Average Error: 0.2 → 0.2
Time: 23.5s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(\left(\sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4}\right) \cdot \sqrt[3]{\left(\left(a \cdot a\right) \cdot \left(a + 1\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right) \cdot 4} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\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(1 - 3 \cdot a\right)\right)\right) - 1
↓
\left(\left(\sqrt[3]{\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} \cdot \sqrt[3]{\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) \cdot \sqrt[3]{\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} + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r7258400 = a;
        double r7258401 = r7258400 * r7258400;
        double r7258402 = b;
        double r7258403 = r7258402 * r7258402;
        double r7258404 = r7258401 + r7258403;
        double r7258405 = 2.0;
        double r7258406 = pow(r7258404, r7258405);
        double r7258407 = 4.0;
        double r7258408 = 1.0;
        double r7258409 = r7258408 + r7258400;
        double r7258410 = r7258401 * r7258409;
        double r7258411 = 3.0;
        double r7258412 = r7258411 * r7258400;
        double r7258413 = r7258408 - r7258412;
        double r7258414 = r7258403 * r7258413;
        double r7258415 = r7258410 + r7258414;
        double r7258416 = r7258407 * r7258415;
        double r7258417 = r7258406 + r7258416;
        double r7258418 = r7258417 - r7258408;
        return r7258418;
}
↓
double f(double a, double b) {
        double r7258419 = a;
        double r7258420 = r7258419 * r7258419;
        double r7258421 = 1.0;
        double r7258422 = r7258419 + r7258421;
        double r7258423 = r7258420 * r7258422;
        double r7258424 = b;
        double r7258425 = r7258424 * r7258424;
        double r7258426 = 3.0;
        double r7258427 = r7258426 * r7258419;
        double r7258428 = r7258421 - r7258427;
        double r7258429 = r7258425 * r7258428;
        double r7258430 = r7258423 + r7258429;
        double r7258431 = 4.0;
        double r7258432 = r7258430 * r7258431;
        double r7258433 = cbrt(r7258432);
        double r7258434 = r7258433 * r7258433;
        double r7258435 = r7258434 * r7258433;
        double r7258436 = r7258420 + r7258425;
        double r7258437 = 2.0;
        double r7258438 = pow(r7258436, r7258437);
        double r7258439 = r7258435 + r7258438;
        double r7258440 = r7258439 - r7258421;
        return r7258440;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019172 
(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))