Average Error: 0.2 → 0.5
Time: 16.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
↓
\[\left(4 \cdot \left(b \cdot b\right) + \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1
↓
\left(4 \cdot \left(b \cdot b\right) + \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right)\right) - 1
double f(double a, double b) {
        double r144443 = a;
        double r144444 = r144443 * r144443;
        double r144445 = b;
        double r144446 = r144445 * r144445;
        double r144447 = r144444 + r144446;
        double r144448 = 2.0;
        double r144449 = pow(r144447, r144448);
        double r144450 = 4.0;
        double r144451 = r144450 * r144446;
        double r144452 = r144449 + r144451;
        double r144453 = 1.0;
        double r144454 = r144452 - r144453;
        return r144454;
}
↓
double f(double a, double b) {
        double r144455 = 4.0;
        double r144456 = b;
        double r144457 = r144456 * r144456;
        double r144458 = r144455 * r144457;
        double r144459 = a;
        double r144460 = r144459 * r144459;
        double r144461 = r144457 + r144460;
        double r144462 = 2.0;
        double r144463 = pow(r144461, r144462);
        double r144464 = cbrt(r144463);
        double r144465 = r144464 * r144464;
        double r144466 = r144464 * r144465;
        double r144467 = r144458 + r144466;
        double r144468 = 1.0;
        double r144469 = r144467 - r144468;
        return r144469;
}

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

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

  4. Simplified0.5

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

  5. Simplified0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))