Average Error: 0.1 → 0.1
Time: 1.6m
Precision: 64
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
\[\frac{x}{2 \cdot y} + \left(\left({y}^{6} \cdot 333.75 + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(\sqrt[3]{\left(\left(\left(11 \cdot x\right) \cdot y\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)} \cdot x\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + {y}^{8} \cdot 5.5\right)\]
\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}
\frac{x}{2 \cdot y} + \left(\left({y}^{6} \cdot 333.75 + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(\sqrt[3]{\left(\left(\left(11 \cdot x\right) \cdot y\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)} \cdot x\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + {y}^{8} \cdot 5.5\right)
double f(double y, double x) {
        double r42537032 = 333.75;
        double r42537033 = y;
        double r42537034 = 6.0;
        double r42537035 = pow(r42537033, r42537034);
        double r42537036 = r42537032 * r42537035;
        double r42537037 = x;
        double r42537038 = r42537037 * r42537037;
        double r42537039 = 11.0;
        double r42537040 = r42537039 * r42537037;
        double r42537041 = r42537040 * r42537037;
        double r42537042 = r42537041 * r42537033;
        double r42537043 = r42537042 * r42537033;
        double r42537044 = r42537043 - r42537035;
        double r42537045 = 121.0;
        double r42537046 = 4.0;
        double r42537047 = pow(r42537033, r42537046);
        double r42537048 = r42537045 * r42537047;
        double r42537049 = r42537044 - r42537048;
        double r42537050 = 2.0;
        double r42537051 = r42537049 - r42537050;
        double r42537052 = r42537038 * r42537051;
        double r42537053 = r42537036 + r42537052;
        double r42537054 = 5.5;
        double r42537055 = 8.0;
        double r42537056 = pow(r42537033, r42537055);
        double r42537057 = r42537054 * r42537056;
        double r42537058 = r42537053 + r42537057;
        double r42537059 = r42537050 * r42537033;
        double r42537060 = r42537037 / r42537059;
        double r42537061 = r42537058 + r42537060;
        return r42537061;
}

double f(double y, double x) {
        double r42537062 = x;
        double r42537063 = 2.0;
        double r42537064 = y;
        double r42537065 = r42537063 * r42537064;
        double r42537066 = r42537062 / r42537065;
        double r42537067 = 6.0;
        double r42537068 = pow(r42537064, r42537067);
        double r42537069 = 333.75;
        double r42537070 = r42537068 * r42537069;
        double r42537071 = r42537062 * r42537062;
        double r42537072 = 11.0;
        double r42537073 = r42537072 * r42537062;
        double r42537074 = r42537073 * r42537064;
        double r42537075 = r42537074 * r42537074;
        double r42537076 = r42537075 * r42537074;
        double r42537077 = cbrt(r42537076);
        double r42537078 = r42537077 * r42537062;
        double r42537079 = r42537064 * r42537078;
        double r42537080 = r42537079 - r42537068;
        double r42537081 = 121.0;
        double r42537082 = 4.0;
        double r42537083 = pow(r42537064, r42537082);
        double r42537084 = r42537081 * r42537083;
        double r42537085 = r42537080 - r42537084;
        double r42537086 = r42537085 - r42537063;
        double r42537087 = r42537071 * r42537086;
        double r42537088 = r42537070 + r42537087;
        double r42537089 = 8.0;
        double r42537090 = pow(r42537064, r42537089);
        double r42537091 = 5.5;
        double r42537092 = r42537090 * r42537091;
        double r42537093 = r42537088 + r42537092;
        double r42537094 = r42537066 + r42537093;
        return r42537094;
}

Error

Bits error versus y

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
  2. Taylor expanded around inf 0.1

    \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\color{blue}{\left(11 \cdot \left({x}^{2} \cdot y\right)\right)} \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
  3. Simplified0.1

    \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\color{blue}{\left(\left(\left(x \cdot 11\right) \cdot y\right) \cdot x\right)} \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube0.1

    \[\leadsto \left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\color{blue}{\sqrt[3]{\left(\left(\left(x \cdot 11\right) \cdot y\right) \cdot \left(\left(x \cdot 11\right) \cdot y\right)\right) \cdot \left(\left(x \cdot 11\right) \cdot y\right)}} \cdot x\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
  6. Final simplification0.1

    \[\leadsto \frac{x}{2 \cdot y} + \left(\left({y}^{6} \cdot 333.75 + \left(x \cdot x\right) \cdot \left(\left(\left(y \cdot \left(\sqrt[3]{\left(\left(\left(11 \cdot x\right) \cdot y\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)\right) \cdot \left(\left(11 \cdot x\right) \cdot y\right)} \cdot x\right) - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + {y}^{8} \cdot 5.5\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (y x)
  :name "333.75 * pow(y, 6) + x * x * (11 * x * x * y * y - pow(y, 6) - 121 * pow(y, 4) - 2) + 5.5 * pow(y, 8) + x / (2 * y)"
  (+ (+ (+ (* 333.75 (pow y 6)) (* (* x x) (- (- (- (* (* (* (* 11 x) x) y) y) (pow y 6)) (* 121 (pow y 4))) 2))) (* 5.5 (pow y 8))) (/ x (* 2 y))))