Average Error: 0.2 → 0.2
Time: 52.2s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left(4 \cdot \left(\left(b \cdot b\right) \cdot \left(1 - a \cdot 3\right) + \left(\left(\sqrt[3]{a + 1} \cdot \sqrt[3]{a + 1}\right) \cdot \left(a \cdot a\right)\right) \cdot \sqrt[3]{a + 1}\right) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1\]
\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(4 \cdot \left(\left(b \cdot b\right) \cdot \left(1 - a \cdot 3\right) + \left(\left(\sqrt[3]{a + 1} \cdot \sqrt[3]{a + 1}\right) \cdot \left(a \cdot a\right)\right) \cdot \sqrt[3]{a + 1}\right) + {\left(a \cdot a + b \cdot b\right)}^{2}\right) - 1
double f(double a, double b) {
        double r54767395 = a;
        double r54767396 = r54767395 * r54767395;
        double r54767397 = b;
        double r54767398 = r54767397 * r54767397;
        double r54767399 = r54767396 + r54767398;
        double r54767400 = 2.0;
        double r54767401 = pow(r54767399, r54767400);
        double r54767402 = 4.0;
        double r54767403 = 1.0;
        double r54767404 = r54767403 + r54767395;
        double r54767405 = r54767396 * r54767404;
        double r54767406 = 3.0;
        double r54767407 = r54767406 * r54767395;
        double r54767408 = r54767403 - r54767407;
        double r54767409 = r54767398 * r54767408;
        double r54767410 = r54767405 + r54767409;
        double r54767411 = r54767402 * r54767410;
        double r54767412 = r54767401 + r54767411;
        double r54767413 = r54767412 - r54767403;
        return r54767413;
}
↓
double f(double a, double b) {
        double r54767414 = 4.0;
        double r54767415 = b;
        double r54767416 = r54767415 * r54767415;
        double r54767417 = 1.0;
        double r54767418 = a;
        double r54767419 = 3.0;
        double r54767420 = r54767418 * r54767419;
        double r54767421 = r54767417 - r54767420;
        double r54767422 = r54767416 * r54767421;
        double r54767423 = r54767418 + r54767417;
        double r54767424 = cbrt(r54767423);
        double r54767425 = r54767424 * r54767424;
        double r54767426 = r54767418 * r54767418;
        double r54767427 = r54767425 * r54767426;
        double r54767428 = r54767427 * r54767424;
        double r54767429 = r54767422 + r54767428;
        double r54767430 = r54767414 * r54767429;
        double r54767431 = r54767426 + r54767416;
        double r54767432 = 2.0;
        double r54767433 = pow(r54767431, r54767432);
        double r54767434 = r54767430 + r54767433;
        double r54767435 = r54767434 - r54767417;
        return r54767435;
}

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

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

Reproduce

herbie shell --seed 2019107 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))