Average Error: 0.2 → 0.2
Time: 41.0s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)}\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left(\left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \left(\sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)} \cdot \sqrt[3]{\left(1 - a\right) \cdot \left(a \cdot a\right)}\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right) \cdot 4 + {\left(b \cdot b + a \cdot a\right)}^{2}\right) - 1
double f(double a, double b) {
        double r10165240 = a;
        double r10165241 = r10165240 * r10165240;
        double r10165242 = b;
        double r10165243 = r10165242 * r10165242;
        double r10165244 = r10165241 + r10165243;
        double r10165245 = 2.0;
        double r10165246 = pow(r10165244, r10165245);
        double r10165247 = 4.0;
        double r10165248 = 1.0;
        double r10165249 = r10165248 - r10165240;
        double r10165250 = r10165241 * r10165249;
        double r10165251 = 3.0;
        double r10165252 = r10165251 + r10165240;
        double r10165253 = r10165243 * r10165252;
        double r10165254 = r10165250 + r10165253;
        double r10165255 = r10165247 * r10165254;
        double r10165256 = r10165246 + r10165255;
        double r10165257 = r10165256 - r10165248;
        return r10165257;
}
↓
double f(double a, double b) {
        double r10165258 = 1.0;
        double r10165259 = a;
        double r10165260 = r10165258 - r10165259;
        double r10165261 = r10165259 * r10165259;
        double r10165262 = r10165260 * r10165261;
        double r10165263 = cbrt(r10165262);
        double r10165264 = r10165263 * r10165263;
        double r10165265 = r10165263 * r10165264;
        double r10165266 = b;
        double r10165267 = r10165266 * r10165266;
        double r10165268 = 3.0;
        double r10165269 = r10165268 + r10165259;
        double r10165270 = r10165267 * r10165269;
        double r10165271 = r10165265 + r10165270;
        double r10165272 = 4.0;
        double r10165273 = r10165271 * r10165272;
        double r10165274 = r10165267 + r10165261;
        double r10165275 = 2.0;
        double r10165276 = pow(r10165274, r10165275);
        double r10165277 = r10165273 + r10165276;
        double r10165278 = r10165277 - r10165258;
        return r10165278;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))