Average Error: 0.2 → 0.2
Time: 28.1s
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 r7371224 = a;
        double r7371225 = r7371224 * r7371224;
        double r7371226 = b;
        double r7371227 = r7371226 * r7371226;
        double r7371228 = r7371225 + r7371227;
        double r7371229 = 2.0;
        double r7371230 = pow(r7371228, r7371229);
        double r7371231 = 4.0;
        double r7371232 = 1.0;
        double r7371233 = r7371232 + r7371224;
        double r7371234 = r7371225 * r7371233;
        double r7371235 = 3.0;
        double r7371236 = r7371235 * r7371224;
        double r7371237 = r7371232 - r7371236;
        double r7371238 = r7371227 * r7371237;
        double r7371239 = r7371234 + r7371238;
        double r7371240 = r7371231 * r7371239;
        double r7371241 = r7371230 + r7371240;
        double r7371242 = r7371241 - r7371232;
        return r7371242;
}
↓
double f(double a, double b) {
        double r7371243 = a;
        double r7371244 = r7371243 * r7371243;
        double r7371245 = 1.0;
        double r7371246 = r7371243 + r7371245;
        double r7371247 = r7371244 * r7371246;
        double r7371248 = b;
        double r7371249 = r7371248 * r7371248;
        double r7371250 = 3.0;
        double r7371251 = r7371250 * r7371243;
        double r7371252 = r7371245 - r7371251;
        double r7371253 = r7371249 * r7371252;
        double r7371254 = r7371247 + r7371253;
        double r7371255 = 4.0;
        double r7371256 = r7371254 * r7371255;
        double r7371257 = cbrt(r7371256);
        double r7371258 = r7371257 * r7371257;
        double r7371259 = r7371258 * r7371257;
        double r7371260 = r7371244 + r7371249;
        double r7371261 = 2.0;
        double r7371262 = pow(r7371260, r7371261);
        double r7371263 = r7371259 + r7371262;
        double r7371264 = r7371263 - r7371245;
        return r7371264;
}

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 
(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))