Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.7% → 98.9%

Time: 37.6s

Alternatives: 23

Speedup: 1.6×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x2 \cdot -2 - x1, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(t_0, 4, -6\right), t_0 \cdot \left(\left(-3 + t_0\right) \cdot \left(x1 \cdot 2\right)\right)\right), \left(x1 \cdot x1\right) \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (/ (fma x1 (* x1 3.0) (- (* x2 2.0) x1)) (fma x1 x1 1.0))))
   (if (<= x1 -3.1e+107)
     (+
      x1
      (+
       (+ x1 (+ (* 6.0 (pow x1 4.0)) (* -3.0 (pow x1 3.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 2e+151)
       (+
        x1
        (fma
         3.0
         (- (* x2 -2.0) x1)
         (+
          x1
          (fma
           (fma x1 x1 1.0)
           (fma
            x1
            (* x1 (fma t_0 4.0 -6.0))
            (* t_0 (* (+ -3.0 t_0) (* x1 2.0))))
           (* (* x1 x1) (+ x1 9.0))))))
       (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))))))

C

double code(double x1, double x2) {
	double t_0 = fma(x1, (x1 * 3.0), ((x2 * 2.0) - x1)) / fma(x1, x1, 1.0);
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 + ((6.0 * pow(x1, 4.0)) + (-3.0 * pow(x1, 3.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+151) {
		tmp = x1 + fma(3.0, ((x2 * -2.0) - x1), (x1 + fma(fma(x1, x1, 1.0), fma(x1, (x1 * fma(t_0, 4.0, -6.0)), (t_0 * ((-3.0 + t_0) * (x1 * 2.0)))), ((x1 * x1) * (x1 + 9.0)))));
	} else {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(fma(x1, Float64(x1 * 3.0), Float64(Float64(x2 * 2.0) - x1)) / fma(x1, x1, 1.0))
	tmp = 0.0
	if (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(6.0 * (x1 ^ 4.0)) + Float64(-3.0 * (x1 ^ 3.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 2e+151)
		tmp = Float64(x1 + fma(3.0, Float64(Float64(x2 * -2.0) - x1), Float64(x1 + fma(fma(x1, x1, 1.0), fma(x1, Float64(x1 * fma(t_0, 4.0, -6.0)), Float64(t_0 * Float64(Float64(-3.0 + t_0) * Float64(x1 * 2.0)))), Float64(Float64(x1 * x1) * Float64(x1 + 9.0))))));
	else
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * N[(x1 * 3.0), $MachinePrecision] + N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(N[(x1 + N[(N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+151], N[(x1 + N[(3.0 * N[(N[(x2 * -2.0), $MachinePrecision] - x1), $MachinePrecision] + N[(x1 + N[(N[(x1 * x1 + 1.0), $MachinePrecision] * N[(x1 * N[(x1 * N[(t$95$0 * 4.0 + -6.0), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * N[(N[(-3.0 + t$95$0), $MachinePrecision] * N[(x1 * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(x1 + 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000026e107

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 19.6%

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

   3. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.10000000000000026e107 < x1 < 2.00000000000000003e151

   1. Initial program 98.7%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x1 around inf 98.7%

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

      1. +-commutative 98.7%

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

      2. cube-mult 98.7%

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

      3. unpow2 98.7%

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

      4. distribute-rgt-out 98.7%

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

      5. unpow2 98.7%

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

   6. Simplified 98.7%

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

   7. Taylor expanded in x1 around 0 99.1%

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

   if 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

      3. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \mathsf{fma}\left(3, x2 \cdot -2 - x1, x1 + \mathsf{fma}\left(\mathsf{fma}\left(x1, x1, 1\right), \mathsf{fma}\left(x1, x1 \cdot \mathsf{fma}\left(\frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}, 4, -6\right), \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)} \cdot \left(\left(-3 + \frac{\mathsf{fma}\left(x1, x1 \cdot 3, x2 \cdot 2 - x1\right)}{\mathsf{fma}\left(x1, x1, 1\right)}\right) \cdot \left(x1 \cdot 2\right)\right)\right), \left(x1 \cdot x1\right) \cdot \left(x1 + 9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \]

Alternative 2: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(t_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \left(\left(\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right) - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(t_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right)\right) + t_0 \cdot t_2\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -3.1e+107)
     (+
      x1
      (+
       (+ x1 (+ (* 6.0 (pow x1 4.0)) (* -3.0 (pow x1 3.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 2e+151)
       (+
        x1
        (+
         (+
          x1
          (+
           (+
            (*
             t_1
             (+
              (*
               (*
                (* x1 2.0)
                (*
                 (- (fma (* x1 3.0) x1 (+ x2 x2)) x1)
                 (/ 1.0 (fma x1 x1 1.0))))
               (- t_2 3.0))
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))))
            (* t_0 t_2))
           (* x1 (* x1 x1))))
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))))
       (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 + ((6.0 * pow(x1, 4.0)) + (-3.0 * pow(x1, 3.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+151) {
		tmp = x1 + ((x1 + (((t_1 * ((((x1 * 2.0) * ((fma((x1 * 3.0), x1, (x2 + x2)) - x1) * (1.0 / fma(x1, x1, 1.0)))) * (t_2 - 3.0)) + ((x1 * x1) * ((4.0 * t_2) - 6.0)))) + (t_0 * t_2)) + (x1 * (x1 * x1)))) + (3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)));
	} else {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(6.0 * (x1 ^ 4.0)) + Float64(-3.0 * (x1 ^ 3.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 2e+151)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(fma(Float64(x1 * 3.0), x1, Float64(x2 + x2)) - x1) * Float64(1.0 / fma(x1, x1, 1.0)))) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)))) + Float64(t_0 * t_2)) + Float64(x1 * Float64(x1 * x1)))) + Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))));
	else
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(N[(x1 + N[(N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+151], N[(x1 + N[(N[(x1 + N[(N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(N[(N[(x1 * 3.0), $MachinePrecision] * x1 + N[(x2 + x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] * N[(1.0 / N[(x1 * x1 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$0 * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000026e107

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 19.6%

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

   3. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.10000000000000026e107 < x1 < 2.00000000000000003e151

   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%

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

      2. div-inv 98.7%

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

      3. fma-def 98.7%

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

      4. count-2 98.7%

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

   3. Applied egg-rr 98.7%

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

   if 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

      3. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(\left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \left(\left(\mathsf{fma}\left(x1 \cdot 3, x1, x2 + x2\right) - x1\right) \cdot \frac{1}{\mathsf{fma}\left(x1, x1, 1\right)}\right)\right) \cdot \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right) + \left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) + x1 \cdot \left(x1 \cdot x1\right)\right)\right) + 3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1}\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \]

Alternative 3: 95.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around 0 0.0%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 87.7%

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

      1. fma-def 87.7%

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

      2. *-commutative 87.7%

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

      3. unpow2 87.7%

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

   8. Simplified 87.7%

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

4. Final simplification 95.5%

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

Alternative 4: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + x1 \cdot x1\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := \frac{\left(x2 \cdot 2 + t_1\right) - x1}{t_0}\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot t_2 + t_0 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_2\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* x1 x1)))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (/ (- (+ (* x2 2.0) t_1) x1) t_0)))
   (if (<= x1 -3.1e+107)
     (+
      x1
      (+
       (+ x1 (+ (* 6.0 (pow x1 4.0)) (* -3.0 (pow x1 3.0))))
       (* 3.0 (* x2 -2.0))))
     (if (<= x1 2e+151)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* t_1 t_2)
            (*
             t_0
             (+
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))
              (* (- t_2 3.0) (* (* x1 2.0) t_2)))))))))
       (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))))))

C

double code(double x1, double x2) {
	double t_0 = 1.0 + (x1 * x1);
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = (((x2 * 2.0) + t_1) - x1) / t_0;
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 + ((6.0 * pow(x1, 4.0)) + (-3.0 * pow(x1, 3.0)))) + (3.0 * (x2 * -2.0)));
	} else if (x1 <= 2e+151) {
		tmp = x1 + ((3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_2) + (t_0 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * t_2))))))));
	} else {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(1.0 + Float64(x1 * x1))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(Float64(x1 + Float64(Float64(6.0 * (x1 ^ 4.0)) + Float64(-3.0 * (x1 ^ 3.0)))) + Float64(3.0 * Float64(x2 * -2.0))));
	elseif (x1 <= 2e+151)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_2) + Float64(t_0 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * t_2)))))))));
	else
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(N[(x1 + N[(N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision] + N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+151], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000026e107

   1. Initial program 0.0%

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

   2. Taylor expanded in x1 around inf 19.6%

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

   3. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.10000000000000026e107 < x1 < 2.00000000000000003e151

   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 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

      3. unpow2 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(\left(x1 + \left(6 \cdot {x1}^{4} + -3 \cdot {x1}^{3}\right)\right) + 3 \cdot \left(x2 \cdot -2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \]

Alternative 5: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ t_1 := x1 \cdot \left(x1 \cdot 3\right)\\ t_2 := 1 + x1 \cdot x1\\ t_3 := 3 \cdot \frac{\left(t_1 - x2 \cdot 2\right) - x1}{t_2}\\ t_4 := \frac{\left(x2 \cdot 2 + t_1\right) - x1}{t_2}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + -3 \cdot {x1}^{3}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot t_4 + t_2 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right) + \left(t_4 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_4\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0))))
        (t_1 (* x1 (* x1 3.0)))
        (t_2 (+ 1.0 (* x1 x1)))
        (t_3 (* 3.0 (/ (- (- t_1 (* x2 2.0)) x1) t_2)))
        (t_4 (/ (- (+ (* x2 2.0) t_1) x1) t_2)))
   (if (<= x1 -5e+159)
     t_0
     (if (<= x1 -3.1e+107)
       (+ x1 (+ t_3 (+ x1 (* -3.0 (pow x1 3.0)))))
       (if (<= x1 2e+151)
         (+
          x1
          (+
           t_3
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_1 t_4)
              (*
               t_2
               (+
                (* (* x1 x1) (- (* 4.0 t_4) 6.0))
                (* (- t_4 3.0) (* (* x1 2.0) t_4)))))))))
         t_0)))))

C

double code(double x1, double x2) {
	double t_0 = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	double t_1 = x1 * (x1 * 3.0);
	double t_2 = 1.0 + (x1 * x1);
	double t_3 = 3.0 * (((t_1 - (x2 * 2.0)) - x1) / t_2);
	double t_4 = (((x2 * 2.0) + t_1) - x1) / t_2;
	double tmp;
	if (x1 <= -5e+159) {
		tmp = t_0;
	} else if (x1 <= -3.1e+107) {
		tmp = x1 + (t_3 + (x1 + (-3.0 * pow(x1, 3.0))));
	} else if (x1 <= 2e+151) {
		tmp = x1 + (t_3 + (x1 + ((x1 * (x1 * x1)) + ((t_1 * t_4) + (t_2 * (((x1 * x1) * ((4.0 * t_4) - 6.0)) + ((t_4 - 3.0) * ((x1 * 2.0) * t_4))))))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)))
	t_1 = Float64(x1 * Float64(x1 * 3.0))
	t_2 = Float64(1.0 + Float64(x1 * x1))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_1 - Float64(x2 * 2.0)) - x1) / t_2))
	t_4 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_1) - x1) / t_2)
	tmp = 0.0
	if (x1 <= -5e+159)
		tmp = t_0;
	elseif (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(-3.0 * (x1 ^ 3.0)))));
	elseif (x1 <= 2e+151)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * t_4) + Float64(t_2 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0)) + Float64(Float64(t_4 - 3.0) * Float64(Float64(x1 * 2.0) * t_4)))))))));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$1 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$1), $MachinePrecision] - x1), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[x1, -5e+159], t$95$0, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(t$95$3 + N[(x1 + N[(-3.0 * N[Power[x1, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2e+151], N[(x1 + N[(t$95$3 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * t$95$4), $MachinePrecision] + N[(t$95$2 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$4 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.00000000000000003e159 or 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 100.0%

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

      1. fma-def 100.0%

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

      2. *-commutative 100.0%

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

      3. unpow2 100.0%

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

   8. Simplified 100.0%

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

   if -5.00000000000000003e159 < x1 < -3.10000000000000026e107

   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 100.0%

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

   3. Taylor expanded in x1 around 0 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -3.10000000000000026e107 < x1 < 2.00000000000000003e151

   1. Initial program 98.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+159}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{elif}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + -3 \cdot {x1}^{3}\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \end{array} \]

Alternative 6: 94.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+109} \lor \neg \left(x1 \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_2\right)\right) + 3 \cdot t_0\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (or (<= x1 -1.55e+109) (not (<= x1 2e+151)))
     (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (*
           t_1
           (+
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))
            (* (- t_2 3.0) (* (* x1 2.0) t_2))))
          (* 3.0 t_0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.55e+109) || !(x1 <= 2e+151)) {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * t_2)))) + (3.0 * t_0)))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.55e+109) || !(x1 <= 2e+151))
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * t_2)))) + Float64(3.0 * t_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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.55e+109], N[Not[LessEqual[x1, 2e+151]], $MachinePrecision]], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.54999999999999996e109 or 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 88.8%

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

      1. fma-def 88.8%

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

      2. *-commutative 88.8%

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

      3. unpow2 88.8%

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

   8. Simplified 88.8%

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

   if -1.54999999999999996e109 < x1 < 2.00000000000000003e151

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around inf 98.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.55 \cdot 10^{+109} \lor \neg \left(x1 \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right)\right) + 3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 7: 91.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+109} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (or (<= x1 -1.6e+109) (not (<= x1 5e+153)))
     (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* 3.0 t_0)
          (*
           t_1
           (+
            (* (* x1 x1) (- (* 4.0 t_2) 6.0))
            (* (- t_2 3.0) (* (* x1 2.0) (- (* x2 2.0) x1)))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if ((x1 <= -1.6e+109) || !(x1 <= 5e+153)) {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -1.6e+109) || !(x1 <= 5e+153))
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x2 * 2.0) - x1))))))))));
	end
	return tmp
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -1.6e+109], N[Not[LessEqual[x1, 5e+153]], $MachinePrecision]], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.6000000000000001e109 or 5.00000000000000018e153 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 88.8%

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

      1. fma-def 88.8%

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

      2. *-commutative 88.8%

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

      3. unpow2 88.8%

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

   8. Simplified 88.8%

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

   if -1.6000000000000001e109 < x1 < 5.00000000000000018e153

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 95.4%

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

   3. Taylor expanded in x1 around inf 95.3%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.6 \cdot 10^{+109} \lor \neg \left(x1 \leq 5 \cdot 10^{+153}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 8: 93.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+107} \lor \neg \left(x1 \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot t_2 + t_1 \cdot \left(\left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot t_2\right) + 6 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (or (<= x1 -5.8e+107) (not (<= x1 2e+151)))
     (+ x1 (fma -2.0 x1 (* (* x1 x1) 9.0)))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (- t_2 3.0) (* (* x1 2.0) t_2)) (* 6.0 (* x1 x1))))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if ((x1 <= -5.8e+107) || !(x1 <= 2e+151)) {
		tmp = x1 + fma(-2.0, x1, ((x1 * x1) * 9.0));
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * (((t_2 - 3.0) * ((x1 * 2.0) * t_2)) + (6.0 * (x1 * x1))))))));
	}
	return tmp;
}

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5.8e+107) || !(x1 <= 2e+151))
		tmp = Float64(x1 + fma(-2.0, x1, Float64(Float64(x1 * x1) * 9.0)));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * t_2)) + Float64(6.0 * Float64(x1 * x1)))))))));
	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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5.8e+107], N[Not[LessEqual[x1, 2e+151]], $MachinePrecision]], N[(x1 + N[(-2.0 * x1 + N[(N[(x1 * x1), $MachinePrecision] * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] + N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5.79999999999999975e107 or 2.00000000000000003e151 < 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%

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

   3. Taylor expanded in x2 around 0 0.0%

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

      1. associate-*r/ 0.0%

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

      2. *-commutative 0.0%

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

      3. unpow2 0.0%

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

      4. associate-*r* 0.0%

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

      5. +-commutative 0.0%

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

      6. unpow2 0.0%

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

      7. fma-udef 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in x1 around 0 88.8%

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

      1. fma-def 88.8%

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

      2. *-commutative 88.8%

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

      3. unpow2 88.8%

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

   8. Simplified 88.8%

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

   if -5.79999999999999975e107 < x1 < 2.00000000000000003e151

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around inf 97.1%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.8 \cdot 10^{+107} \lor \neg \left(x1 \leq 2 \cdot 10^{+151}\right):\\ \;\;\;\;x1 + \mathsf{fma}\left(-2, x1, \left(x1 \cdot x1\right) \cdot 9\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1}\right) + 6 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \end{array} \]

Alternative 9: 78.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1}\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot t_2 - 6\right) + \left(t_2 - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (/ (- (+ (* x2 2.0) t_0) x1) t_1)))
   (if (<= x1 -3.1e+107)
     (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
     (if (<= x1 7.6e+153)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_0)
            (*
             t_1
             (+
              (* (* x1 x1) (- (* 4.0 t_2) 6.0))
              (* (- t_2 3.0) (* (* x1 2.0) (- (* x2 2.0) x1))))))))))
       (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 7.6e+153) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = 1.0d0 + (x1 * x1)
    t_2 = (((x2 * 2.0d0) + t_0) - x1) / t_1
    if (x1 <= (-3.1d+107)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= 7.6d+153) then
        tmp = x1 + ((3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * (((x1 * x1) * ((4.0d0 * t_2) - 6.0d0)) + ((t_2 - 3.0d0) * ((x1 * 2.0d0) * ((x2 * 2.0d0) - x1)))))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 7.6e+153) {
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1
	tmp = 0
	if x1 <= -3.1e+107:
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	elif x1 <= 7.6e+153:
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= 7.6e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_2) - 6.0)) + Float64(Float64(t_2 - 3.0) * Float64(Float64(x1 * 2.0) * Float64(Float64(x2 * 2.0) - x1))))))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = (((x2 * 2.0) + t_0) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -3.1e+107)
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= 7.6e+153)
		tmp = x1 + ((3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * (((x1 * x1) * ((4.0 * t_2) - 6.0)) + ((t_2 - 3.0) * ((x1 * 2.0) * ((x2 * 2.0) - x1)))))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 7.6e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$2), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$2 - 3.0), $MachinePrecision] * N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -3.10000000000000026e107

   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%

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

   3. Taylor expanded in x2 around 0 2.2%

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

      1. *-commutative 2.2%

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

      2. *-commutative 2.2%

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

      3. associate-*l* 2.2%

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

   5. Simplified 2.2%

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

   6. Taylor expanded in x1 around 0 25.1%

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

   if -3.10000000000000026e107 < x1 < 7.59999999999999933e153

   1. Initial program 98.7%

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

   2. Taylor expanded in x1 around 0 95.4%

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

   3. Taylor expanded in x1 around inf 95.3%

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

   if 7.59999999999999933e153 < 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%

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

   3. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   5. Simplified 5.6%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

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

   9. Simplified 77.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 7.6 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 3\right) \cdot \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 10: 78.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot x1\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := 3 \cdot \frac{\left(t_2 - x2 \cdot 2\right) - x1}{t_1}\\ t_4 := \frac{\left(x2 \cdot 2 + t_2\right) - x1}{t_1}\\ t_5 := \left(x1 \cdot x1\right) \cdot \left(4 \cdot t_4 - 6\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -5500000000:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_0 + \left(t_2 \cdot t_4 + t_1 \cdot \left(t_5 + \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1950:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(t_3 + \left(x1 + \left(t_0 + \left(3 \cdot t_2 + t_1 \cdot \left(x1 \cdot 2 + t_5\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 x1)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (* 3.0 (/ (- (- t_2 (* x2 2.0)) x1) t_1)))
        (t_4 (/ (- (+ (* x2 2.0) t_2) x1) t_1))
        (t_5 (* (* x1 x1) (- (* 4.0 t_4) 6.0))))
   (if (<= x1 -5.5e+102)
     (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
     (if (<= x1 -5500000000.0)
       (+
        x1
        (+
         t_3
         (+
          x1
          (+
           t_0
           (+
            (* t_2 t_4)
            (* t_1 (+ t_5 (* (* (* x1 2.0) (- (* x2 2.0) x1)) 0.0))))))))
       (if (<= x1 1950.0)
         (+ x1 (+ t_3 (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
         (if (<= x1 1.35e+154)
           (+
            x1
            (+ t_3 (+ x1 (+ t_0 (+ (* 3.0 t_2) (* t_1 (+ (* x1 2.0) t_5)))))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	double t_4 = (((x2 * 2.0) + t_2) - x1) / t_1;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -5500000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((t_2 * t_4) + (t_1 * (t_5 + (((x1 * 2.0) * ((x2 * 2.0) - x1)) * 0.0)))))));
	} else if (x1 <= 1950.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_2) + (t_1 * ((x1 * 2.0) + t_5))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = 1.0d0 + (x1 * x1)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = 3.0d0 * (((t_2 - (x2 * 2.0d0)) - x1) / t_1)
    t_4 = (((x2 * 2.0d0) + t_2) - x1) / t_1
    t_5 = (x1 * x1) * ((4.0d0 * t_4) - 6.0d0)
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= (-5500000000.0d0)) then
        tmp = x1 + (t_3 + (x1 + (t_0 + ((t_2 * t_4) + (t_1 * (t_5 + (((x1 * 2.0d0) * ((x2 * 2.0d0) - x1)) * 0.0d0)))))))
    else if (x1 <= 1950.0d0) then
        tmp = x1 + (t_3 + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0d0 * t_2) + (t_1 * ((x1 * 2.0d0) + t_5))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * x1);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	double t_4 = (((x2 * 2.0) + t_2) - x1) / t_1;
	double t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -5500000000.0) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((t_2 * t_4) + (t_1 * (t_5 + (((x1 * 2.0) * ((x2 * 2.0) - x1)) * 0.0)))))));
	} else if (x1 <= 1950.0) {
		tmp = x1 + (t_3 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_2) + (t_1 * ((x1 * 2.0) + t_5))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * x1)
	t_1 = 1.0 + (x1 * x1)
	t_2 = x1 * (x1 * 3.0)
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1)
	t_4 = (((x2 * 2.0) + t_2) - x1) / t_1
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0)
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	elif x1 <= -5500000000.0:
		tmp = x1 + (t_3 + (x1 + (t_0 + ((t_2 * t_4) + (t_1 * (t_5 + (((x1 * 2.0) * ((x2 * 2.0) - x1)) * 0.0)))))))
	elif x1 <= 1950.0:
		tmp = x1 + (t_3 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	elif x1 <= 1.35e+154:
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_2) + (t_1 * ((x1 * 2.0) + t_5))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * x1))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(x2 * 2.0)) - x1) / t_1))
	t_4 = Float64(Float64(Float64(Float64(x2 * 2.0) + t_2) - x1) / t_1)
	t_5 = Float64(Float64(x1 * x1) * Float64(Float64(4.0 * t_4) - 6.0))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= -5500000000.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(Float64(t_2 * t_4) + Float64(t_1 * Float64(t_5 + Float64(Float64(Float64(x1 * 2.0) * Float64(Float64(x2 * 2.0) - x1)) * 0.0))))))));
	elseif (x1 <= 1950.0)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(t_3 + Float64(x1 + Float64(t_0 + Float64(Float64(3.0 * t_2) + Float64(t_1 * Float64(Float64(x1 * 2.0) + t_5)))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * x1);
	t_1 = 1.0 + (x1 * x1);
	t_2 = x1 * (x1 * 3.0);
	t_3 = 3.0 * (((t_2 - (x2 * 2.0)) - x1) / t_1);
	t_4 = (((x2 * 2.0) + t_2) - x1) / t_1;
	t_5 = (x1 * x1) * ((4.0 * t_4) - 6.0);
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= -5500000000.0)
		tmp = x1 + (t_3 + (x1 + (t_0 + ((t_2 * t_4) + (t_1 * (t_5 + (((x1 * 2.0) * ((x2 * 2.0) - x1)) * 0.0)))))));
	elseif (x1 <= 1950.0)
		tmp = x1 + (t_3 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + (t_3 + (x1 + (t_0 + ((3.0 * t_2) + (t_1 * ((x1 * 2.0) + t_5))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(N[(N[(t$95$2 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$2), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * t$95$4), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -5500000000.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(N[(t$95$2 * t$95$4), $MachinePrecision] + N[(t$95$1 * N[(t$95$5 + N[(N[(N[(x1 * 2.0), $MachinePrecision] * N[(N[(x2 * 2.0), $MachinePrecision] - x1), $MachinePrecision]), $MachinePrecision] * 0.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1950.0], N[(x1 + N[(t$95$3 + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], N[(x1 + N[(t$95$3 + N[(x1 + N[(t$95$0 + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + t$95$5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 1.9%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 4.1%

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

      1. *-commutative 4.1%

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

      2. *-commutative 4.1%

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

      3. associate-*l* 4.1%

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

   5. Simplified 4.1%

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

   6. Taylor expanded in x1 around 0 26.5%

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

   if -5.49999999999999981e102 < x1 < -5.5e9

   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 0 93.8%

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

   3. Taylor expanded in x1 around inf 83.4%

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

   if -5.5e9 < x1 < 1950

   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 0 83.9%

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

   3. Taylor expanded in x2 around inf 83.9%

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

      1. *-commutative 83.9%

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

      2. unpow2 83.9%

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

      3. associate-*l* 98.6%

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

   5. Simplified 98.6%

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

   if 1950 < x1 < 1.35000000000000003e154

   1. Initial program 95.9%

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

   2. Taylor expanded in x1 around 0 83.4%

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

   3. Taylor expanded in x1 around inf 82.4%

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

   4. Taylor expanded in x1 around inf 82.4%

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

   if 1.35000000000000003e154 < 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%

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

   3. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   5. Simplified 5.6%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

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

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -5500000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right) + \left(\left(x1 \cdot 2\right) \cdot \left(x2 \cdot 2 - x1\right)\right) \cdot 0\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1950:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 11: 78.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\\ t_3 := x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t_0 + t_1 \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -37000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 9600:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1)))
        (t_3
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* 3.0 t_0)
              (*
               t_1
               (+
                (* x1 2.0)
                (*
                 (* x1 x1)
                 (- (* 4.0 (/ (- (+ (* x2 2.0) t_0) x1) t_1)) 6.0)))))))))))
   (if (<= x1 -3.1e+107)
     (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
     (if (<= x1 -37000000.0)
       t_3
       (if (<= x1 9600.0)
         (+ x1 (+ t_2 (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
         (if (<= x1 1.35e+154)
           t_3
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -37000000.0) {
		tmp = t_3;
	} else if (x1 <= 9600.0) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = 1.0d0 + (x1 * x1)
    t_2 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)
    t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * ((x1 * 2.0d0) + ((x1 * x1) * ((4.0d0 * ((((x2 * 2.0d0) + t_0) - x1) / t_1)) - 6.0d0))))))))
    if (x1 <= (-3.1d+107)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= (-37000000.0d0)) then
        tmp = t_3
    else if (x1 <= 9600.0d0) then
        tmp = x1 + (t_2 + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_3
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	double tmp;
	if (x1 <= -3.1e+107) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -37000000.0) {
		tmp = t_3;
	} else if (x1 <= 9600.0) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))))
	tmp = 0
	if x1 <= -3.1e+107:
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	elif x1 <= -37000000.0:
		tmp = t_3
	elif x1 <= 9600.0:
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	elif x1 <= 1.35e+154:
		tmp = t_3
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))
	t_3 = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(x1 * 2.0) + Float64(Float64(x1 * x1) * Float64(Float64(4.0 * Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)) - 6.0)))))))))
	tmp = 0.0
	if (x1 <= -3.1e+107)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= -37000000.0)
		tmp = t_3;
	elseif (x1 <= 9600.0)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((x1 * 2.0) + ((x1 * x1) * ((4.0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) - 6.0))))))));
	tmp = 0.0;
	if (x1 <= -3.1e+107)
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= -37000000.0)
		tmp = t_3;
	elseif (x1 <= 9600.0)
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(4.0 * N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -3.1e+107], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -37000000.0], t$95$3, If[LessEqual[x1, 9600.0], N[(x1 + N[(t$95$2 + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$3, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -3.10000000000000026e107

   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%

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

   3. Taylor expanded in x2 around 0 2.2%

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

      1. *-commutative 2.2%

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

      2. *-commutative 2.2%

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

      3. associate-*l* 2.2%

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

   5. Simplified 2.2%

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

   6. Taylor expanded in x1 around 0 25.1%

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

   if -3.10000000000000026e107 < x1 < -3.7e7 or 9600 < x1 < 1.35000000000000003e154

   1. Initial program 97.5%

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

   2. Taylor expanded in x1 around 0 88.3%

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

   3. Taylor expanded in x1 around inf 83.0%

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

   4. Taylor expanded in x1 around inf 83.0%

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

   if -3.7e7 < x1 < 9600

   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 0 83.9%

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

   3. Taylor expanded in x2 around inf 83.9%

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

      1. *-commutative 83.9%

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

      2. unpow2 83.9%

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

      3. associate-*l* 98.6%

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

   5. Simplified 98.6%

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

   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%

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

   3. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   5. Simplified 5.6%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

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

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -3.1 \cdot 10^{+107}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -37000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 9600:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} - 6\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 12: 76.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := 1 + x1 \cdot x1\\ t_2 := 3 \cdot \frac{\left(t_0 - x2 \cdot 2\right) - x1}{t_1}\\ t_3 := x1 + \left(t_2 + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t_0 \cdot \frac{\left(x2 \cdot 2 + t_0\right) - x1}{t_1} + t_1 \cdot \left(x1 \cdot 2 + 6 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -68000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x1 \leq 42000000000000:\\ \;\;\;\;x1 + \left(t_2 + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ 1.0 (* x1 x1)))
        (t_2 (* 3.0 (/ (- (- t_0 (* x2 2.0)) x1) t_1)))
        (t_3
         (+
          x1
          (+
           t_2
           (+
            x1
            (+
             (* x1 (* x1 x1))
             (+
              (* t_0 (/ (- (+ (* x2 2.0) t_0) x1) t_1))
              (* t_1 (+ (* x1 2.0) (* 6.0 (* x1 x1)))))))))))
   (if (<= x1 -5.5e+102)
     (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
     (if (<= x1 -68000000.0)
       t_3
       (if (<= x1 42000000000000.0)
         (+ x1 (+ t_2 (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
         (if (<= x1 1.35e+154)
           t_3
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) + (t_1 * ((x1 * 2.0) + (6.0 * (x1 * x1))))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -68000000.0) {
		tmp = t_3;
	} else if (x1 <= 42000000000000.0) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: 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 = 1.0d0 + (x1 * x1)
    t_2 = 3.0d0 * (((t_0 - (x2 * 2.0d0)) - x1) / t_1)
    t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x2 * 2.0d0) + t_0) - x1) / t_1)) + (t_1 * ((x1 * 2.0d0) + (6.0d0 * (x1 * x1))))))))
    if (x1 <= (-5.5d+102)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= (-68000000.0d0)) then
        tmp = t_3
    else if (x1 <= 42000000000000.0d0) then
        tmp = x1 + (t_2 + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else if (x1 <= 1.35d+154) then
        tmp = t_3
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = 1.0 + (x1 * x1);
	double t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	double t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) + (t_1 * ((x1 * 2.0) + (6.0 * (x1 * x1))))))));
	double tmp;
	if (x1 <= -5.5e+102) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= -68000000.0) {
		tmp = t_3;
	} else if (x1 <= 42000000000000.0) {
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else if (x1 <= 1.35e+154) {
		tmp = t_3;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = 1.0 + (x1 * x1)
	t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1)
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) + (t_1 * ((x1 * 2.0) + (6.0 * (x1 * x1))))))))
	tmp = 0
	if x1 <= -5.5e+102:
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	elif x1 <= -68000000.0:
		tmp = t_3
	elif x1 <= 42000000000000.0:
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	elif x1 <= 1.35e+154:
		tmp = t_3
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(1.0 + Float64(x1 * x1))
	t_2 = Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(x2 * 2.0)) - x1) / t_1))
	t_3 = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * Float64(Float64(Float64(Float64(x2 * 2.0) + t_0) - x1) / t_1)) + Float64(t_1 * Float64(Float64(x1 * 2.0) + Float64(6.0 * Float64(x1 * x1)))))))))
	tmp = 0.0
	if (x1 <= -5.5e+102)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= -68000000.0)
		tmp = t_3;
	elseif (x1 <= 42000000000000.0)
		tmp = Float64(x1 + Float64(t_2 + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = 1.0 + (x1 * x1);
	t_2 = 3.0 * (((t_0 - (x2 * 2.0)) - x1) / t_1);
	t_3 = x1 + (t_2 + (x1 + ((x1 * (x1 * x1)) + ((t_0 * ((((x2 * 2.0) + t_0) - x1) / t_1)) + (t_1 * ((x1 * 2.0) + (6.0 * (x1 * x1))))))));
	tmp = 0.0;
	if (x1 <= -5.5e+102)
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= -68000000.0)
		tmp = t_3;
	elseif (x1 <= 42000000000000.0)
		tmp = x1 + (t_2 + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	elseif (x1 <= 1.35e+154)
		tmp = t_3;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (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[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(3.0 * N[(N[(N[(t$95$0 - N[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x1 + N[(t$95$2 + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * N[(N[(N[(N[(x2 * 2.0), $MachinePrecision] + t$95$0), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(N[(x1 * 2.0), $MachinePrecision] + N[(6.0 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -5.5e+102], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -68000000.0], t$95$3, If[LessEqual[x1, 42000000000000.0], N[(x1 + N[(t$95$2 + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.35e+154], t$95$3, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -5.49999999999999981e102

   1. Initial program 1.9%

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

   2. Taylor expanded in x1 around 0 1.9%

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

   3. Taylor expanded in x2 around 0 4.1%

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

      1. *-commutative 4.1%

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

      2. *-commutative 4.1%

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

      3. associate-*l* 4.1%

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

   5. Simplified 4.1%

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

   6. Taylor expanded in x1 around 0 26.5%

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

   if -5.49999999999999981e102 < x1 < -6.8e7 or 4.2e13 < x1 < 1.35000000000000003e154

   1. Initial program 97.4%

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

   2. Taylor expanded in x1 around 0 91.2%

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

   3. Taylor expanded in x1 around inf 85.5%

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

   4. Taylor expanded in x1 around inf 80.2%

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

   if -6.8e7 < x1 < 4.2e13

   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 0 82.7%

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

   3. Taylor expanded in x2 around inf 82.7%

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

      1. *-commutative 82.7%

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

      2. unpow2 82.7%

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

      3. associate-*l* 97.2%

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

   5. Simplified 97.2%

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

   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%

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

   3. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   5. Simplified 5.6%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

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

   9. Simplified 77.4%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.5 \cdot 10^{+102}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -68000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + 6 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 42000000000000:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x2 \cdot 2 + x1 \cdot \left(x1 \cdot 3\right)\right) - x1}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(x1 \cdot 2 + 6 \cdot \left(x1 \cdot x1\right)\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 13: 68.2% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -1.75e+75)
   (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
   (if (<= x1 1.35e+154)
     (+
      x1
      (+
       (* 3.0 (/ (- (- (* x1 (* x1 3.0)) (* x2 2.0)) x1) (+ 1.0 (* x1 x1))))
       (+ x1 (* 4.0 (* 2.0 (* x2 (* x1 x2)))))))
     (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-1.75d+75)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else if (x1 <= 1.35d+154) then
        tmp = x1 + ((3.0d0 * ((((x1 * (x1 * 3.0d0)) - (x2 * 2.0d0)) - x1) / (1.0d0 + (x1 * x1)))) + (x1 + (4.0d0 * (2.0d0 * (x2 * (x1 * x2))))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else if (x1 <= 1.35e+154) {
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -1.75e+75:
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	elif x1 <= 1.35e+154:
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -1.75e+75)
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	elseif (x1 <= 1.35e+154)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(Float64(x1 * Float64(x1 * 3.0)) - Float64(x2 * 2.0)) - x1) / Float64(1.0 + Float64(x1 * x1)))) + Float64(x1 + Float64(4.0 * Float64(2.0 * Float64(x2 * Float64(x1 * x2)))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -1.75e+75)
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	elseif (x1 <= 1.35e+154)
		tmp = x1 + ((3.0 * ((((x1 * (x1 * 3.0)) - (x2 * 2.0)) - x1) / (1.0 + (x1 * x1)))) + (x1 + (4.0 * (2.0 * (x2 * (x1 * x2))))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -1.75e+75], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $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[(x2 * 2.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / N[(1.0 + N[(x1 * x1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(4.0 * N[(2.0 * N[(x2 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.7499999999999999e75

   1. Initial program 15.0%

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

   2. Taylor expanded in x1 around 0 1.7%

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

   3. Taylor expanded in x2 around 0 3.7%

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

      1. *-commutative 3.7%

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

      2. *-commutative 3.7%

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

      3. associate-*l* 3.7%

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

   5. Simplified 3.7%

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

   6. Taylor expanded in x1 around 0 23.5%

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

   if -1.7499999999999999e75 < 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 69.7%

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

   3. Taylor expanded in x2 around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. unpow2 69.7%

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

      3. associate-*l* 80.5%

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

   5. Simplified 80.5%

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

   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%

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

   3. Taylor expanded in x1 around 0 5.6%

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

      1. *-commutative 5.6%

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

   5. Simplified 5.6%

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

      1. flip-+ 77.4%

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

   7. Applied egg-rr 77.4%

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

      1. swap-sqr 77.4%

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

      2. metadata-eval 77.4%

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

   9. Simplified 77.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - x2 \cdot 2\right) - x1}{1 + x1 \cdot x1} + \left(x1 + 4 \cdot \left(2 \cdot \left(x2 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 14: 63.6% accurate, 4.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ t_1 := x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq -1.95 \cdot 10^{-190}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0
         (+
          x1
          (+ (* x2 -6.0) (* x1 (- (* 4.0 (* x2 (- (* x2 2.0) 3.0))) 2.0)))))
        (t_1 (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -1.75e+75)
     t_1
     (if (<= x1 -1.95e-190)
       t_0
       (if (<= x1 2e-226)
         t_1
         (if (<= x1 7.5e+169)
           t_0
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double t_1 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = t_1;
	} else if (x1 <= -1.95e-190) {
		tmp = t_0;
	} else if (x1 <= 2e-226) {
		tmp = t_1;
	} else if (x1 <= 7.5e+169) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x1 + ((x2 * (-6.0d0)) + (x1 * ((4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0))) - 2.0d0)))
    t_1 = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-1.75d+75)) then
        tmp = t_1
    else if (x1 <= (-1.95d-190)) then
        tmp = t_0
    else if (x1 <= 2d-226) then
        tmp = t_1
    else if (x1 <= 7.5d+169) then
        tmp = t_0
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	double t_1 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = t_1;
	} else if (x1 <= -1.95e-190) {
		tmp = t_0;
	} else if (x1 <= 2e-226) {
		tmp = t_1;
	} else if (x1 <= 7.5e+169) {
		tmp = t_0;
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)))
	t_1 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -1.75e+75:
		tmp = t_1
	elif x1 <= -1.95e-190:
		tmp = t_0
	elif x1 <= 2e-226:
		tmp = t_1
	elif x1 <= 7.5e+169:
		tmp = t_0
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))) - 2.0))))
	t_1 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -1.75e+75)
		tmp = t_1;
	elseif (x1 <= -1.95e-190)
		tmp = t_0;
	elseif (x1 <= 2e-226)
		tmp = t_1;
	elseif (x1 <= 7.5e+169)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x2 * -6.0) + (x1 * ((4.0 * (x2 * ((x2 * 2.0) - 3.0))) - 2.0)));
	t_1 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -1.75e+75)
		tmp = t_1;
	elseif (x1 <= -1.95e-190)
		tmp = t_0;
	elseif (x1 <= 2e-226)
		tmp = t_1;
	elseif (x1 <= 7.5e+169)
		tmp = t_0;
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.75e+75], t$95$1, If[LessEqual[x1, -1.95e-190], t$95$0, If[LessEqual[x1, 2e-226], t$95$1, If[LessEqual[x1, 7.5e+169], t$95$0, N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.7499999999999999e75 or -1.94999999999999997e-190 < x1 < 1.99999999999999984e-226

   1. Initial program 50.7%

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

   2. Taylor expanded in x1 around 0 30.5%

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

   3. Taylor expanded in x2 around 0 40.8%

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

      1. *-commutative 40.8%

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

      2. *-commutative 40.8%

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

      3. associate-*l* 40.8%

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

   5. Simplified 40.8%

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

   6. Taylor expanded in x1 around 0 52.3%

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

   if -1.7499999999999999e75 < x1 < -1.94999999999999997e-190 or 1.99999999999999984e-226 < x1 < 7.49999999999999992e169

   1. Initial program 95.2%

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

   2. Taylor expanded in x1 around 0 67.5%

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

   3. Taylor expanded in x1 around 0 70.0%

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

   if 7.49999999999999992e169 < 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%

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

   3. Taylor expanded in x1 around 0 6.2%

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

      1. *-commutative 6.2%

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

   5. Simplified 6.2%

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

      1. flip-+ 85.2%

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

   7. Applied egg-rr 85.2%

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

      1. swap-sqr 85.2%

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

      2. metadata-eval 85.2%

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

   9. Simplified 85.2%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -1.95 \cdot 10^{-190}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{elif}\;x1 \leq 2 \cdot 10^{-226}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + x1 \cdot \left(4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right) - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 15: 55.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -3.05 \cdot 10^{-16}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -1.45e+75)
     t_0
     (if (<= x1 -3.05e-16)
       (+ x1 (* x1 (* (* x2 x2) 8.0)))
       (if (<= x1 5e-38)
         t_0
         (if (<= x1 7.5e+169)
           (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0))))))
           (/ (- (* x1 x1) (* (* x2 x2) 36.0)) (- x1 (* x2 -6.0)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.45e+75) {
		tmp = t_0;
	} else if (x1 <= -3.05e-16) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} else if (x1 <= 5e-38) {
		tmp = t_0;
	} else if (x1 <= 7.5e+169) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-1.45d+75)) then
        tmp = t_0
    else if (x1 <= (-3.05d-16)) then
        tmp = x1 + (x1 * ((x2 * x2) * 8.0d0))
    else if (x1 <= 5d-38) then
        tmp = t_0
    else if (x1 <= 7.5d+169) then
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    else
        tmp = ((x1 * x1) - ((x2 * x2) * 36.0d0)) / (x1 - (x2 * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.45e+75) {
		tmp = t_0;
	} else if (x1 <= -3.05e-16) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} else if (x1 <= 5e-38) {
		tmp = t_0;
	} else if (x1 <= 7.5e+169) {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	} else {
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -1.45e+75:
		tmp = t_0
	elif x1 <= -3.05e-16:
		tmp = x1 + (x1 * ((x2 * x2) * 8.0))
	elif x1 <= 5e-38:
		tmp = t_0
	elif x1 <= 7.5e+169:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	else:
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -1.45e+75)
		tmp = t_0;
	elseif (x1 <= -3.05e-16)
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)));
	elseif (x1 <= 5e-38)
		tmp = t_0;
	elseif (x1 <= 7.5e+169)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	else
		tmp = Float64(Float64(Float64(x1 * x1) - Float64(Float64(x2 * x2) * 36.0)) / Float64(x1 - Float64(x2 * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -1.45e+75)
		tmp = t_0;
	elseif (x1 <= -3.05e-16)
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	elseif (x1 <= 5e-38)
		tmp = t_0;
	elseif (x1 <= 7.5e+169)
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	else
		tmp = ((x1 * x1) - ((x2 * x2) * 36.0)) / (x1 - (x2 * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.45e+75], t$95$0, If[LessEqual[x1, -3.05e-16], N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e-38], t$95$0, If[LessEqual[x1, 7.5e+169], N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x1 * x1), $MachinePrecision] - N[(N[(x2 * x2), $MachinePrecision] * 36.0), $MachinePrecision]), $MachinePrecision] / N[(x1 - N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.4499999999999999e75 or -3.04999999999999976e-16 < x1 < 5.00000000000000033e-38

   1. Initial program 69.1%

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

   2. Taylor expanded in x1 around 0 53.9%

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

   3. Taylor expanded in x2 around 0 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-*l* 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in x1 around 0 60.9%

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

   if -1.4499999999999999e75 < x1 < -3.04999999999999976e-16

   1. Initial program 99.0%

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

   2. Taylor expanded in x1 around 0 36.6%

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

   3. Taylor expanded in x2 around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. associate-*l* 36.6%

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

      3. unpow2 36.6%

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

   5. Simplified 36.6%

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

   if 5.00000000000000033e-38 < x1 < 7.49999999999999992e169

   1. Initial program 88.1%

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

   2. Taylor expanded in x1 around 0 44.1%

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

   3. Taylor expanded in x1 around inf 43.8%

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

   if 7.49999999999999992e169 < 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%

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

   3. Taylor expanded in x1 around 0 6.2%

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

      1. *-commutative 6.2%

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

   5. Simplified 6.2%

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

      1. flip-+ 85.2%

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

   7. Applied egg-rr 85.2%

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

      1. swap-sqr 85.2%

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

      2. metadata-eval 85.2%

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

   9. Simplified 85.2%

      \[\leadsto \color{blue}{\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.45 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -3.05 \cdot 10^{-16}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{-38}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq 7.5 \cdot 10^{+169}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x1 \cdot x1 - \left(x2 \cdot x2\right) \cdot 36}{x1 - x2 \cdot -6}\\ \end{array} \]

Alternative 16: 51.6% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{-41}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))))
   (if (<= x1 -1.75e+75)
     t_0
     (if (<= x1 -7.2e-29)
       (+ x1 (* x1 (* (* x2 x2) 8.0)))
       (if (<= x1 3e-41)
         t_0
         (+ x1 (* x1 (+ 1.0 (* 4.0 (* x2 (- (* x2 2.0) 3.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = t_0;
	} else if (x1 <= -7.2e-29) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} else if (x1 <= 3e-41) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    if (x1 <= (-1.75d+75)) then
        tmp = t_0
    else if (x1 <= (-7.2d-29)) then
        tmp = x1 + (x1 * ((x2 * x2) * 8.0d0))
    else if (x1 <= 3d-41) then
        tmp = t_0
    else
        tmp = x1 + (x1 * (1.0d0 + (4.0d0 * (x2 * ((x2 * 2.0d0) - 3.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = t_0;
	} else if (x1 <= -7.2e-29) {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	} else if (x1 <= 3e-41) {
		tmp = t_0;
	} else {
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	tmp = 0
	if x1 <= -1.75e+75:
		tmp = t_0
	elif x1 <= -7.2e-29:
		tmp = x1 + (x1 * ((x2 * x2) * 8.0))
	elif x1 <= 3e-41:
		tmp = t_0
	else:
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)))
	tmp = 0.0
	if (x1 <= -1.75e+75)
		tmp = t_0;
	elseif (x1 <= -7.2e-29)
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)));
	elseif (x1 <= 3e-41)
		tmp = t_0;
	else
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(4.0 * Float64(x2 * Float64(Float64(x2 * 2.0) - 3.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	tmp = 0.0;
	if (x1 <= -1.75e+75)
		tmp = t_0;
	elseif (x1 <= -7.2e-29)
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	elseif (x1 <= 3e-41)
		tmp = t_0;
	else
		tmp = x1 + (x1 * (1.0 + (4.0 * (x2 * ((x2 * 2.0) - 3.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.75e+75], t$95$0, If[LessEqual[x1, -7.2e-29], N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 3e-41], t$95$0, N[(x1 + N[(x1 * N[(1.0 + N[(4.0 * N[(x2 * N[(N[(x2 * 2.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.7499999999999999e75 or -7.19999999999999948e-29 < x1 < 2.99999999999999989e-41

   1. Initial program 69.1%

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

   2. Taylor expanded in x1 around 0 53.9%

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

   3. Taylor expanded in x2 around 0 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-*l* 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in x1 around 0 60.9%

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

   if -1.7499999999999999e75 < x1 < -7.19999999999999948e-29

   1. Initial program 99.0%

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

   2. Taylor expanded in x1 around 0 36.6%

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

   3. Taylor expanded in x2 around inf 36.6%

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

      1. *-commutative 36.6%

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

      2. associate-*l* 36.6%

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

      3. unpow2 36.6%

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

   5. Simplified 36.6%

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

   if 2.99999999999999989e-41 < x1

   1. Initial program 54.6%

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

   2. Taylor expanded in x1 around 0 27.3%

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

   3. Taylor expanded in x1 around inf 45.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{elif}\;x1 \leq -7.2 \cdot 10^{-29}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq 3 \cdot 10^{-41}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + 4 \cdot \left(x2 \cdot \left(x2 \cdot 2 - 3\right)\right)\right)\\ \end{array} \]

Alternative 17: 51.8% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75} \lor \neg \left(x1 \leq -2.2 \cdot 10^{-13}\right) \land x1 \leq 5.4 \cdot 10^{-37}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.75e+75) (and (not (<= x1 -2.2e-13)) (<= x1 5.4e-37)))
   (+ x1 (+ (* x1 (- (* x2 -12.0) 2.0)) (* x2 -6.0)))
   (+ x1 (* x1 (* (* x2 x2) 8.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.75e+75) || (!(x1 <= -2.2e-13) && (x1 <= 5.4e-37))) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.75d+75)) .or. (.not. (x1 <= (-2.2d-13))) .and. (x1 <= 5.4d-37)) then
        tmp = x1 + ((x1 * ((x2 * (-12.0d0)) - 2.0d0)) + (x2 * (-6.0d0)))
    else
        tmp = x1 + (x1 * ((x2 * x2) * 8.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.75e+75) || (!(x1 <= -2.2e-13) && (x1 <= 5.4e-37))) {
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	} else {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.75e+75) or (not (x1 <= -2.2e-13) and (x1 <= 5.4e-37)):
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0))
	else:
		tmp = x1 + (x1 * ((x2 * x2) * 8.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.75e+75) || (!(x1 <= -2.2e-13) && (x1 <= 5.4e-37)))
		tmp = Float64(x1 + Float64(Float64(x1 * Float64(Float64(x2 * -12.0) - 2.0)) + Float64(x2 * -6.0)));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.75e+75) || (~((x1 <= -2.2e-13)) && (x1 <= 5.4e-37)))
		tmp = x1 + ((x1 * ((x2 * -12.0) - 2.0)) + (x2 * -6.0));
	else
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.75e+75], And[N[Not[LessEqual[x1, -2.2e-13]], $MachinePrecision], LessEqual[x1, 5.4e-37]]], N[(x1 + N[(N[(x1 * N[(N[(x2 * -12.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.7499999999999999e75 or -2.19999999999999997e-13 < x1 < 5.40000000000000032e-37

   1. Initial program 69.1%

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

   2. Taylor expanded in x1 around 0 53.9%

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

   3. Taylor expanded in x2 around 0 53.5%

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

      1. *-commutative 53.5%

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

      2. *-commutative 53.5%

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

      3. associate-*l* 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in x1 around 0 60.9%

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

   if -1.7499999999999999e75 < x1 < -2.19999999999999997e-13 or 5.40000000000000032e-37 < x1

   1. Initial program 63.2%

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

   2. Taylor expanded in x1 around 0 29.1%

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

   3. Taylor expanded in x2 around inf 43.7%

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

      1. *-commutative 43.7%

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

      2. associate-*l* 43.7%

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

      3. unpow2 43.7%

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

   5. Simplified 43.7%

      \[\leadsto x1 + \color{blue}{x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75} \lor \neg \left(x1 \leq -2.2 \cdot 10^{-13}\right) \land x1 \leq 5.4 \cdot 10^{-37}:\\ \;\;\;\;x1 + \left(x1 \cdot \left(x2 \cdot -12 - 2\right) + x2 \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \]

Alternative 18: 41.2% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (* (* x2 x2) 8.0)))))
   (if (<= x1 -1.75e+75)
     (+ x1 (* x1 (+ 1.0 (* x2 -12.0))))
     (if (<= x1 -2.2e-19)
       t_0
       (if (<= x1 -9.2e-179)
         (+ x1 (* x1 -2.0))
         (if (<= x1 2.1e-52) (* x2 -6.0) t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	} else if (x1 <= -2.2e-19) {
		tmp = t_0;
	} else if (x1 <= -9.2e-179) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 2.1e-52) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x1 + (x1 * ((x2 * x2) * 8.0d0))
    if (x1 <= (-1.75d+75)) then
        tmp = x1 + (x1 * (1.0d0 + (x2 * (-12.0d0))))
    else if (x1 <= (-2.2d-19)) then
        tmp = t_0
    else if (x1 <= (-9.2d-179)) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x1 <= 2.1d-52) then
        tmp = x2 * (-6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x2 * x2) * 8.0));
	double tmp;
	if (x1 <= -1.75e+75) {
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	} else if (x1 <= -2.2e-19) {
		tmp = t_0;
	} else if (x1 <= -9.2e-179) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 2.1e-52) {
		tmp = x2 * -6.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((x2 * x2) * 8.0))
	tmp = 0
	if x1 <= -1.75e+75:
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)))
	elif x1 <= -2.2e-19:
		tmp = t_0
	elif x1 <= -9.2e-179:
		tmp = x1 + (x1 * -2.0)
	elif x1 <= 2.1e-52:
		tmp = x2 * -6.0
	else:
		tmp = t_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 <= -1.75e+75)
		tmp = Float64(x1 + Float64(x1 * Float64(1.0 + Float64(x2 * -12.0))));
	elseif (x1 <= -2.2e-19)
		tmp = t_0;
	elseif (x1 <= -9.2e-179)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x1 <= 2.1e-52)
		tmp = Float64(x2 * -6.0);
	else
		tmp = t_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 <= -1.75e+75)
		tmp = x1 + (x1 * (1.0 + (x2 * -12.0)));
	elseif (x1 <= -2.2e-19)
		tmp = t_0;
	elseif (x1 <= -9.2e-179)
		tmp = x1 + (x1 * -2.0);
	elseif (x1 <= 2.1e-52)
		tmp = x2 * -6.0;
	else
		tmp = t_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, -1.75e+75], N[(x1 + N[(x1 * N[(1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, -2.2e-19], t$95$0, If[LessEqual[x1, -9.2e-179], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.1e-52], N[(x2 * -6.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x1 < -1.7499999999999999e75

   1. Initial program 15.0%

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

   2. Taylor expanded in x1 around 0 1.7%

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

   3. Taylor expanded in x2 around 0 3.7%

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

      1. *-commutative 3.7%

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

      2. *-commutative 3.7%

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

      3. associate-*l* 3.7%

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

   5. Simplified 3.7%

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

   6. Taylor expanded in x1 around inf 20.5%

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

      1. *-commutative 20.5%

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

   8. Simplified 20.5%

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

   if -1.7499999999999999e75 < x1 < -2.1999999999999998e-19 or 2.0999999999999999e-52 < x1

   1. Initial program 63.2%

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

   2. Taylor expanded in x1 around 0 29.1%

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

   3. Taylor expanded in x2 around inf 43.7%

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

      1. *-commutative 43.7%

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

      2. associate-*l* 43.7%

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

      3. unpow2 43.7%

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

   5. Simplified 43.7%

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

   if -2.1999999999999998e-19 < x1 < -9.1999999999999995e-179

   1. Initial program 98.8%

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

   2. Taylor expanded in x1 around 0 95.3%

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

   3. Taylor expanded in x2 around 0 53.4%

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

      1. associate-*r/ 53.4%

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

      2. *-commutative 53.4%

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

      3. unpow2 53.4%

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

      4. associate-*r* 53.4%

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

      5. +-commutative 53.4%

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

      6. unpow2 53.4%

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

      7. fma-udef 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in x1 around 0 54.6%

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

      1. *-commutative 54.6%

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

   8. Simplified 54.6%

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

   if -9.1999999999999995e-179 < x1 < 2.0999999999999999e-52

   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 78.9%

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

   3. Taylor expanded in x1 around 0 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x1 around 0 65.6%

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

      1. *-commutative 65.6%

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

   8. Simplified 65.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.75 \cdot 10^{+75}:\\ \;\;\;\;x1 + x1 \cdot \left(1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq -2.2 \cdot 10^{-19}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \mathbf{elif}\;x1 \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \]

Alternative 19: 37.6% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -9.2e-179)
   (+ x1 (* x1 -2.0))
   (if (<= x1 1.6e-64) (* x2 -6.0) (+ x1 (* x1 (* (* x2 x2) 8.0))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.2e-179) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 1.6e-64) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x1 <= (-9.2d-179)) then
        tmp = x1 + (x1 * (-2.0d0))
    else if (x1 <= 1.6d-64) then
        tmp = x2 * (-6.0d0)
    else
        tmp = x1 + (x1 * ((x2 * x2) * 8.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -9.2e-179) {
		tmp = x1 + (x1 * -2.0);
	} else if (x1 <= 1.6e-64) {
		tmp = x2 * -6.0;
	} else {
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -9.2e-179:
		tmp = x1 + (x1 * -2.0)
	elif x1 <= 1.6e-64:
		tmp = x2 * -6.0
	else:
		tmp = x1 + (x1 * ((x2 * x2) * 8.0))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -9.2e-179)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	elseif (x1 <= 1.6e-64)
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x2 * x2) * 8.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -9.2e-179)
		tmp = x1 + (x1 * -2.0);
	elseif (x1 <= 1.6e-64)
		tmp = x2 * -6.0;
	else
		tmp = x1 + (x1 * ((x2 * x2) * 8.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -9.2e-179], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 1.6e-64], N[(x2 * -6.0), $MachinePrecision], N[(x1 + N[(x1 * N[(N[(x2 * x2), $MachinePrecision] * 8.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -9.1999999999999995e-179

   1. Initial program 50.0%

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

   2. Taylor expanded in x1 around 0 31.1%

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

   3. Taylor expanded in x2 around 0 13.9%

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

      1. associate-*r/ 13.9%

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

      2. *-commutative 13.9%

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

      3. unpow2 13.9%

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

      4. associate-*r* 13.9%

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

      5. +-commutative 13.9%

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

      6. unpow2 13.9%

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

      7. fma-udef 13.9%

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

   5. Simplified 13.9%

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

   6. Taylor expanded in x1 around 0 18.1%

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

      1. *-commutative 18.1%

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

   8. Simplified 18.1%

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

   if -9.1999999999999995e-179 < x1 < 1.59999999999999988e-64

   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 78.9%

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

   3. Taylor expanded in x1 around 0 65.2%

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

      1. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x1 around 0 65.6%

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

      1. *-commutative 65.6%

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

   8. Simplified 65.6%

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

   if 1.59999999999999988e-64 < x1

   1. Initial program 54.6%

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

   2. Taylor expanded in x1 around 0 27.3%

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

   3. Taylor expanded in x2 around inf 45.4%

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

      1. *-commutative 45.4%

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

      2. associate-*l* 45.4%

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

      3. unpow2 45.4%

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

   5. Simplified 45.4%

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

4. Final simplification 40.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{elif}\;x1 \leq 1.6 \cdot 10^{-64}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(\left(x2 \cdot x2\right) \cdot 8\right)\\ \end{array} \]

Alternative 20: 31.3% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.85 \cdot 10^{-73}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.15e-173)
   (* x2 -6.0)
   (if (<= x2 1.85e-73) (+ x1 (* x1 -2.0)) (* x2 -6.0))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.15e-173) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.85e-73) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.15d-173)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 1.85d-73) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x2 * (-6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.15e-173) {
		tmp = x2 * -6.0;
	} else if (x2 <= 1.85e-73) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x2 * -6.0;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.15e-173:
		tmp = x2 * -6.0
	elif x2 <= 1.85e-73:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x2 * -6.0
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.15e-173)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 1.85e-73)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x2 * -6.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.15e-173)
		tmp = x2 * -6.0;
	elseif (x2 <= 1.85e-73)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x2 * -6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.15e-173], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 1.85e-73], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x2 * -6.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x2 < -1.14999999999999994e-173 or 1.85e-73 < x2

   1. Initial program 65.2%

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

   2. Taylor expanded in x1 around 0 43.8%

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

   3. Taylor expanded in x1 around 0 29.0%

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

      1. *-commutative 29.0%

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

   5. Simplified 29.0%

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

   6. Taylor expanded in x1 around 0 28.9%

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

      1. *-commutative 28.9%

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

   8. Simplified 28.9%

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

   if -1.14999999999999994e-173 < x2 < 1.85e-73

   1. Initial program 71.2%

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

   2. Taylor expanded in x1 around 0 48.8%

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

   3. Taylor expanded in x2 around 0 37.3%

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

      1. associate-*r/ 37.3%

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

      2. *-commutative 37.3%

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

      3. unpow2 37.3%

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

      4. associate-*r* 37.3%

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

      5. +-commutative 37.3%

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

      6. unpow2 37.3%

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

      7. fma-udef 37.3%

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

   5. Simplified 37.3%

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

   6. Taylor expanded in x1 around 0 39.1%

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

      1. *-commutative 39.1%

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

   8. Simplified 39.1%

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

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.15 \cdot 10^{-173}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 1.85 \cdot 10^{-73}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6\\ \end{array} \]

Alternative 21: 31.6% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 -1.05e-173)
   (* x2 -6.0)
   (if (<= x2 5.2e-83) (+ x1 (* x1 -2.0)) (+ x1 (* x2 -6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-173) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.2e-83) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= (-1.05d-173)) then
        tmp = x2 * (-6.0d0)
    else if (x2 <= 5.2d-83) then
        tmp = x1 + (x1 * (-2.0d0))
    else
        tmp = x1 + (x2 * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= -1.05e-173) {
		tmp = x2 * -6.0;
	} else if (x2 <= 5.2e-83) {
		tmp = x1 + (x1 * -2.0);
	} else {
		tmp = x1 + (x2 * -6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= -1.05e-173:
		tmp = x2 * -6.0
	elif x2 <= 5.2e-83:
		tmp = x1 + (x1 * -2.0)
	else:
		tmp = x1 + (x2 * -6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= -1.05e-173)
		tmp = Float64(x2 * -6.0);
	elseif (x2 <= 5.2e-83)
		tmp = Float64(x1 + Float64(x1 * -2.0));
	else
		tmp = Float64(x1 + Float64(x2 * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= -1.05e-173)
		tmp = x2 * -6.0;
	elseif (x2 <= 5.2e-83)
		tmp = x1 + (x1 * -2.0);
	else
		tmp = x1 + (x2 * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, -1.05e-173], N[(x2 * -6.0), $MachinePrecision], If[LessEqual[x2, 5.2e-83], N[(x1 + N[(x1 * -2.0), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x2 * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x2 < -1.05000000000000001e-173

   1. Initial program 65.3%

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

   2. Taylor expanded in x1 around 0 45.5%

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

   3. Taylor expanded in x1 around 0 31.6%

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

      1. *-commutative 31.6%

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

   5. Simplified 31.6%

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

   6. Taylor expanded in x1 around 0 31.9%

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

      1. *-commutative 31.9%

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

   8. Simplified 31.9%

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

   if -1.05000000000000001e-173 < x2 < 5.20000000000000018e-83

   1. Initial program 73.0%

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

   2. Taylor expanded in x1 around 0 50.1%

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

   3. Taylor expanded in x2 around 0 38.2%

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

      1. associate-*r/ 38.2%

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

      2. *-commutative 38.2%

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

      3. unpow2 38.2%

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

      4. associate-*r* 38.2%

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

      5. +-commutative 38.2%

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

      6. unpow2 38.2%

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

      7. fma-udef 38.2%

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

   5. Simplified 38.2%

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

   6. Taylor expanded in x1 around 0 40.0%

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

      1. *-commutative 40.0%

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

   8. Simplified 40.0%

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

   if 5.20000000000000018e-83 < x2

   1. Initial program 63.5%

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

   2. Taylor expanded in x1 around 0 40.7%

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

   3. Taylor expanded in x1 around 0 25.1%

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

      1. *-commutative 25.1%

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

   5. Simplified 25.1%

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

4. Final simplification 32.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -1.05 \cdot 10^{-173}:\\ \;\;\;\;x2 \cdot -6\\ \mathbf{elif}\;x2 \leq 5.2 \cdot 10^{-83}:\\ \;\;\;\;x1 + x1 \cdot -2\\ \mathbf{else}:\\ \;\;\;\;x1 + x2 \cdot -6\\ \end{array} \]

Alternative 22: 26.1% accurate, 42.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 67.1%

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

2. Taylor expanded in x1 around 0 45.4%

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

3. Taylor expanded in x1 around 0 23.9%

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

   1. *-commutative 23.9%

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

5. Simplified 23.9%

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

6. Taylor expanded in x1 around 0 23.9%

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

   1. *-commutative 23.9%

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

8. Simplified 23.9%

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

9. Final simplification 23.9%

   \[\leadsto x2 \cdot -6 \]

Alternative 23: 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 67.1%

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

2. Taylor expanded in x1 around 0 45.4%

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

3. Taylor expanded in x1 around 0 23.9%

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

   1. *-commutative 23.9%

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

5. Simplified 23.9%

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

6. Taylor expanded in x1 around inf 3.0%

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

7. Final simplification 3.0%

   \[\leadsto x1 \]

Reproduce

herbie shell --seed 2023268 
(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))))))