Average Error: 0.2 → 0.5
Time: 5.1s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)} - 1
double f(double a, double b) {
        double r369457 = a;
        double r369458 = r369457 * r369457;
        double r369459 = b;
        double r369460 = r369459 * r369459;
        double r369461 = r369458 + r369460;
        double r369462 = 2.0;
        double r369463 = pow(r369461, r369462);
        double r369464 = 4.0;
        double r369465 = r369464 * r369460;
        double r369466 = r369463 + r369465;
        double r369467 = 1.0;
        double r369468 = r369466 - r369467;
        return r369468;
}
↓
double f(double a, double b) {
        double r369469 = a;
        double r369470 = r369469 * r369469;
        double r369471 = b;
        double r369472 = r369471 * r369471;
        double r369473 = r369470 + r369472;
        double r369474 = 2.0;
        double r369475 = pow(r369473, r369474);
        double r369476 = 4.0;
        double r369477 = r369476 * r369472;
        double r369478 = r369475 + r369477;
        double r369479 = cbrt(r369478);
        double r369480 = r369479 * r369479;
        double r369481 = r369480 * r369479;
        double r369482 = 1.0;
        double r369483 = r369481 - r369482;
        return r369483;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020020 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))