Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n} \cdot \frac{-\left(f + n\right)}{f - n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\sqrt[3]{{\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}}} \cdot \sqrt[3]{\frac{-\left(f + n\right)}{f - n} \cdot \frac{-\left(f + n\right)}{f - n}}
double f(double f, double n) {
        double r18441 = f;
        double r18442 = n;
        double r18443 = r18441 + r18442;
        double r18444 = -r18443;
        double r18445 = r18441 - r18442;
        double r18446 = r18444 / r18445;
        return r18446;
}
↓
double f(double f, double n) {
        double r18447 = f;
        double r18448 = n;
        double r18449 = r18447 + r18448;
        double r18450 = -r18449;
        double r18451 = r18447 - r18448;
        double r18452 = r18450 / r18451;
        double r18453 = 3.0;
        double r18454 = pow(r18452, r18453);
        double r18455 = cbrt(r18454);
        double r18456 = cbrt(r18455);
        double r18457 = r18452 * r18452;
        double r18458 = cbrt(r18457);
        double r18459 = r18456 * r18458;
        return r18459;
}

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-cube41.6

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

  6. Applied add-cbrt-cube42.4

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

  7. Applied cbrt-undiv42.4

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

  8. Simplified0.0

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

  10. Applied add-cube-cbrt0.0

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

  11. Applied cbrt-prod0.1

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

  12. Applied exp-prod0.1

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

  13. Applied log-pow0.1

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

  14. Simplified0.0

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

  15. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))