Average Error: 0.2 → 0.2
Time: 3.2s
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 r280941 = a;
        double r280942 = r280941 * r280941;
        double r280943 = b;
        double r280944 = r280943 * r280943;
        double r280945 = r280942 + r280944;
        double r280946 = 2.0;
        double r280947 = pow(r280945, r280946);
        double r280948 = 4.0;
        double r280949 = r280948 * r280944;
        double r280950 = r280947 + r280949;
        double r280951 = 1.0;
        double r280952 = r280950 - r280951;
        return r280952;
}
↓
double f(double a, double b) {
        double r280953 = a;
        double r280954 = r280953 * r280953;
        double r280955 = b;
        double r280956 = r280955 * r280955;
        double r280957 = r280954 + r280956;
        double r280958 = 2.0;
        double r280959 = pow(r280957, r280958);
        double r280960 = 4.0;
        double r280961 = r280960 * r280956;
        double r280962 = r280959 + r280961;
        double r280963 = 1.0;
        double r280964 = r280962 - r280963;
        return r280964;
}

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 2020021 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))