Average Error: 0.2 → 0.2
Time: 4.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right)\right) - 1\]
\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(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(3 + a\right)}\right)\right) - 1
double f(double a, double b) {
        double r238318 = a;
        double r238319 = r238318 * r238318;
        double r238320 = b;
        double r238321 = r238320 * r238320;
        double r238322 = r238319 + r238321;
        double r238323 = 2.0;
        double r238324 = pow(r238322, r238323);
        double r238325 = 4.0;
        double r238326 = 1.0;
        double r238327 = r238326 - r238318;
        double r238328 = r238319 * r238327;
        double r238329 = 3.0;
        double r238330 = r238329 + r238318;
        double r238331 = r238321 * r238330;
        double r238332 = r238328 + r238331;
        double r238333 = r238325 * r238332;
        double r238334 = r238324 + r238333;
        double r238335 = r238334 - r238326;
        return r238335;
}
↓
double f(double a, double b) {
        double r238336 = a;
        double r238337 = r238336 * r238336;
        double r238338 = b;
        double r238339 = r238338 * r238338;
        double r238340 = r238337 + r238339;
        double r238341 = 2.0;
        double r238342 = pow(r238340, r238341);
        double r238343 = 4.0;
        double r238344 = 1.0;
        double r238345 = r238344 - r238336;
        double r238346 = r238337 * r238345;
        double r238347 = 3.0;
        double r238348 = r238347 + r238336;
        double r238349 = r238339 * r238348;
        double r238350 = cbrt(r238349);
        double r238351 = r238350 * r238350;
        double r238352 = r238351 * r238350;
        double r238353 = r238346 + r238352;
        double r238354 = r238343 * r238353;
        double r238355 = r238342 + r238354;
        double r238356 = r238355 - r238344;
        return r238356;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))