0, If[LessEqual[x1, 3.8e-122], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$0, N[(N[(x1 * x1), $MachinePrecision] / N[(x1 + N[(x2 * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -2.75000000000000005e-106 or 3.8000000000000001e-122 < x1 < 1.35000000000000003e154

   1. Initial program 72.9%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 39.8%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 24.9%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 24.9%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 24.9%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. associate-*l* 24.9%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left({x2}^{2} \cdot 8\right)} \]

      4. unpow2 24.9%

         \[\leadsto x1 + x1 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot 8\right) \]

   5. Simplified 24.9%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)} \]

   if -2.75000000000000005e-106 < x1 < 3.8000000000000001e-122

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

   4. Taylor expanded in x1 around 0 59.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

   if 1.35000000000000003e154 < x1

   1. Initial program 0.0%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 0.0%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 6.3%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
   4. Step-by-step derivation

      1. flip-+ 83.3%

         \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

      2. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

      3. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

      4. *-commutative 83.3%

         \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

   5. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
   6. Step-by-step derivation

      1. fma-neg 90.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

      2. swap-sqr 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      3. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      4. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

      5. unpow2 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

      6. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

      7. metadata-eval 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

      8. sub-neg 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

      9. distribute-rgt-neg-in 90.0%

         \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

      10. metadata-eval 90.0%

          \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

   7. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

   8. Taylor expanded in x1 around inf 93.3%

      \[\leadsto \frac{\color{blue}{{x1}^{2}}}{x1 + x2 \cdot 6} \]
   9. Step-by-step derivation

      1. unpow2 93.3%

         \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]

   10. Simplified 93.3%

       \[\leadsto \frac{\color{blue}{x1 \cdot x1}}{x1 + x2 \cdot 6} \]
3. Recombined 3 regimes into one program.

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.75 \cdot 10^{-106}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 3.8 \cdot 10^{-122}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1}{x1 + x2 \cdot 6}\\ \end{array} \]

Alternative 26: 39.8% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -8.1 \cdot 10^{-106} \lor \neg \left(x1 \leq 3.7 \cdot 10^{-122}\right):\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -8.1e-106) (not (<= x1 3.7e-122)))
   (+ x1 (* x1 (* (* x2 x2) 8.0)))
   (* x2 -6.0)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -8.1e-106) || !(x1 <= 3.7e-122)) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} 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 <= (-8.1d-106)) .or. (.not. (x1 <= 3.7d-122))) then
        tmp = x1 + (x1 * ((x2 * x2) * 8.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -8.1e-106) || !(x1 <= 3.7e-122)) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -8.1e-106) or not (x1 <= 3.7e-122):
		tmp = x1 + (x1 * ((x2 * x2) * 8.0))
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -8.1e-106) || !(x1 <= 3.7e-122))
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -8.1e-106) || ~((x1 <= 3.7e-122)))
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -8.1e-106], N[Not[LessEqual[x1, 3.7e-122]], $MachinePrecision]], N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -8.1000000000000002e-106 or 3.6999999999999997e-122 < x1

   1. Initial program 60.5%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 33.1%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x2 around inf 29.2%

      \[\leadsto x1 + \color{blue}{8 \cdot \left({x2}^{2} \cdot x1\right)} \]
   4. Step-by-step derivation

      1. *-commutative 29.2%

         \[\leadsto x1 + \color{blue}{\left({x2}^{2} \cdot x1\right) \cdot 8} \]

      2. *-commutative 29.2%

         \[\leadsto x1 + \color{blue}{\left(x1 \cdot {x2}^{2}\right)} \cdot 8 \]

      3. associate-*l* 29.2%

         \[\leadsto x1 + \color{blue}{x1 \cdot \left({x2}^{2} \cdot 8\right)} \]

      4. unpow2 29.2%

         \[\leadsto x1 + x1 \cdot \left(\color{blue}{\left(x2 \cdot x2\right)} \cdot 8\right) \]

   5. Simplified 29.2%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)} \]

   if -8.1000000000000002e-106 < x1 < 3.6999999999999997e-122

   1. Initial program 99.3%

      \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   2. Taylor expanded in x1 around 0 99.3%

      \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

   3. Taylor expanded in x1 around 0 59.4%

      \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

   4. Taylor expanded in x1 around 0 59.8%

      \[\leadsto \color{blue}{-6 \cdot x2} \]
   5. Step-by-step derivation

      1. *-commutative 59.8%

         \[\leadsto \color{blue}{x2 \cdot -6} \]

   6. Simplified 59.8%

      \[\leadsto \color{blue}{x2 \cdot -6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -8.1 \cdot 10^{-106} \lor \neg \left(x1 \leq 3.7 \cdot 10^{-122}\right):\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 27: 27.1% accurate, 25.4× speedup

Math

\[\begin{array}{l} \\ x1 + x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ x1 (* x2 -6.0)))

C

double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1 + (x2 * (-6.0d0))
end function

Java

public static double code(double x1, double x2) {
	return x1 + (x2 * -6.0);
}

Python

def code(x1, x2):
	return x1 + (x2 * -6.0)

Julia

function code(x1, x2)
	return Float64(x1 + Float64(x2 * -6.0))
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1 + (x2 * -6.0);
end

Wolfram

code[x1_, x2_] := N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.5%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 53.5%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 21.9%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

4. Final simplification 21.9%

   \[\leadsto x1 + x2 \cdot -6 \]

Alternative 28: 26.9% accurate, 42.3× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (* x2 -6.0))

C

double code(double x1, double x2) {
	return x2 * -6.0;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x2 * (-6.0d0)
end function

Java

public static double code(double x1, double x2) {
	return x2 * -6.0;
}

Python

def code(x1, x2):
	return x2 * -6.0

Julia

function code(x1, x2)
	return Float64(x2 * -6.0)
end

MATLAB

function tmp = code(x1, x2)
	tmp = x2 * -6.0;
end

Wolfram

code[x1_, x2_] := N[(x2 * -6.0), $MachinePrecision]

Derivation

1. Initial program 72.5%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 53.5%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 21.9%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]

4. Taylor expanded in x1 around 0 21.9%

   \[\leadsto \color{blue}{-6 \cdot x2} \]
5. Step-by-step derivation

   1. *-commutative 21.9%

      \[\leadsto \color{blue}{x2 \cdot -6} \]

6. Simplified 21.9%

   \[\leadsto \color{blue}{x2 \cdot -6} \]

7. Final simplification 21.9%

   \[\leadsto x2 \cdot -6 \]

Alternative 29: 3.3% accurate, 127.0× speedup

Math

\[\begin{array}{l} \\ x1 \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 x1)

C

double code(double x1, double x2) {
	return x1;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = x1
end function

Java

public static double code(double x1, double x2) {
	return x1;
}

Python

def code(x1, x2):
	return x1

Julia

function code(x1, x2)
	return x1
end

MATLAB

function tmp = code(x1, x2)
	tmp = x1;
end

Wolfram

code[x1_, x2_] := x1

Derivation

1. Initial program 72.5%

   \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

2. Taylor expanded in x1 around 0 53.5%

   \[\leadsto x1 + \left(\left(\color{blue}{4 \cdot \left(x2 \cdot \left(x1 \cdot \left(2 \cdot x2 - 3\right)\right)\right)} + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \]

3. Taylor expanded in x1 around 0 21.9%

   \[\leadsto x1 + \color{blue}{-6 \cdot x2} \]
4. Step-by-step derivation

   1. flip-+ 31.5%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(-6 \cdot x2\right) \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2}} \]

   2. *-commutative 31.5%

      \[\leadsto \frac{x1 \cdot x1 - \color{blue}{\left(x2 \cdot -6\right)} \cdot \left(-6 \cdot x2\right)}{x1 - -6 \cdot x2} \]

   3. *-commutative 31.5%

      \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \color{blue}{\left(x2 \cdot -6\right)}}{x1 - -6 \cdot x2} \]

   4. *-commutative 31.5%

      \[\leadsto \frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - \color{blue}{x2 \cdot -6}} \]

5. Applied egg-rr 31.5%

   \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)}{x1 - x2 \cdot -6}} \]
6. Step-by-step derivation

   1. fma-neg 34.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(x1, x1, -\left(x2 \cdot -6\right) \cdot \left(x2 \cdot -6\right)\right)}}{x1 - x2 \cdot -6} \]

   2. swap-sqr 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{\left(x2 \cdot x2\right) \cdot \left(-6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

   3. unpow2 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, -\color{blue}{{x2}^{2}} \cdot \left(-6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

   4. distribute-rgt-neg-in 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{{x2}^{2} \cdot \left(--6 \cdot -6\right)}\right)}{x1 - x2 \cdot -6} \]

   5. unpow2 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \color{blue}{\left(x2 \cdot x2\right)} \cdot \left(--6 \cdot -6\right)\right)}{x1 - x2 \cdot -6} \]

   6. metadata-eval 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \left(-\color{blue}{36}\right)\right)}{x1 - x2 \cdot -6} \]

   7. metadata-eval 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot \color{blue}{-36}\right)}{x1 - x2 \cdot -6} \]

   8. sub-neg 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{\color{blue}{x1 + \left(-x2 \cdot -6\right)}} \]

   9. distribute-rgt-neg-in 34.2%

      \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + \color{blue}{x2 \cdot \left(--6\right)}} \]

   10. metadata-eval 34.2%

       \[\leadsto \frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot \color{blue}{6}} \]

7. Simplified 34.2%

   \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x1, x1, \left(x2 \cdot x2\right) \cdot -36\right)}{x1 + x2 \cdot 6}} \]

8. Taylor expanded in x1 around inf 3.4%

   \[\leadsto \color{blue}{x1} \]

9. Final simplification 3.4%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023221 
(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))))))