Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}}\right)
double f(double f, double n) {
        double r50217 = f;
        double r50218 = n;
        double r50219 = r50217 + r50218;
        double r50220 = -r50219;
        double r50221 = r50217 - r50218;
        double r50222 = r50220 / r50221;
        return r50222;
}
↓
double f(double f, double n) {
        double r50223 = f;
        double r50224 = n;
        double r50225 = r50223 + r50224;
        double r50226 = -r50225;
        double r50227 = r50223 - r50224;
        double r50228 = r50226 / r50227;
        double r50229 = 3.0;
        double r50230 = pow(r50228, r50229);
        double r50231 = cbrt(r50230);
        double r50232 = exp(r50231);
        double r50233 = log(r50232);
        return r50233;
}

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-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube42.1

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

  6. Applied add-cbrt-cube43.0

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

  7. Applied cbrt-undiv43.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))