Average Error: 0.2 → 0.2
Time: 4.2s
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 r262173 = a;
        double r262174 = r262173 * r262173;
        double r262175 = b;
        double r262176 = r262175 * r262175;
        double r262177 = r262174 + r262176;
        double r262178 = 2.0;
        double r262179 = pow(r262177, r262178);
        double r262180 = 4.0;
        double r262181 = r262180 * r262176;
        double r262182 = r262179 + r262181;
        double r262183 = 1.0;
        double r262184 = r262182 - r262183;
        return r262184;
}
↓
double f(double a, double b) {
        double r262185 = a;
        double r262186 = r262185 * r262185;
        double r262187 = b;
        double r262188 = r262187 * r262187;
        double r262189 = r262186 + r262188;
        double r262190 = 2.0;
        double r262191 = pow(r262189, r262190);
        double r262192 = 4.0;
        double r262193 = r262192 * r262188;
        double r262194 = r262191 + r262193;
        double r262195 = 1.0;
        double r262196 = r262194 - r262195;
        return r262196;
}

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 2019353 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))