Average Error: 0.2 → 0.5
Time: 5.8s
Precision: 64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)} - 1\]
\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(3 + a\right)\right)\right) - 1
↓
\left(\sqrt[3]{{\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(3 + a\right)\right)} \cdot \sqrt[3]{{\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(3 + a\right)\right)}\right) \cdot \sqrt[3]{{\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(3 + a\right)\right)} - 1
double f(double a, double b) {
        double r239343 = a;
        double r239344 = r239343 * r239343;
        double r239345 = b;
        double r239346 = r239345 * r239345;
        double r239347 = r239344 + r239346;
        double r239348 = 2.0;
        double r239349 = pow(r239347, r239348);
        double r239350 = 4.0;
        double r239351 = 1.0;
        double r239352 = r239351 - r239343;
        double r239353 = r239344 * r239352;
        double r239354 = 3.0;
        double r239355 = r239354 + r239343;
        double r239356 = r239346 * r239355;
        double r239357 = r239353 + r239356;
        double r239358 = r239350 * r239357;
        double r239359 = r239349 + r239358;
        double r239360 = r239359 - r239351;
        return r239360;
}
↓
double f(double a, double b) {
        double r239361 = a;
        double r239362 = r239361 * r239361;
        double r239363 = b;
        double r239364 = r239363 * r239363;
        double r239365 = r239362 + r239364;
        double r239366 = 2.0;
        double r239367 = pow(r239365, r239366);
        double r239368 = 4.0;
        double r239369 = 1.0;
        double r239370 = r239369 - r239361;
        double r239371 = r239362 * r239370;
        double r239372 = 3.0;
        double r239373 = r239372 + r239361;
        double r239374 = r239364 * r239373;
        double r239375 = r239371 + r239374;
        double r239376 = r239368 * r239375;
        double r239377 = r239367 + r239376;
        double r239378 = cbrt(r239377);
        double r239379 = r239378 * r239378;
        double r239380 = r239379 * r239378;
        double r239381 = r239380 - r239369;
        return r239381;
}

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

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))