Average Error: 0.2 → 0.2
Time: 22.0s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\left(b \cdot b\right) \cdot 4 + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r8156185 = a;
        double r8156186 = r8156185 * r8156185;
        double r8156187 = b;
        double r8156188 = r8156187 * r8156187;
        double r8156189 = r8156186 + r8156188;
        double r8156190 = 2.0;
        double r8156191 = pow(r8156189, r8156190);
        double r8156192 = 4.0;
        double r8156193 = r8156192 * r8156188;
        double r8156194 = r8156191 + r8156193;
        double r8156195 = 1.0;
        double r8156196 = r8156194 - r8156195;
        return r8156196;
}
↓
double f(double a, double b) {
        double r8156197 = b;
        double r8156198 = r8156197 * r8156197;
        double r8156199 = 4.0;
        double r8156200 = r8156198 * r8156199;
        double r8156201 = a;
        double r8156202 = r8156201 * r8156201;
        double r8156203 = r8156202 + r8156198;
        double r8156204 = 2.0;
        double r8156205 = pow(r8156203, r8156204);
        double r8156206 = r8156200 + r8156205;
        double r8156207 = 1.0;
        double r8156208 = r8156206 - r8156207;
        return r8156208;
}

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

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

Reproduce

herbie shell --seed 2019129 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))