Average Error: 0.0 → 0.0
Time: 4.7s
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 r18210 = f;
        double r18211 = n;
        double r18212 = r18210 + r18211;
        double r18213 = -r18212;
        double r18214 = r18210 - r18211;
        double r18215 = r18213 / r18214;
        return r18215;
}
↓
double f(double f, double n) {
        double r18216 = f;
        double r18217 = n;
        double r18218 = r18216 + r18217;
        double r18219 = -r18218;
        double r18220 = r18216 - r18217;
        double r18221 = r18219 / r18220;
        double r18222 = 3.0;
        double r18223 = pow(r18221, r18222);
        double r18224 = cbrt(r18223);
        double r18225 = cbrt(r18224);
        double r18226 = r18221 * r18221;
        double r18227 = cbrt(r18226);
        double r18228 = r18225 * r18227;
        return r18228;
}

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 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))