Average Error: 0.2 → 0.2
Time: 7.8s
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 r193071 = a;
        double r193072 = r193071 * r193071;
        double r193073 = b;
        double r193074 = r193073 * r193073;
        double r193075 = r193072 + r193074;
        double r193076 = 2.0;
        double r193077 = pow(r193075, r193076);
        double r193078 = 4.0;
        double r193079 = 1.0;
        double r193080 = r193079 + r193071;
        double r193081 = r193072 * r193080;
        double r193082 = 3.0;
        double r193083 = r193082 * r193071;
        double r193084 = r193079 - r193083;
        double r193085 = r193074 * r193084;
        double r193086 = r193081 + r193085;
        double r193087 = r193078 * r193086;
        double r193088 = r193077 + r193087;
        double r193089 = r193088 - r193079;
        return r193089;
}
↓
double f(double a, double b) {
        double r193090 = a;
        double r193091 = r193090 * r193090;
        double r193092 = b;
        double r193093 = r193092 * r193092;
        double r193094 = r193091 + r193093;
        double r193095 = 2.0;
        double r193096 = pow(r193094, r193095);
        double r193097 = 4.0;
        double r193098 = 1.0;
        double r193099 = r193098 + r193090;
        double r193100 = r193091 * r193099;
        double r193101 = 3.0;
        double r193102 = r193101 * r193090;
        double r193103 = r193098 - r193102;
        double r193104 = r193093 * r193103;
        double r193105 = r193100 + r193104;
        double r193106 = r193097 * r193105;
        double r193107 = r193096 + r193106;
        double r193108 = r193107 - r193098;
        return r193108;
}

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 2019353 +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))