Average Error: 0.2 → 0.2
Time: 25.8s
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 r5276550 = a;
        double r5276551 = r5276550 * r5276550;
        double r5276552 = b;
        double r5276553 = r5276552 * r5276552;
        double r5276554 = r5276551 + r5276553;
        double r5276555 = 2.0;
        double r5276556 = pow(r5276554, r5276555);
        double r5276557 = 4.0;
        double r5276558 = 1.0;
        double r5276559 = r5276558 + r5276550;
        double r5276560 = r5276551 * r5276559;
        double r5276561 = 3.0;
        double r5276562 = r5276561 * r5276550;
        double r5276563 = r5276558 - r5276562;
        double r5276564 = r5276553 * r5276563;
        double r5276565 = r5276560 + r5276564;
        double r5276566 = r5276557 * r5276565;
        double r5276567 = r5276556 + r5276566;
        double r5276568 = r5276567 - r5276558;
        return r5276568;
}
↓
double f(double a, double b) {
        double r5276569 = a;
        double r5276570 = r5276569 * r5276569;
        double r5276571 = 1.0;
        double r5276572 = r5276569 + r5276571;
        double r5276573 = r5276570 * r5276572;
        double r5276574 = b;
        double r5276575 = r5276574 * r5276574;
        double r5276576 = 3.0;
        double r5276577 = r5276576 * r5276569;
        double r5276578 = r5276571 - r5276577;
        double r5276579 = r5276575 * r5276578;
        double r5276580 = r5276573 + r5276579;
        double r5276581 = 4.0;
        double r5276582 = r5276580 * r5276581;
        double r5276583 = cbrt(r5276582);
        double r5276584 = r5276583 * r5276583;
        double r5276585 = r5276584 * r5276583;
        double r5276586 = r5276570 + r5276575;
        double r5276587 = 2.0;
        double r5276588 = pow(r5276586, r5276587);
        double r5276589 = r5276585 + r5276588;
        double r5276590 = r5276589 - r5276571;
        return r5276590;
}

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 +o rules:numerics
(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))