Average Error: 0.2 → 0.2
Time: 19.5s
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 r1969266 = a;
        double r1969267 = r1969266 * r1969266;
        double r1969268 = b;
        double r1969269 = r1969268 * r1969268;
        double r1969270 = r1969267 + r1969269;
        double r1969271 = 2.0;
        double r1969272 = pow(r1969270, r1969271);
        double r1969273 = 4.0;
        double r1969274 = 1.0;
        double r1969275 = r1969274 + r1969266;
        double r1969276 = r1969267 * r1969275;
        double r1969277 = 3.0;
        double r1969278 = r1969277 * r1969266;
        double r1969279 = r1969274 - r1969278;
        double r1969280 = r1969269 * r1969279;
        double r1969281 = r1969276 + r1969280;
        double r1969282 = r1969273 * r1969281;
        double r1969283 = r1969272 + r1969282;
        double r1969284 = r1969283 - r1969274;
        return r1969284;
}
↓
double f(double a, double b) {
        double r1969285 = a;
        double r1969286 = r1969285 * r1969285;
        double r1969287 = 1.0;
        double r1969288 = r1969285 + r1969287;
        double r1969289 = r1969286 * r1969288;
        double r1969290 = b;
        double r1969291 = r1969290 * r1969290;
        double r1969292 = 3.0;
        double r1969293 = r1969292 * r1969285;
        double r1969294 = r1969287 - r1969293;
        double r1969295 = r1969291 * r1969294;
        double r1969296 = r1969289 + r1969295;
        double r1969297 = 4.0;
        double r1969298 = r1969296 * r1969297;
        double r1969299 = cbrt(r1969298);
        double r1969300 = r1969299 * r1969299;
        double r1969301 = r1969300 * r1969299;
        double r1969302 = r1969286 + r1969291;
        double r1969303 = 2.0;
        double r1969304 = pow(r1969302, r1969303);
        double r1969305 = r1969301 + r1969304;
        double r1969306 = r1969305 - r1969287;
        return r1969306;
}

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 2019154 
(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))