Average Error: 0.2 → 0.2
Time: 13.7s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]
↓
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right)\right) - 1\]
\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(a \cdot a\right) \cdot \left(1 + a\right) + \left(\sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)} \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right) \cdot \sqrt[3]{\left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)}\right)\right) - 1
double f(double a, double b) {
        double r358548 = a;
        double r358549 = r358548 * r358548;
        double r358550 = b;
        double r358551 = r358550 * r358550;
        double r358552 = r358549 + r358551;
        double r358553 = 2.0;
        double r358554 = pow(r358552, r358553);
        double r358555 = 4.0;
        double r358556 = 1.0;
        double r358557 = r358556 + r358548;
        double r358558 = r358549 * r358557;
        double r358559 = 3.0;
        double r358560 = r358559 * r358548;
        double r358561 = r358556 - r358560;
        double r358562 = r358551 * r358561;
        double r358563 = r358558 + r358562;
        double r358564 = r358555 * r358563;
        double r358565 = r358554 + r358564;
        double r358566 = r358565 - r358556;
        return r358566;
}
↓
double f(double a, double b) {
        double r358567 = a;
        double r358568 = r358567 * r358567;
        double r358569 = b;
        double r358570 = r358569 * r358569;
        double r358571 = r358568 + r358570;
        double r358572 = 2.0;
        double r358573 = pow(r358571, r358572);
        double r358574 = 4.0;
        double r358575 = 1.0;
        double r358576 = r358575 + r358567;
        double r358577 = r358568 * r358576;
        double r358578 = 3.0;
        double r358579 = r358578 * r358567;
        double r358580 = r358575 - r358579;
        double r358581 = r358570 * r358580;
        double r358582 = cbrt(r358581);
        double r358583 = r358582 * r358582;
        double r358584 = r358583 * r358582;
        double r358585 = r358577 + r358584;
        double r358586 = r358574 * r358585;
        double r358587 = r358573 + r358586;
        double r358588 = r358587 - r358575;
        return r358588;
}

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

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020045 
(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))