Average Error: 0.2 → 0.2
Time: 1.0m
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1\]
\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} + \left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4\right) - 1
double f(double a, double b) {
        double r49005009 = a;
        double r49005010 = r49005009 * r49005009;
        double r49005011 = b;
        double r49005012 = r49005011 * r49005011;
        double r49005013 = r49005010 + r49005012;
        double r49005014 = 2.0;
        double r49005015 = pow(r49005013, r49005014);
        double r49005016 = 4.0;
        double r49005017 = 1.0;
        double r49005018 = r49005017 + r49005009;
        double r49005019 = r49005010 * r49005018;
        double r49005020 = 3.0;
        double r49005021 = r49005020 * r49005009;
        double r49005022 = r49005017 - r49005021;
        double r49005023 = r49005012 * r49005022;
        double r49005024 = r49005019 + r49005023;
        double r49005025 = r49005016 * r49005024;
        double r49005026 = r49005015 + r49005025;
        double r49005027 = r49005026 - r49005017;
        return r49005027;
}
↓
double f(double a, double b) {
        double r49005028 = a;
        double r49005029 = r49005028 * r49005028;
        double r49005030 = b;
        double r49005031 = r49005030 * r49005030;
        double r49005032 = r49005029 + r49005031;
        double r49005033 = 2.0;
        double r49005034 = pow(r49005032, r49005033);
        double r49005035 = 1.0;
        double r49005036 = r49005028 + r49005035;
        double r49005037 = r49005029 * r49005036;
        double r49005038 = 3.0;
        double r49005039 = r49005038 * r49005028;
        double r49005040 = r49005035 - r49005039;
        double r49005041 = r49005031 * r49005040;
        double r49005042 = r49005037 + r49005041;
        double r49005043 = 4.0;
        double r49005044 = r49005042 * r49005043;
        double r49005045 = r49005034 + r49005044;
        double r49005046 = r49005045 - r49005035;
        return r49005046;
}

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

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))