Average Error: 0.0 → 0.1
Time: 10.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{-\left(f + n\right)}\right) \cdot \sqrt[3]{-\left(f + n\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{\left(\sqrt[3]{\frac{-\left(f + n\right)}{f - n}} \cdot \sqrt[3]{-\left(f + n\right)}\right) \cdot \sqrt[3]{-\left(f + n\right)}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}}
double f(double f, double n) {
        double r37342 = f;
        double r37343 = n;
        double r37344 = r37342 + r37343;
        double r37345 = -r37344;
        double r37346 = r37342 - r37343;
        double r37347 = r37345 / r37346;
        return r37347;
}
↓
double f(double f, double n) {
        double r37348 = f;
        double r37349 = n;
        double r37350 = r37348 + r37349;
        double r37351 = -r37350;
        double r37352 = r37348 - r37349;
        double r37353 = r37351 / r37352;
        double r37354 = cbrt(r37353);
        double r37355 = cbrt(r37351);
        double r37356 = r37354 * r37355;
        double r37357 = r37356 * r37355;
        double r37358 = cbrt(r37352);
        double r37359 = r37358 * r37358;
        double r37360 = r37357 / r37359;
        return r37360;
}

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-cube-cbrt0.1

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

  5. Applied cbrt-div0.1

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

  6. Applied cbrt-div0.1

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

  7. Applied associate-*r/0.1

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

  8. Applied frac-times0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019308 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))