Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}
double f(double f, double n) {
        double r22338 = f;
        double r22339 = n;
        double r22340 = r22338 + r22339;
        double r22341 = -r22340;
        double r22342 = r22338 - r22339;
        double r22343 = r22341 / r22342;
        return r22343;
}
↓
double f(double f, double n) {
        double r22344 = f;
        double r22345 = n;
        double r22346 = r22344 + r22345;
        double r22347 = -r22346;
        double r22348 = r22344 - r22345;
        double r22349 = r22347 / r22348;
        double r22350 = 3.0;
        double r22351 = pow(r22349, r22350);
        double r22352 = cbrt(r22351);
        return r22352;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube41.3

    \[\leadsto \frac{-\left(f + n\right)}{\color{blue}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}\]

  4. Applied add-cbrt-cube42.2

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}}}{\sqrt[3]{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}\]

  5. Applied cbrt-undiv42.1

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(-\left(f + n\right)\right) \cdot \left(-\left(f + n\right)\right)\right) \cdot \left(-\left(f + n\right)\right)}{\left(\left(f - n\right) \cdot \left(f - n\right)\right) \cdot \left(f - n\right)}}}\]

  6. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot \sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\]

  9. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))