Average Error: 0.2 → 0.2
Time: 43.6s
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 r7862192 = a;
        double r7862193 = r7862192 * r7862192;
        double r7862194 = b;
        double r7862195 = r7862194 * r7862194;
        double r7862196 = r7862193 + r7862195;
        double r7862197 = 2.0;
        double r7862198 = pow(r7862196, r7862197);
        double r7862199 = 4.0;
        double r7862200 = 1.0;
        double r7862201 = r7862200 + r7862192;
        double r7862202 = r7862193 * r7862201;
        double r7862203 = 3.0;
        double r7862204 = r7862203 * r7862192;
        double r7862205 = r7862200 - r7862204;
        double r7862206 = r7862195 * r7862205;
        double r7862207 = r7862202 + r7862206;
        double r7862208 = r7862199 * r7862207;
        double r7862209 = r7862198 + r7862208;
        double r7862210 = r7862209 - r7862200;
        return r7862210;
}
↓
double f(double a, double b) {
        double r7862211 = a;
        double r7862212 = r7862211 * r7862211;
        double r7862213 = b;
        double r7862214 = r7862213 * r7862213;
        double r7862215 = r7862212 + r7862214;
        double r7862216 = 2.0;
        double r7862217 = pow(r7862215, r7862216);
        double r7862218 = 1.0;
        double r7862219 = r7862211 + r7862218;
        double r7862220 = r7862212 * r7862219;
        double r7862221 = 3.0;
        double r7862222 = r7862221 * r7862211;
        double r7862223 = r7862218 - r7862222;
        double r7862224 = r7862214 * r7862223;
        double r7862225 = r7862220 + r7862224;
        double r7862226 = 4.0;
        double r7862227 = r7862225 * r7862226;
        double r7862228 = r7862217 + r7862227;
        double r7862229 = r7862228 - r7862218;
        return r7862229;
}

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 2019149 +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))