Average Error: 0.2 → 0.2
Time: 6.0s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r289046 = a;
        double r289047 = r289046 * r289046;
        double r289048 = b;
        double r289049 = r289048 * r289048;
        double r289050 = r289047 + r289049;
        double r289051 = 2.0;
        double r289052 = pow(r289050, r289051);
        double r289053 = 4.0;
        double r289054 = 1.0;
        double r289055 = r289054 + r289046;
        double r289056 = r289047 * r289055;
        double r289057 = 3.0;
        double r289058 = r289057 * r289046;
        double r289059 = r289054 - r289058;
        double r289060 = r289049 * r289059;
        double r289061 = r289056 + r289060;
        double r289062 = r289053 * r289061;
        double r289063 = r289052 + r289062;
        double r289064 = r289063 - r289054;
        return r289064;
}
↓
double f(double a, double b) {
        double r289065 = a;
        double r289066 = r289065 * r289065;
        double r289067 = b;
        double r289068 = r289067 * r289067;
        double r289069 = r289066 + r289068;
        double r289070 = 2.0;
        double r289071 = pow(r289069, r289070);
        double r289072 = 4.0;
        double r289073 = 1.0;
        double r289074 = r289073 + r289065;
        double r289075 = r289066 * r289074;
        double r289076 = 3.0;
        double r289077 = r289076 * r289065;
        double r289078 = r289073 - r289077;
        double r289079 = r289068 * r289078;
        double r289080 = r289075 + r289079;
        double r289081 = r289072 * r289080;
        double r289082 = r289071 + r289081;
        double r289083 = r289082 - r289073;
        return r289083;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

  2. Final simplification0.2

    \[\leadsto \left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))