Average Error: 0.2 → 0.2
Time: 18.3s
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 r170194 = a;
        double r170195 = r170194 * r170194;
        double r170196 = b;
        double r170197 = r170196 * r170196;
        double r170198 = r170195 + r170197;
        double r170199 = 2.0;
        double r170200 = pow(r170198, r170199);
        double r170201 = 4.0;
        double r170202 = 1.0;
        double r170203 = r170202 + r170194;
        double r170204 = r170195 * r170203;
        double r170205 = 3.0;
        double r170206 = r170205 * r170194;
        double r170207 = r170202 - r170206;
        double r170208 = r170197 * r170207;
        double r170209 = r170204 + r170208;
        double r170210 = r170201 * r170209;
        double r170211 = r170200 + r170210;
        double r170212 = r170211 - r170202;
        return r170212;
}
↓
double f(double a, double b) {
        double r170213 = a;
        double r170214 = r170213 * r170213;
        double r170215 = b;
        double r170216 = r170215 * r170215;
        double r170217 = r170214 + r170216;
        double r170218 = 2.0;
        double r170219 = pow(r170217, r170218);
        double r170220 = 1.0;
        double r170221 = r170213 + r170220;
        double r170222 = r170214 * r170221;
        double r170223 = 3.0;
        double r170224 = r170223 * r170213;
        double r170225 = r170220 - r170224;
        double r170226 = r170216 * r170225;
        double r170227 = r170222 + r170226;
        double r170228 = 4.0;
        double r170229 = r170227 * r170228;
        double r170230 = r170219 + r170229;
        double r170231 = r170230 - r170220;
        return r170231;
}

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 2019194 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))) 1.0))