Rosa's FloatVsDoubleBenchmark

Percentage Accurate: 69.4% → 99.3%

Time: 19.0s

Alternatives: 19

Speedup: 5.1×

• 46.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.4%

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

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

   1. Initial program 0.0%

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

   3. Simplified 10.6%

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

   5. Taylor expanded in x1 around inf 100.0%

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

4. Final simplification 99.6%

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

Alternative 2: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot \left(t\_2 \cdot 4 - 6\right)\right) + 3 \cdot t\_0\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (<= x1 -5.6e+102)
     (* 6.0 (pow x1 4.0))
     (if (<= x1 5e+153)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (*
             t_1
             (+
              (* (* (* x1 2.0) t_2) (- t_2 3.0))
              (* (* x1 x1) (- (* t_2 4.0) 6.0))))
            (* 3.0 t_0))))))
       (+ x1 (* x1 (- (* x1 9.0) 2.0)))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = 6.0 * pow(x1, 4.0);
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))));
	} else {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if (x1 <= (-5.6d+102)) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * ((t_2 * 4.0d0) - 6.0d0)))) + (3.0d0 * t_0)))))
    else
        tmp = x1 + (x1 * ((x1 * 9.0d0) - 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))));
	} else {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = 6.0 * math.pow(x1, 4.0)
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))))
	else:
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(6.0 * (x1 ^ 4.0));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * Float64(Float64(t_2 * 4.0) - 6.0)))) + Float64(3.0 * t_0))))));
	else
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = 6.0 * (x1 ^ 4.0);
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * ((t_2 * 4.0) - 6.0)))) + (3.0 * t_0)))));
	else
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * N[(N[(t$95$2 * 4.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(3.0 * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 20.6%

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

   5. Taylor expanded in x1 around inf 100.0%

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

   if -5.60000000000000037e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 81.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 99.1%

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

Alternative 3: 96.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+102} \lor \neg \left(x1 \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(t\_0 \cdot t\_2 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -5e+102) (not (<= x1 3e+64)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* t_0 t_2)
          (*
           t_1
           (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5e+102) || !(x1 <= 3e+64)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-5d+102)) .or. (.not. (x1 <= 3d+64))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5e+102) || !(x1 <= 3e+64)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -5e+102) or not (x1 <= 3e+64):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5e+102) || !(x1 <= 3e+64))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(t_0 * t_2) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -5e+102) || ~((x1 <= 3e+64)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((t_0 * t_2) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5e+102], N[Not[LessEqual[x1, 3e+64]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$0 * t$95$2), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -5e102 or 3.0000000000000002e64 < x1

   1. Initial program 17.5%

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

   3. Simplified 26.2%

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

   5. Taylor expanded in x1 around inf 97.5%

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

   if -5e102 < x1 < 3.0000000000000002e64

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 97.7%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+102} \lor \neg \left(x1 \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(\left(x1 \cdot \left(x1 \cdot 3\right)\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 96.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 3\right)\\ t_1 := x1 \cdot x1 + 1\\ t_2 := \frac{\left(t\_0 + 2 \cdot x2\right) - x1}{t\_1}\\ \mathbf{if}\;x1 \leq -5 \cdot 10^{+101} \lor \neg \left(x1 \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_0 - 2 \cdot x2\right) - x1}{t\_1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_0 + t\_1 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_2\right) \cdot \left(t\_2 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (* x1 3.0)))
        (t_1 (+ (* x1 x1) 1.0))
        (t_2 (/ (- (+ t_0 (* 2.0 x2)) x1) t_1)))
   (if (or (<= x1 -5e+101) (not (<= x1 3e+64)))
     (* 6.0 (pow x1 4.0))
     (+
      x1
      (+
       (* 3.0 (/ (- (- t_0 (* 2.0 x2)) x1) t_1))
       (+
        x1
        (+
         (* x1 (* x1 x1))
         (+
          (* 3.0 t_0)
          (*
           t_1
           (+ (* (* (* x1 2.0) t_2) (- t_2 3.0)) (* (* x1 x1) 6.0)))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5e+101) || !(x1 <= 3e+64)) {
		tmp = 6.0 * pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = x1 * (x1 * 3.0d0)
    t_1 = (x1 * x1) + 1.0d0
    t_2 = ((t_0 + (2.0d0 * x2)) - x1) / t_1
    if ((x1 <= (-5d+101)) .or. (.not. (x1 <= 3d+64))) then
        tmp = 6.0d0 * (x1 ** 4.0d0)
    else
        tmp = x1 + ((3.0d0 * (((t_0 - (2.0d0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_0) + (t_1 * ((((x1 * 2.0d0) * t_2) * (t_2 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * (x1 * 3.0);
	double t_1 = (x1 * x1) + 1.0;
	double t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	double tmp;
	if ((x1 <= -5e+101) || !(x1 <= 3e+64)) {
		tmp = 6.0 * Math.pow(x1, 4.0);
	} else {
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * (x1 * 3.0)
	t_1 = (x1 * x1) + 1.0
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1
	tmp = 0
	if (x1 <= -5e+101) or not (x1 <= 3e+64):
		tmp = 6.0 * math.pow(x1, 4.0)
	else:
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(x1 * 3.0))
	t_1 = Float64(Float64(x1 * x1) + 1.0)
	t_2 = Float64(Float64(Float64(t_0 + Float64(2.0 * x2)) - x1) / t_1)
	tmp = 0.0
	if ((x1 <= -5e+101) || !(x1 <= 3e+64))
		tmp = Float64(6.0 * (x1 ^ 4.0));
	else
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_0 - Float64(2.0 * x2)) - x1) / t_1)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_0) + Float64(t_1 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_2) * Float64(t_2 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * (x1 * 3.0);
	t_1 = (x1 * x1) + 1.0;
	t_2 = ((t_0 + (2.0 * x2)) - x1) / t_1;
	tmp = 0.0;
	if ((x1 <= -5e+101) || ~((x1 <= 3e+64)))
		tmp = 6.0 * (x1 ^ 4.0);
	else
		tmp = x1 + ((3.0 * (((t_0 - (2.0 * x2)) - x1) / t_1)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_0) + (t_1 * ((((x1 * 2.0) * t_2) * (t_2 - 3.0)) + ((x1 * x1) * 6.0)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t$95$0 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[Or[LessEqual[x1, -5e+101], N[Not[LessEqual[x1, 3e+64]], $MachinePrecision]], N[(6.0 * N[Power[x1, 4.0], $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$0), $MachinePrecision] + N[(t$95$1 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$2), $MachinePrecision] * N[(t$95$2 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.99999999999999989e101 or 3.0000000000000002e64 < x1

   1. Initial program 17.5%

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

   3. Simplified 26.2%

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

   5. Taylor expanded in x1 around inf 97.5%

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

   if -4.99999999999999989e101 < x1 < 3.0000000000000002e64

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.7%

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

   4. Taylor expanded in x1 around inf 97.7%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5 \cdot 10^{+101} \lor \neg \left(x1 \leq 3 \cdot 10^{+64}\right):\\ \;\;\;\;6 \cdot {x1}^{4}\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot x1 + 1\\ t_1 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_2 := x1 \cdot \left(x1 \cdot 3\right)\\ t_3 := \frac{\left(t\_2 + 2 \cdot x2\right) - x1}{t\_0}\\ \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{t\_1}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(t\_2 - 2 \cdot x2\right) - x1}{t\_0} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot t\_2 + t\_0 \cdot \left(\left(\left(x1 \cdot 2\right) \cdot t\_3\right) \cdot \left(t\_3 - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ (* x1 x1) 1.0))
        (t_1 (* x1 (- (* x1 9.0) 2.0)))
        (t_2 (* x1 (* x1 3.0)))
        (t_3 (/ (- (+ t_2 (* 2.0 x2)) x1) t_0)))
   (if (<= x1 -5.6e+102)
     (+ x1 (* x2 (- (+ (* x1 -12.0) (/ t_1 x2)) 6.0)))
     (if (<= x1 5e+153)
       (+
        x1
        (+
         (* 3.0 (/ (- (- t_2 (* 2.0 x2)) x1) t_0))
         (+
          x1
          (+
           (* x1 (* x1 x1))
           (+
            (* 3.0 t_2)
            (*
             t_0
             (+ (* (* (* x1 2.0) t_3) (- t_3 3.0)) (* (* x1 x1) 6.0))))))))
       (+ x1 t_1)))))

C

double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_1 / x2)) - 6.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (x1 * x1) + 1.0d0
    t_1 = x1 * ((x1 * 9.0d0) - 2.0d0)
    t_2 = x1 * (x1 * 3.0d0)
    t_3 = ((t_2 + (2.0d0 * x2)) - x1) / t_0
    if (x1 <= (-5.6d+102)) then
        tmp = x1 + (x2 * (((x1 * (-12.0d0)) + (t_1 / x2)) - 6.0d0))
    else if (x1 <= 5d+153) then
        tmp = x1 + ((3.0d0 * (((t_2 - (2.0d0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0d0 * t_2) + (t_0 * ((((x1 * 2.0d0) * t_3) * (t_3 - 3.0d0)) + ((x1 * x1) * 6.0d0)))))))
    else
        tmp = x1 + t_1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = (x1 * x1) + 1.0;
	double t_1 = x1 * ((x1 * 9.0) - 2.0);
	double t_2 = x1 * (x1 * 3.0);
	double t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	double tmp;
	if (x1 <= -5.6e+102) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_1 / x2)) - 6.0));
	} else if (x1 <= 5e+153) {
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	} else {
		tmp = x1 + t_1;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = (x1 * x1) + 1.0
	t_1 = x1 * ((x1 * 9.0) - 2.0)
	t_2 = x1 * (x1 * 3.0)
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0
	tmp = 0
	if x1 <= -5.6e+102:
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_1 / x2)) - 6.0))
	elif x1 <= 5e+153:
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))))
	else:
		tmp = x1 + t_1
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(Float64(x1 * x1) + 1.0)
	t_1 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	t_2 = Float64(x1 * Float64(x1 * 3.0))
	t_3 = Float64(Float64(Float64(t_2 + Float64(2.0 * x2)) - x1) / t_0)
	tmp = 0.0
	if (x1 <= -5.6e+102)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(t_1 / x2)) - 6.0)));
	elseif (x1 <= 5e+153)
		tmp = Float64(x1 + Float64(Float64(3.0 * Float64(Float64(Float64(t_2 - Float64(2.0 * x2)) - x1) / t_0)) + Float64(x1 + Float64(Float64(x1 * Float64(x1 * x1)) + Float64(Float64(3.0 * t_2) + Float64(t_0 * Float64(Float64(Float64(Float64(x1 * 2.0) * t_3) * Float64(t_3 - 3.0)) + Float64(Float64(x1 * x1) * 6.0))))))));
	else
		tmp = Float64(x1 + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = (x1 * x1) + 1.0;
	t_1 = x1 * ((x1 * 9.0) - 2.0);
	t_2 = x1 * (x1 * 3.0);
	t_3 = ((t_2 + (2.0 * x2)) - x1) / t_0;
	tmp = 0.0;
	if (x1 <= -5.6e+102)
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_1 / x2)) - 6.0));
	elseif (x1 <= 5e+153)
		tmp = x1 + ((3.0 * (((t_2 - (2.0 * x2)) - x1) / t_0)) + (x1 + ((x1 * (x1 * x1)) + ((3.0 * t_2) + (t_0 * ((((x1 * 2.0) * t_3) * (t_3 - 3.0)) + ((x1 * x1) * 6.0)))))));
	else
		tmp = x1 + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(N[(x1 * x1), $MachinePrecision] + 1.0), $MachinePrecision]}, Block[{t$95$1 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x1 * N[(x1 * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t$95$2 + N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]}, If[LessEqual[x1, -5.6e+102], N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(t$95$1 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 5e+153], N[(x1 + N[(N[(3.0 * N[(N[(N[(t$95$2 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] + N[(x1 + N[(N[(x1 * N[(x1 * x1), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 * t$95$2), $MachinePrecision] + N[(t$95$0 * N[(N[(N[(N[(x1 * 2.0), $MachinePrecision] * t$95$3), $MachinePrecision] * N[(t$95$3 - 3.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x1 * x1), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + t$95$1), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -5.60000000000000037e102

   1. Initial program 0.0%

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

   3. Simplified 20.6%

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

   5. Taylor expanded in x1 around 0 41.8%

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

   6. Taylor expanded in x2 around 0 47.7%

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

      1. *-commutative 47.7%

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

   8. Simplified 47.7%

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

   9. Taylor expanded in x2 around 0 71.5%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 - 6\right)\right)} \]

   10. Taylor expanded in x2 around inf 82.8%

       \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + \frac{x1 \cdot \left(9 \cdot x1 - 2\right)}{x2}\right) - 6\right)} \]

   if -5.60000000000000037e102 < x1 < 5.00000000000000018e153

   1. Initial program 99.4%

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

   3. Taylor expanded in x1 around inf 98.8%

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

   4. Taylor expanded in x1 around inf 96.8%

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

   if 5.00000000000000018e153 < x1

   1. Initial program 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in x1 around 0 81.3%

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

   6. Taylor expanded in x2 around 0 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x2 around 0 100.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{x1 \cdot \left(x1 \cdot 9 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{elif}\;x1 \leq 5 \cdot 10^{+153}:\\ \;\;\;\;x1 + \left(3 \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} + \left(x1 + \left(x1 \cdot \left(x1 \cdot x1\right) + \left(3 \cdot \left(x1 \cdot \left(x1 \cdot 3\right)\right) + \left(x1 \cdot x1 + 1\right) \cdot \left(\left(\left(x1 \cdot 2\right) \cdot \frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(x1 \cdot \left(x1 \cdot 3\right) + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot 6\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 3.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ t_1 := x2 \cdot -6 + x1 \cdot \left(-1 + -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\\ \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-226}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-230}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (+ x1 (* x1 (- (* x1 9.0) 2.0))))
        (t_1
         (+ (* x2 -6.0) (* x1 (+ -1.0 (* -4.0 (* x2 (+ 3.0 (* x2 -2.0)))))))))
   (if (<= x1 -1.25e+101)
     t_0
     (if (<= x1 -9.5e-226)
       t_1
       (if (<= x1 2.1e-230)
         (* x2 (- (- 6.0) (/ x1 x2)))
         (if (<= x1 2.05e+106) t_1 t_0))))))

C

double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x1 * 9.0) - 2.0));
	double t_1 = (x2 * -6.0) + (x1 * (-1.0 + (-4.0 * (x2 * (3.0 + (x2 * -2.0))))));
	double tmp;
	if (x1 <= -1.25e+101) {
		tmp = t_0;
	} else if (x1 <= -9.5e-226) {
		tmp = t_1;
	} else if (x1 <= 2.1e-230) {
		tmp = x2 * (-6.0 - (x1 / x2));
	} else if (x1 <= 2.05e+106) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x1 + (x1 * ((x1 * 9.0d0) - 2.0d0))
    t_1 = (x2 * (-6.0d0)) + (x1 * ((-1.0d0) + ((-4.0d0) * (x2 * (3.0d0 + (x2 * (-2.0d0)))))))
    if (x1 <= (-1.25d+101)) then
        tmp = t_0
    else if (x1 <= (-9.5d-226)) then
        tmp = t_1
    else if (x1 <= 2.1d-230) then
        tmp = x2 * (-6.0d0 - (x1 / x2))
    else if (x1 <= 2.05d+106) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 + (x1 * ((x1 * 9.0) - 2.0));
	double t_1 = (x2 * -6.0) + (x1 * (-1.0 + (-4.0 * (x2 * (3.0 + (x2 * -2.0))))));
	double tmp;
	if (x1 <= -1.25e+101) {
		tmp = t_0;
	} else if (x1 <= -9.5e-226) {
		tmp = t_1;
	} else if (x1 <= 2.1e-230) {
		tmp = x2 * (-6.0 - (x1 / x2));
	} else if (x1 <= 2.05e+106) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 + (x1 * ((x1 * 9.0) - 2.0))
	t_1 = (x2 * -6.0) + (x1 * (-1.0 + (-4.0 * (x2 * (3.0 + (x2 * -2.0))))))
	tmp = 0
	if x1 <= -1.25e+101:
		tmp = t_0
	elif x1 <= -9.5e-226:
		tmp = t_1
	elif x1 <= 2.1e-230:
		tmp = x2 * (-6.0 - (x1 / x2))
	elif x1 <= 2.05e+106:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)))
	t_1 = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(-1.0 + Float64(-4.0 * Float64(x2 * Float64(3.0 + Float64(x2 * -2.0)))))))
	tmp = 0.0
	if (x1 <= -1.25e+101)
		tmp = t_0;
	elseif (x1 <= -9.5e-226)
		tmp = t_1;
	elseif (x1 <= 2.1e-230)
		tmp = Float64(x2 * Float64(Float64(-6.0) - Float64(x1 / x2)));
	elseif (x1 <= 2.05e+106)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 + (x1 * ((x1 * 9.0) - 2.0));
	t_1 = (x2 * -6.0) + (x1 * (-1.0 + (-4.0 * (x2 * (3.0 + (x2 * -2.0))))));
	tmp = 0.0;
	if (x1 <= -1.25e+101)
		tmp = t_0;
	elseif (x1 <= -9.5e-226)
		tmp = t_1;
	elseif (x1 <= 2.1e-230)
		tmp = x2 * (-6.0 - (x1 / x2));
	elseif (x1 <= 2.05e+106)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(-1.0 + N[(-4.0 * N[(x2 * N[(3.0 + N[(x2 * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.25e+101], t$95$0, If[LessEqual[x1, -9.5e-226], t$95$1, If[LessEqual[x1, 2.1e-230], N[(x2 * N[((-6.0) - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 2.05e+106], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -1.24999999999999997e101 or 2.0500000000000001e106 < x1

   1. Initial program 9.6%

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

   3. Simplified 19.2%

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

   5. Taylor expanded in x1 around 0 55.9%

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

   6. Taylor expanded in x2 around 0 66.8%

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

      1. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in x2 around 0 82.4%

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

   if -1.24999999999999997e101 < x1 < -9.5000000000000007e-226 or 2.0999999999999998e-230 < x1 < 2.0500000000000001e106

   1. Initial program 99.3%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x1 around 0 71.2%

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

   if -9.5000000000000007e-226 < x1 < 2.0999999999999998e-230

   1. Initial program 99.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in x1 around 0 69.6%

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

      1. fma-define 69.8%

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

      2. associate-*r* 69.8%

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

      3. fmm-def 69.8%

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

      4. *-commutative 69.8%

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

      5. metadata-eval 69.8%

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

      6. cancel-sign-sub-inv 69.8%

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

      7. metadata-eval 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in x2 around 0 95.0%

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

   9. Taylor expanded in x2 around -inf 95.0%

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

       1. mul-1-neg 95.0%

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

       2. *-commutative 95.0%

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

       3. distribute-rgt-neg-in 95.0%

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

       4. +-commutative 95.0%

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

   11. Simplified 95.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.25 \cdot 10^{+101}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{elif}\;x1 \leq -9.5 \cdot 10^{-226}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\\ \mathbf{elif}\;x1 \leq 2.1 \cdot 10^{-230}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \mathbf{elif}\;x1 \leq 2.05 \cdot 10^{+106}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(-1 + -4 \cdot \left(x2 \cdot \left(3 + x2 \cdot -2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.0% accurate, 4.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{t\_0}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -1.5e+99)
     (+ x1 (* x2 (- (+ (* x1 -12.0) (/ t_0 x2)) 6.0)))
     (+
      x1
      (+ (* x2 -6.0) (+ t_0 (* x2 (+ (* x1 -12.0) (* 8.0 (* x1 x2))))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -1.5e+99) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	}
	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 * 9.0d0) - 2.0d0)
    if (x1 <= (-1.5d+99)) then
        tmp = x1 + (x2 * (((x1 * (-12.0d0)) + (t_0 / x2)) - 6.0d0))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * ((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -1.5e+99) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -1.5e+99:
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -1.5e+99)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(t_0 / x2)) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -1.5e+99)
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	else
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * ((x1 * -12.0) + (8.0 * (x1 * x2))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+99], N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(t$95$0 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.50000000000000007e99

   1. Initial program 2.9%

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

   3. Simplified 22.9%

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

   5. Taylor expanded in x1 around 0 40.8%

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

   6. Taylor expanded in x2 around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in x2 around 0 69.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 - 6\right)\right)} \]

   10. Taylor expanded in x2 around inf 83.3%

       \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + \frac{x1 \cdot \left(9 \cdot x1 - 2\right)}{x2}\right) - 6\right)} \]

   if -1.50000000000000007e99 < x1

   1. Initial program 85.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x1 around 0 70.4%

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

   6. Taylor expanded in x2 around 0 74.1%

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

      1. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in x2 around 0 83.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{x1 \cdot \left(x1 \cdot 9 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.7% accurate, 4.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99} \lor \neg \left(x1 \leq 8.5 \cdot 10^{+16}\right):\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{x1 \cdot \left(x1 \cdot 9 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -1.5e+99) (not (<= x1 8.5e+16)))
   (+ x1 (* x2 (- (+ (* x1 -12.0) (/ (* x1 (- (* x1 9.0) 2.0)) x2)) 6.0)))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.5e+99) || !(x1 <= 8.5e+16)) {
		tmp = x1 + (x2 * (((x1 * -12.0) + ((x1 * ((x1 * 9.0) - 2.0)) / x2)) - 6.0));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-1.5d+99)) .or. (.not. (x1 <= 8.5d+16))) then
        tmp = x1 + (x2 * (((x1 * (-12.0d0)) + ((x1 * ((x1 * 9.0d0) - 2.0d0)) / x2)) - 6.0d0))
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -1.5e+99) || !(x1 <= 8.5e+16)) {
		tmp = x1 + (x2 * (((x1 * -12.0) + ((x1 * ((x1 * 9.0) - 2.0)) / x2)) - 6.0));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -1.5e+99) or not (x1 <= 8.5e+16):
		tmp = x1 + (x2 * (((x1 * -12.0) + ((x1 * ((x1 * 9.0) - 2.0)) / x2)) - 6.0))
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -1.5e+99) || !(x1 <= 8.5e+16))
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)) / x2)) - 6.0)));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -1.5e+99) || ~((x1 <= 8.5e+16)))
		tmp = x1 + (x2 * (((x1 * -12.0) + ((x1 * ((x1 * 9.0) - 2.0)) / x2)) - 6.0));
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -1.5e+99], N[Not[LessEqual[x1, 8.5e+16]], $MachinePrecision]], N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.50000000000000007e99 or 8.5e16 < x1

   1. Initial program 26.6%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in x1 around 0 47.2%

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

   6. Taylor expanded in x2 around 0 57.4%

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

      1. *-commutative 57.4%

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

   8. Simplified 57.4%

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

   9. Taylor expanded in x2 around 0 55.1%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 - 6\right)\right)} \]

   10. Taylor expanded in x2 around inf 75.6%

       \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + \frac{x1 \cdot \left(9 \cdot x1 - 2\right)}{x2}\right) - 6\right)} \]

   if -1.50000000000000007e99 < x1 < 8.5e16

   1. Initial program 99.4%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in x1 around 0 76.7%

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

      1. fma-define 76.8%

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

      2. associate-*r* 76.8%

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

      3. fmm-def 76.8%

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

      4. *-commutative 76.8%

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

      5. metadata-eval 76.8%

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

      6. cancel-sign-sub-inv 76.8%

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

      7. metadata-eval 76.8%

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

   7. Simplified 76.8%

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

   8. Taylor expanded in x2 around 0 89.2%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99} \lor \neg \left(x1 \leq 8.5 \cdot 10^{+16}\right):\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{x1 \cdot \left(x1 \cdot 9 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.0% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{t\_0}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(t\_0 + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (let* ((t_0 (* x1 (- (* x1 9.0) 2.0))))
   (if (<= x1 -1.5e+99)
     (+ x1 (* x2 (- (+ (* x1 -12.0) (/ t_0 x2)) 6.0)))
     (+ x1 (+ (* x2 -6.0) (+ t_0 (* x2 (* 8.0 (* x1 x2)))))))))

C

double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -1.5e+99) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (8.0 * (x1 * x2)))));
	}
	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 * 9.0d0) - 2.0d0)
    if (x1 <= (-1.5d+99)) then
        tmp = x1 + (x2 * (((x1 * (-12.0d0)) + (t_0 / x2)) - 6.0d0))
    else
        tmp = x1 + ((x2 * (-6.0d0)) + (t_0 + (x2 * (8.0d0 * (x1 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double t_0 = x1 * ((x1 * 9.0) - 2.0);
	double tmp;
	if (x1 <= -1.5e+99) {
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	} else {
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (8.0 * (x1 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	t_0 = x1 * ((x1 * 9.0) - 2.0)
	tmp = 0
	if x1 <= -1.5e+99:
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0))
	else:
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (8.0 * (x1 * x2)))))
	return tmp

Julia

function code(x1, x2)
	t_0 = Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0))
	tmp = 0.0
	if (x1 <= -1.5e+99)
		tmp = Float64(x1 + Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(t_0 / x2)) - 6.0)));
	else
		tmp = Float64(x1 + Float64(Float64(x2 * -6.0) + Float64(t_0 + Float64(x2 * Float64(8.0 * Float64(x1 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	t_0 = x1 * ((x1 * 9.0) - 2.0);
	tmp = 0.0;
	if (x1 <= -1.5e+99)
		tmp = x1 + (x2 * (((x1 * -12.0) + (t_0 / x2)) - 6.0));
	else
		tmp = x1 + ((x2 * -6.0) + (t_0 + (x2 * (8.0 * (x1 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := Block[{t$95$0 = N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x1, -1.5e+99], N[(x1 + N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(t$95$0 / x2), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 + N[(N[(x2 * -6.0), $MachinePrecision] + N[(t$95$0 + N[(x2 * N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x1 < -1.50000000000000007e99

   1. Initial program 2.9%

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

   3. Simplified 22.9%

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

   5. Taylor expanded in x1 around 0 40.8%

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

   6. Taylor expanded in x2 around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   9. Taylor expanded in x2 around 0 69.6%

      \[\leadsto x1 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 - 6\right)\right)} \]

   10. Taylor expanded in x2 around inf 83.3%

       \[\leadsto x1 + \color{blue}{x2 \cdot \left(\left(-12 \cdot x1 + \frac{x1 \cdot \left(9 \cdot x1 - 2\right)}{x2}\right) - 6\right)} \]

   if -1.50000000000000007e99 < x1

   1. Initial program 85.0%

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

   3. Simplified 75.0%

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

   5. Taylor expanded in x1 around 0 70.4%

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

   6. Taylor expanded in x2 around 0 74.1%

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

      1. *-commutative 74.1%

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

   8. Simplified 74.1%

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

   9. Taylor expanded in x2 around 0 83.5%

      \[\leadsto x1 + \left(-6 \cdot x2 + \color{blue}{\left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right)\right)}\right) \]

   10. Taylor expanded in x2 around inf 83.5%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(8 \cdot \left(x1 \cdot x2\right)\right)}\right)\right) \]
   11. Step-by-step derivation

       1. *-commutative 83.5%

          \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot 8\right)}\right)\right) \]

   12. Simplified 83.5%

       \[\leadsto x1 + \left(-6 \cdot x2 + \left(x1 \cdot \left(9 \cdot x1 - 2\right) + x2 \cdot \color{blue}{\left(\left(x1 \cdot x2\right) \cdot 8\right)}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;x1 + x2 \cdot \left(\left(x1 \cdot -12 + \frac{x1 \cdot \left(x1 \cdot 9 - 2\right)}{x2}\right) - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x1 + \left(x2 \cdot -6 + \left(x1 \cdot \left(x1 \cdot 9 - 2\right) + x2 \cdot \left(8 \cdot \left(x1 \cdot x2\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.9% accurate, 5.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+99} \lor \neg \left(x1 \leq 2.05 \cdot 10^{+106}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -4.5e+99) (not (<= x1 2.05e+106)))
   (+ x1 (* x1 (- (* x1 9.0) 2.0)))
   (- (* x2 (- (+ (* x1 -12.0) (* 8.0 (* x1 x2))) 6.0)) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.5e+99) || !(x1 <= 2.05e+106)) {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-4.5d+99)) .or. (.not. (x1 <= 2.05d+106))) then
        tmp = x1 + (x1 * ((x1 * 9.0d0) - 2.0d0))
    else
        tmp = (x2 * (((x1 * (-12.0d0)) + (8.0d0 * (x1 * x2))) - 6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -4.5e+99) || !(x1 <= 2.05e+106)) {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	} else {
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -4.5e+99) or not (x1 <= 2.05e+106):
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0))
	else:
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -4.5e+99) || !(x1 <= 2.05e+106))
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)));
	else
		tmp = Float64(Float64(x2 * Float64(Float64(Float64(x1 * -12.0) + Float64(8.0 * Float64(x1 * x2))) - 6.0)) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -4.5e+99) || ~((x1 <= 2.05e+106)))
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	else
		tmp = (x2 * (((x1 * -12.0) + (8.0 * (x1 * x2))) - 6.0)) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -4.5e+99], N[Not[LessEqual[x1, 2.05e+106]], $MachinePrecision]], N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * N[(N[(N[(x1 * -12.0), $MachinePrecision] + N[(8.0 * N[(x1 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -4.5e99 or 2.0500000000000001e106 < x1

   1. Initial program 9.6%

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

   3. Simplified 19.2%

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

   5. Taylor expanded in x1 around 0 55.9%

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

   6. Taylor expanded in x2 around 0 66.8%

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

      1. *-commutative 66.8%

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

   8. Simplified 66.8%

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

   9. Taylor expanded in x2 around 0 82.4%

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

   if -4.5e99 < x1 < 2.0500000000000001e106

   1. Initial program 99.4%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in x1 around 0 70.9%

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

      1. fma-define 71.0%

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

      2. associate-*r* 71.0%

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

      3. fmm-def 71.0%

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

      4. *-commutative 71.0%

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

      5. metadata-eval 71.0%

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

      6. cancel-sign-sub-inv 71.0%

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

      7. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   8. Taylor expanded in x2 around 0 82.2%

      \[\leadsto \color{blue}{-1 \cdot x1 + x2 \cdot \left(\left(-12 \cdot x1 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -4.5 \cdot 10^{+99} \lor \neg \left(x1 \leq 2.05 \cdot 10^{+106}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(x1 \cdot -12 + 8 \cdot \left(x1 \cdot x2\right)\right) - 6\right) - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.7% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+163} \lor \neg \left(x1 \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -2.2e+163) (not (<= x1 7.4e-34)))
   (+ x1 (* x1 (- (* x1 9.0) 2.0)))
   (* x2 (- (- 6.0) (/ x1 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.2e+163) || !(x1 <= 7.4e-34)) {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-2.2d+163)) .or. (.not. (x1 <= 7.4d-34))) then
        tmp = x1 + (x1 * ((x1 * 9.0d0) - 2.0d0))
    else
        tmp = x2 * (-6.0d0 - (x1 / x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -2.2e+163) || !(x1 <= 7.4e-34)) {
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -2.2e+163) or not (x1 <= 7.4e-34):
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0))
	else:
		tmp = x2 * (-6.0 - (x1 / x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -2.2e+163) || !(x1 <= 7.4e-34))
		tmp = Float64(x1 + Float64(x1 * Float64(Float64(x1 * 9.0) - 2.0)));
	else
		tmp = Float64(x2 * Float64(Float64(-6.0) - Float64(x1 / x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -2.2e+163) || ~((x1 <= 7.4e-34)))
		tmp = x1 + (x1 * ((x1 * 9.0) - 2.0));
	else
		tmp = x2 * (-6.0 - (x1 / x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -2.2e+163], N[Not[LessEqual[x1, 7.4e-34]], $MachinePrecision]], N[(x1 + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x2 * N[((-6.0) - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.19999999999999986e163 or 7.39999999999999976e-34 < x1

   1. Initial program 33.9%

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

   3. Simplified 31.9%

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

   5. Taylor expanded in x1 around 0 53.2%

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

   6. Taylor expanded in x2 around 0 63.5%

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

      1. *-commutative 63.5%

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

   8. Simplified 63.5%

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

   9. Taylor expanded in x2 around 0 69.8%

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

   if -2.19999999999999986e163 < x1 < 7.39999999999999976e-34

   1. Initial program 94.7%

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

   3. Simplified 86.7%

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

   5. Taylor expanded in x1 around 0 72.7%

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

      1. fma-define 72.8%

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

      2. associate-*r* 72.8%

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

      3. fmm-def 72.8%

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

      4. *-commutative 72.8%

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

      5. metadata-eval 72.8%

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

      6. cancel-sign-sub-inv 72.8%

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

      7. metadata-eval 72.8%

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

   7. Simplified 72.8%

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

   8. Taylor expanded in x2 around 0 60.7%

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

   9. Taylor expanded in x2 around -inf 62.4%

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

       1. mul-1-neg 62.4%

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

       2. *-commutative 62.4%

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

       3. distribute-rgt-neg-in 62.4%

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

       4. +-commutative 62.4%

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

   11. Simplified 62.4%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -2.2 \cdot 10^{+163} \lor \neg \left(x1 \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x1 + x1 \cdot \left(x1 \cdot 9 - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.75 \cdot 10^{+17} \lor \neg \left(x2 \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.75e+17) (not (<= x2 1.8e+15)))
   (* x2 (- (* x1 -12.0) 6.0))
   (* x2 (- (- 6.0) (/ x1 x2)))))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.75e+17) || !(x2 <= 1.8e+15)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.75d+17)) .or. (.not. (x2 <= 1.8d+15))) then
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    else
        tmp = x2 * (-6.0d0 - (x1 / x2))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.75e+17) || !(x2 <= 1.8e+15)) {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	} else {
		tmp = x2 * (-6.0 - (x1 / x2));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.75e+17) or not (x2 <= 1.8e+15):
		tmp = x2 * ((x1 * -12.0) - 6.0)
	else:
		tmp = x2 * (-6.0 - (x1 / x2))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.75e+17) || !(x2 <= 1.8e+15))
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	else
		tmp = Float64(x2 * Float64(Float64(-6.0) - Float64(x1 / x2)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.75e+17) || ~((x2 <= 1.8e+15)))
		tmp = x2 * ((x1 * -12.0) - 6.0);
	else
		tmp = x2 * (-6.0 - (x1 / x2));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.75e+17], N[Not[LessEqual[x2, 1.8e+15]], $MachinePrecision]], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision], N[(x2 * N[((-6.0) - N[(x1 / x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.75e17 or 1.8e15 < x2

   1. Initial program 71.8%

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

   3. Simplified 58.5%

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

   5. Taylor expanded in x1 around 0 58.3%

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

      1. fma-define 58.3%

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

      2. associate-*r* 58.3%

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

      3. fmm-def 58.3%

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

      4. *-commutative 58.3%

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

      5. metadata-eval 58.3%

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

      6. cancel-sign-sub-inv 58.3%

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

      7. metadata-eval 58.3%

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

   7. Simplified 58.3%

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

   8. Taylor expanded in x2 around 0 37.2%

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

      1. fma-define 37.2%

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

      2. mul-1-neg 37.2%

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

      3. fmm-undef 37.2%

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

      4. *-commutative 37.2%

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

   10. Simplified 37.2%

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

   11. Taylor expanded in x2 around inf 37.2%

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

   if -2.75e17 < x2 < 1.8e15

   1. Initial program 75.7%

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

   3. Simplified 76.8%

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

   5. Taylor expanded in x1 around 0 56.5%

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

      1. fma-define 56.6%

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

      2. associate-*r* 56.6%

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

      3. fmm-def 56.6%

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

      4. *-commutative 56.6%

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

      5. metadata-eval 56.6%

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

      6. cancel-sign-sub-inv 56.6%

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

      7. metadata-eval 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in x2 around 0 56.1%

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

   9. Taylor expanded in x2 around -inf 63.1%

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

       1. mul-1-neg 63.1%

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

       2. *-commutative 63.1%

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

       3. distribute-rgt-neg-in 63.1%

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

       4. +-commutative 63.1%

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

   11. Simplified 63.1%

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

4. Final simplification 50.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.75 \cdot 10^{+17} \lor \neg \left(x2 \leq 1.8 \cdot 10^{+15}\right):\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(\left(-6\right) - \frac{x1}{x2}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.1% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq 6.6 \cdot 10^{+117}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + -4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x2 6.6e+117)
   (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0)))
   (* x1 (+ -1.0 (* -4.0 (* x2 (- 3.0 (* 2.0 x2))))))))

C

double code(double x1, double x2) {
	double tmp;
	if (x2 <= 6.6e+117) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	} else {
		tmp = x1 * (-1.0 + (-4.0 * (x2 * (3.0 - (2.0 * x2)))));
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if (x2 <= 6.6d+117) then
        tmp = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
    else
        tmp = x1 * ((-1.0d0) + ((-4.0d0) * (x2 * (3.0d0 - (2.0d0 * x2)))))
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x2 <= 6.6e+117) {
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	} else {
		tmp = x1 * (-1.0 + (-4.0 * (x2 * (3.0 - (2.0 * x2)))));
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x2 <= 6.6e+117:
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))
	else:
		tmp = x1 * (-1.0 + (-4.0 * (x2 * (3.0 - (2.0 * x2)))))
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x2 <= 6.6e+117)
		tmp = Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)));
	else
		tmp = Float64(x1 * Float64(-1.0 + Float64(-4.0 * Float64(x2 * Float64(3.0 - Float64(2.0 * x2))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x2 <= 6.6e+117)
		tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
	else
		tmp = x1 * (-1.0 + (-4.0 * (x2 * (3.0 - (2.0 * x2)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x2, 6.6e+117], N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x1 * N[(-1.0 + N[(-4.0 * N[(x2 * N[(3.0 - N[(2.0 * x2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x2 < 6.5999999999999996e117

   1. Initial program 74.6%

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

   3. Simplified 73.6%

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

   5. Taylor expanded in x1 around 0 69.4%

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

   6. Taylor expanded in x2 around 0 71.2%

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

   if 6.5999999999999996e117 < x2

   1. Initial program 70.5%

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

   3. Simplified 44.8%

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

   5. Taylor expanded in x1 around 0 56.6%

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

      1. fma-define 56.6%

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

      2. associate-*r* 56.6%

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

      3. fmm-def 56.6%

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

      4. *-commutative 56.6%

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

      5. metadata-eval 56.6%

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

      6. cancel-sign-sub-inv 56.6%

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

      7. metadata-eval 56.6%

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

   7. Simplified 56.6%

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

   8. Taylor expanded in x1 around inf 56.6%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq 6.6 \cdot 10^{+117}:\\ \;\;\;\;x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x1 \cdot \left(-1 + -4 \cdot \left(x2 \cdot \left(3 - 2 \cdot x2\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 44.3% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -0.00021 \lor \neg \left(x1 \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x1 -0.00021) (not (<= x1 7.4e-34)))
   (* x1 (+ -1.0 (* x2 -12.0)))
   (- (* x2 -6.0) x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -0.00021) || !(x1 <= 7.4e-34)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x1 <= (-0.00021d0)) .or. (.not. (x1 <= 7.4d-34))) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else
        tmp = (x2 * (-6.0d0)) - x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x1 <= -0.00021) || !(x1 <= 7.4e-34)) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else {
		tmp = (x2 * -6.0) - x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x1 <= -0.00021) or not (x1 <= 7.4e-34):
		tmp = x1 * (-1.0 + (x2 * -12.0))
	else:
		tmp = (x2 * -6.0) - x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x1 <= -0.00021) || !(x1 <= 7.4e-34))
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	else
		tmp = Float64(Float64(x2 * -6.0) - x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x1 <= -0.00021) || ~((x1 <= 7.4e-34)))
		tmp = x1 * (-1.0 + (x2 * -12.0));
	else
		tmp = (x2 * -6.0) - x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x1, -0.00021], N[Not[LessEqual[x1, 7.4e-34]], $MachinePrecision]], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x1 < -2.1000000000000001e-4 or 7.39999999999999976e-34 < x1

   1. Initial program 44.3%

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

   3. Simplified 47.8%

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

   5. Taylor expanded in x1 around 0 25.8%

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

      1. fma-define 25.8%

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

      2. associate-*r* 25.8%

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

      3. fmm-def 25.8%

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

      4. *-commutative 25.8%

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

      5. metadata-eval 25.8%

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

      6. cancel-sign-sub-inv 25.8%

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

      7. metadata-eval 25.8%

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

   7. Simplified 25.8%

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

   8. Taylor expanded in x2 around 0 16.2%

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

      1. fma-define 16.2%

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

      2. mul-1-neg 16.2%

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

      3. fmm-undef 16.2%

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

      4. *-commutative 16.2%

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

   10. Simplified 16.2%

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

   11. Taylor expanded in x1 around inf 16.2%

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

   if -2.1000000000000001e-4 < x1 < 7.39999999999999976e-34

   1. Initial program 99.4%

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

   3. Simplified 85.2%

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

   5. Taylor expanded in x1 around 0 84.8%

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

      1. fma-define 84.9%

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

      2. associate-*r* 84.9%

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

      3. fmm-def 84.9%

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

      4. *-commutative 84.9%

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

      5. metadata-eval 84.9%

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

      6. cancel-sign-sub-inv 84.9%

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

      7. metadata-eval 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x2 around 0 73.5%

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

   9. Taylor expanded in x2 around 0 73.5%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 73.5%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. neg-mul-1 73.5%

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

       3. sub-neg 73.5%

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

   11. Simplified 73.5%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -0.00021 \lor \neg \left(x1 \leq 7.4 \cdot 10^{-34}\right):\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot -6 - x1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 44.7% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x1 \leq -0.0062:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 4500000:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (<= x1 -0.0062)
   (* x1 (+ -1.0 (* x2 -12.0)))
   (if (<= x1 4500000.0) (- (* x2 -6.0) x1) (* x2 (- (* x1 -12.0) 6.0)))))

C

double code(double x1, double x2) {
	double tmp;
	if (x1 <= -0.0062) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 4500000.0) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 * -12.0) - 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 <= (-0.0062d0)) then
        tmp = x1 * ((-1.0d0) + (x2 * (-12.0d0)))
    else if (x1 <= 4500000.0d0) then
        tmp = (x2 * (-6.0d0)) - x1
    else
        tmp = x2 * ((x1 * (-12.0d0)) - 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if (x1 <= -0.0062) {
		tmp = x1 * (-1.0 + (x2 * -12.0));
	} else if (x1 <= 4500000.0) {
		tmp = (x2 * -6.0) - x1;
	} else {
		tmp = x2 * ((x1 * -12.0) - 6.0);
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if x1 <= -0.0062:
		tmp = x1 * (-1.0 + (x2 * -12.0))
	elif x1 <= 4500000.0:
		tmp = (x2 * -6.0) - x1
	else:
		tmp = x2 * ((x1 * -12.0) - 6.0)
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if (x1 <= -0.0062)
		tmp = Float64(x1 * Float64(-1.0 + Float64(x2 * -12.0)));
	elseif (x1 <= 4500000.0)
		tmp = Float64(Float64(x2 * -6.0) - x1);
	else
		tmp = Float64(x2 * Float64(Float64(x1 * -12.0) - 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if (x1 <= -0.0062)
		tmp = x1 * (-1.0 + (x2 * -12.0));
	elseif (x1 <= 4500000.0)
		tmp = (x2 * -6.0) - x1;
	else
		tmp = x2 * ((x1 * -12.0) - 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[LessEqual[x1, -0.0062], N[(x1 * N[(-1.0 + N[(x2 * -12.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x1, 4500000.0], N[(N[(x2 * -6.0), $MachinePrecision] - x1), $MachinePrecision], N[(x2 * N[(N[(x1 * -12.0), $MachinePrecision] - 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x1 < -0.00619999999999999978

   1. Initial program 40.1%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in x1 around 0 12.0%

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

      1. fma-define 12.0%

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

      2. associate-*r* 12.0%

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

      3. fmm-def 12.0%

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

      4. *-commutative 12.0%

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

      5. metadata-eval 12.0%

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

      6. cancel-sign-sub-inv 12.0%

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

      7. metadata-eval 12.0%

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

   7. Simplified 12.0%

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

   8. Taylor expanded in x2 around 0 19.4%

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

      1. fma-define 19.4%

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

      2. mul-1-neg 19.4%

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

      3. fmm-undef 19.4%

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

      4. *-commutative 19.4%

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

   10. Simplified 19.4%

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

   11. Taylor expanded in x1 around inf 19.5%

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

   if -0.00619999999999999978 < x1 < 4.5e6

   1. Initial program 99.4%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in x1 around 0 84.3%

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

      1. fma-define 84.4%

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

      2. associate-*r* 84.4%

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

      3. fmm-def 84.4%

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

      4. *-commutative 84.4%

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

      5. metadata-eval 84.4%

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

      6. cancel-sign-sub-inv 84.4%

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

      7. metadata-eval 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in x2 around 0 71.1%

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

   9. Taylor expanded in x2 around 0 71.1%

      \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
   10. Step-by-step derivation

       1. *-commutative 71.1%

          \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

       2. neg-mul-1 71.1%

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

       3. sub-neg 71.1%

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

   11. Simplified 71.1%

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

   if 4.5e6 < x1

   1. Initial program 41.7%

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

   3. Simplified 39.9%

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

   5. Taylor expanded in x1 around 0 33.9%

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

      1. fma-define 33.9%

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

      2. associate-*r* 33.9%

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

      3. fmm-def 33.9%

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

      4. *-commutative 33.9%

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

      5. metadata-eval 33.9%

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

      6. cancel-sign-sub-inv 33.9%

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

      7. metadata-eval 33.9%

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

   7. Simplified 33.9%

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

   8. Taylor expanded in x2 around 0 11.7%

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

      1. fma-define 11.7%

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

      2. mul-1-neg 11.7%

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

      3. fmm-undef 11.7%

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

      4. *-commutative 11.7%

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

   10. Simplified 11.7%

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

   11. Taylor expanded in x2 around inf 12.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x1 \leq -0.0062:\\ \;\;\;\;x1 \cdot \left(-1 + x2 \cdot -12\right)\\ \mathbf{elif}\;x1 \leq 4500000:\\ \;\;\;\;x2 \cdot -6 - x1\\ \mathbf{else}:\\ \;\;\;\;x2 \cdot \left(x1 \cdot -12 - 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.9% accurate, 9.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x2 \leq -2.6 \cdot 10^{-124} \lor \neg \left(x2 \leq 5.3 \cdot 10^{-121}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \end{array} \]

FPCore

(FPCore (x1 x2)
 :precision binary64
 (if (or (<= x2 -2.6e-124) (not (<= x2 5.3e-121))) (* x2 -6.0) (- x1)))

C

double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.6e-124) || !(x2 <= 5.3e-121)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    real(8) :: tmp
    if ((x2 <= (-2.6d-124)) .or. (.not. (x2 <= 5.3d-121))) then
        tmp = x2 * (-6.0d0)
    else
        tmp = -x1
    end if
    code = tmp
end function

Java

public static double code(double x1, double x2) {
	double tmp;
	if ((x2 <= -2.6e-124) || !(x2 <= 5.3e-121)) {
		tmp = x2 * -6.0;
	} else {
		tmp = -x1;
	}
	return tmp;
}

Python

def code(x1, x2):
	tmp = 0
	if (x2 <= -2.6e-124) or not (x2 <= 5.3e-121):
		tmp = x2 * -6.0
	else:
		tmp = -x1
	return tmp

Julia

function code(x1, x2)
	tmp = 0.0
	if ((x2 <= -2.6e-124) || !(x2 <= 5.3e-121))
		tmp = Float64(x2 * -6.0);
	else
		tmp = Float64(-x1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x1, x2)
	tmp = 0.0;
	if ((x2 <= -2.6e-124) || ~((x2 <= 5.3e-121)))
		tmp = x2 * -6.0;
	else
		tmp = -x1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x1_, x2_] := If[Or[LessEqual[x2, -2.6e-124], N[Not[LessEqual[x2, 5.3e-121]], $MachinePrecision]], N[(x2 * -6.0), $MachinePrecision], (-x1)]

Derivation

1. Split input into 2 regimes

2. if x2 < -2.6e-124 or 5.2999999999999996e-121 < x2

   1. Initial program 72.5%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in x1 around 0 30.8%

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

   if -2.6e-124 < x2 < 5.2999999999999996e-121

   1. Initial program 76.8%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x1 around 0 58.5%

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

      1. fma-define 58.5%

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

      2. associate-*r* 58.5%

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

      3. fmm-def 58.5%

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

      4. *-commutative 58.5%

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

      5. metadata-eval 58.5%

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

      6. cancel-sign-sub-inv 58.5%

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

      7. metadata-eval 58.5%

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

   7. Simplified 58.5%

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

   8. Taylor expanded in x2 around 0 47.5%

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

      1. mul-1-neg 47.5%

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

   10. Simplified 47.5%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x2 \leq -2.6 \cdot 10^{-124} \lor \neg \left(x2 \leq 5.3 \cdot 10^{-121}\right):\\ \;\;\;\;x2 \cdot -6\\ \mathbf{else}:\\ \;\;\;\;-x1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 64.4% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \end{array} \]

FPCore

(FPCore (x1 x2) :precision binary64 (+ (* x2 -6.0) (* x1 (+ (* x1 9.0) -1.0))))

C

double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Fortran

real(8) function code(x1, x2)
    real(8), intent (in) :: x1
    real(8), intent (in) :: x2
    code = (x2 * (-6.0d0)) + (x1 * ((x1 * 9.0d0) + (-1.0d0)))
end function

Java

public static double code(double x1, double x2) {
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
}

Python

def code(x1, x2):
	return (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0))

Julia

function code(x1, x2)
	return Float64(Float64(x2 * -6.0) + Float64(x1 * Float64(Float64(x1 * 9.0) + -1.0)))
end

MATLAB

function tmp = code(x1, x2)
	tmp = (x2 * -6.0) + (x1 * ((x1 * 9.0) + -1.0));
end

Wolfram

code[x1_, x2_] := N[(N[(x2 * -6.0), $MachinePrecision] + N[(x1 * N[(N[(x1 * 9.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 73.8%

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

3. Simplified 67.8%

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

5. Taylor expanded in x1 around 0 66.4%

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

6. Taylor expanded in x2 around 0 64.7%

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

7. Final simplification 64.7%

   \[\leadsto x2 \cdot -6 + x1 \cdot \left(x1 \cdot 9 + -1\right) \]
8. Add Preprocessing

Alternative 18: 38.7% accurate, 25.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.8%

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

3. Simplified 67.8%

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

5. Taylor expanded in x1 around 0 57.4%

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

   1. fma-define 57.4%

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

   2. associate-*r* 57.4%

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

   3. fmm-def 57.4%

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

   4. *-commutative 57.4%

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

   5. metadata-eval 57.4%

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

   6. cancel-sign-sub-inv 57.4%

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

   7. metadata-eval 57.4%

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

7. Simplified 57.4%

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

8. Taylor expanded in x2 around 0 41.2%

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

9. Taylor expanded in x2 around 0 41.2%

   \[\leadsto \color{blue}{-6 \cdot x2 + -1 \cdot x1} \]
10. Step-by-step derivation

    1. *-commutative 41.2%

       \[\leadsto \color{blue}{x2 \cdot -6} + -1 \cdot x1 \]

    2. neg-mul-1 41.2%

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

    3. sub-neg 41.2%

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

11. Simplified 41.2%

    \[\leadsto \color{blue}{x2 \cdot -6 - x1} \]
12. Add Preprocessing

Alternative 19: 14.5% accurate, 63.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x1, x2):
	return -x1

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.8%

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

3. Simplified 67.8%

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

5. Taylor expanded in x1 around 0 57.4%

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

   1. fma-define 57.4%

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

   2. associate-*r* 57.4%

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

   3. fmm-def 57.4%

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

   4. *-commutative 57.4%

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

   5. metadata-eval 57.4%

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

   6. cancel-sign-sub-inv 57.4%

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

   7. metadata-eval 57.4%

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

7. Simplified 57.4%

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

8. Taylor expanded in x2 around 0 17.6%

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

   1. mul-1-neg 17.6%

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

10. Simplified 17.6%

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

Reproduce

herbie shell --seed 2024172 
(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))))))