Average Error: 0.2 → 0.2
Time: 19.3s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(\left(b \cdot b\right) \cdot \left(\sqrt[3]{3 + a} \cdot \sqrt[3]{3 + a}\right)\right) \cdot \sqrt[3]{3 + a}\right)\right) - 1\]
\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(\left(b \cdot b\right) \cdot \left(\sqrt[3]{3 + a} \cdot \sqrt[3]{3 + a}\right)\right) \cdot \sqrt[3]{3 + a}\right)\right) - 1
double f(double a, double b) {
        double r126288 = a;
        double r126289 = r126288 * r126288;
        double r126290 = b;
        double r126291 = r126290 * r126290;
        double r126292 = r126289 + r126291;
        double r126293 = 2.0;
        double r126294 = pow(r126292, r126293);
        double r126295 = 4.0;
        double r126296 = 1.0;
        double r126297 = r126296 - r126288;
        double r126298 = r126289 * r126297;
        double r126299 = 3.0;
        double r126300 = r126299 + r126288;
        double r126301 = r126291 * r126300;
        double r126302 = r126298 + r126301;
        double r126303 = r126295 * r126302;
        double r126304 = r126294 + r126303;
        double r126305 = r126304 - r126296;
        return r126305;
}
↓
double f(double a, double b) {
        double r126306 = a;
        double r126307 = r126306 * r126306;
        double r126308 = b;
        double r126309 = r126308 * r126308;
        double r126310 = r126307 + r126309;
        double r126311 = 2.0;
        double r126312 = pow(r126310, r126311);
        double r126313 = 4.0;
        double r126314 = 1.0;
        double r126315 = r126314 - r126306;
        double r126316 = r126307 * r126315;
        double r126317 = 3.0;
        double r126318 = r126317 + r126306;
        double r126319 = cbrt(r126318);
        double r126320 = r126319 * r126319;
        double r126321 = r126309 * r126320;
        double r126322 = r126321 * r126319;
        double r126323 = r126316 + r126322;
        double r126324 = r126313 * r126323;
        double r126325 = r126312 + r126324;
        double r126326 = r126325 - r126314;
        return r126326;
}

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

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 
(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))