Average Error: 0.2 → 0.2
Time: 25.0s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r7117934 = a;
        double r7117935 = r7117934 * r7117934;
        double r7117936 = b;
        double r7117937 = r7117936 * r7117936;
        double r7117938 = r7117935 + r7117937;
        double r7117939 = 2.0;
        double r7117940 = pow(r7117938, r7117939);
        double r7117941 = 4.0;
        double r7117942 = r7117941 * r7117937;
        double r7117943 = r7117940 + r7117942;
        double r7117944 = 1.0;
        double r7117945 = r7117943 - r7117944;
        return r7117945;
}
↓
double f(double a, double b) {
        double r7117946 = b;
        double r7117947 = r7117946 * r7117946;
        double r7117948 = 4.0;
        double r7117949 = r7117947 * r7117948;
        double r7117950 = a;
        double r7117951 = r7117950 * r7117950;
        double r7117952 = r7117951 + r7117947;
        double r7117953 = 2.0;
        double r7117954 = pow(r7117952, r7117953);
        double r7117955 = r7117949 + r7117954;
        double r7117956 = 1.0;
        double r7117957 = r7117955 - r7117956;
        return r7117957;
}

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

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))