Average Error: 0.2 → 0.2
Time: 7.4s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(\left(a \cdot a\right) \cdot \left(\sqrt[3]{1 + a} \cdot \sqrt[3]{1 + a}\right)\right) \cdot \sqrt[3]{1 + a} + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 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} + 4 \cdot \left(\left(\left(a \cdot a\right) \cdot \left(\sqrt[3]{1 + a} \cdot \sqrt[3]{1 + a}\right)\right) \cdot \sqrt[3]{1 + a} + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1
double f(double a, double b) {
        double r149433 = a;
        double r149434 = r149433 * r149433;
        double r149435 = b;
        double r149436 = r149435 * r149435;
        double r149437 = r149434 + r149436;
        double r149438 = 2.0;
        double r149439 = pow(r149437, r149438);
        double r149440 = 4.0;
        double r149441 = 1.0;
        double r149442 = r149441 + r149433;
        double r149443 = r149434 * r149442;
        double r149444 = 3.0;
        double r149445 = r149444 * r149433;
        double r149446 = r149441 - r149445;
        double r149447 = r149436 * r149446;
        double r149448 = r149443 + r149447;
        double r149449 = r149440 * r149448;
        double r149450 = r149439 + r149449;
        double r149451 = r149450 - r149441;
        return r149451;
}
↓
double f(double a, double b) {
        double r149452 = a;
        double r149453 = r149452 * r149452;
        double r149454 = b;
        double r149455 = r149454 * r149454;
        double r149456 = r149453 + r149455;
        double r149457 = 2.0;
        double r149458 = pow(r149456, r149457);
        double r149459 = 4.0;
        double r149460 = 1.0;
        double r149461 = r149460 + r149452;
        double r149462 = cbrt(r149461);
        double r149463 = r149462 * r149462;
        double r149464 = r149453 * r149463;
        double r149465 = r149464 * r149462;
        double r149466 = 3.0;
        double r149467 = r149466 * r149452;
        double r149468 = r149460 - r149467;
        double r149469 = r149455 * r149468;
        double r149470 = r149465 + r149469;
        double r149471 = r149459 * r149470;
        double r149472 = r149458 + r149471;
        double r149473 = r149472 - r149460;
        return r149473;
}

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. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))