Average Error: 0.2 → 0.2
Time: 3.6s
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 r238972 = a;
        double r238973 = r238972 * r238972;
        double r238974 = b;
        double r238975 = r238974 * r238974;
        double r238976 = r238973 + r238975;
        double r238977 = 2.0;
        double r238978 = pow(r238976, r238977);
        double r238979 = 4.0;
        double r238980 = r238979 * r238975;
        double r238981 = r238978 + r238980;
        double r238982 = 1.0;
        double r238983 = r238981 - r238982;
        return r238983;
}
↓
double f(double a, double b) {
        double r238984 = a;
        double r238985 = r238984 * r238984;
        double r238986 = b;
        double r238987 = r238986 * r238986;
        double r238988 = r238985 + r238987;
        double r238989 = 2.0;
        double r238990 = pow(r238988, r238989);
        double r238991 = 4.0;
        double r238992 = r238991 * r238987;
        double r238993 = r238990 + r238992;
        double r238994 = 1.0;
        double r238995 = r238993 - r238994;
        return r238995;
}

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 2020060 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))