Average Error: 0.2 → 0.2
Time: 16.6s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
double f(double a, double b) {
        double r218874 = a;
        double r218875 = r218874 * r218874;
        double r218876 = b;
        double r218877 = r218876 * r218876;
        double r218878 = r218875 + r218877;
        double r218879 = 2.0;
        double r218880 = pow(r218878, r218879);
        double r218881 = 4.0;
        double r218882 = r218881 * r218877;
        double r218883 = r218880 + r218882;
        double r218884 = 1.0;
        double r218885 = r218883 - r218884;
        return r218885;
}
↓
double f(double a, double b) {
        double r218886 = a;
        double r218887 = r218886 * r218886;
        double r218888 = b;
        double r218889 = r218888 * r218888;
        double r218890 = r218887 + r218889;
        double r218891 = 2.0;
        double r218892 = pow(r218890, r218891);
        double r218893 = 4.0;
        double r218894 = r218893 * r218889;
        double r218895 = r218892 + r218894;
        double r218896 = 1.0;
        double r218897 = r218895 - r218896;
        return r218897;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

Reproduce

herbie shell --seed 2019304 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))