Average Error: 0.2 → 0.2
Time: 15.4s
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 r175970 = a;
        double r175971 = r175970 * r175970;
        double r175972 = b;
        double r175973 = r175972 * r175972;
        double r175974 = r175971 + r175973;
        double r175975 = 2.0;
        double r175976 = pow(r175974, r175975);
        double r175977 = 4.0;
        double r175978 = r175977 * r175973;
        double r175979 = r175976 + r175978;
        double r175980 = 1.0;
        double r175981 = r175979 - r175980;
        return r175981;
}
↓
double f(double a, double b) {
        double r175982 = a;
        double r175983 = r175982 * r175982;
        double r175984 = b;
        double r175985 = r175984 * r175984;
        double r175986 = r175983 + r175985;
        double r175987 = 2.0;
        double r175988 = pow(r175986, r175987);
        double r175989 = 4.0;
        double r175990 = r175989 * r175985;
        double r175991 = r175988 + r175990;
        double r175992 = 1.0;
        double r175993 = r175991 - r175992;
        return r175993;
}

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 2019209 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))