Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{-{\left(\frac{n + f}{f - n}\right)}^{2} \cdot \sqrt[3]{{\left(\frac{n + f}{f - n}\right)}^{3}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{-{\left(\frac{n + f}{f - n}\right)}^{2} \cdot \sqrt[3]{{\left(\frac{n + f}{f - n}\right)}^{3}}}
double f(double f, double n) {
        double r26931 = f;
        double r26932 = n;
        double r26933 = r26931 + r26932;
        double r26934 = -r26933;
        double r26935 = r26931 - r26932;
        double r26936 = r26934 / r26935;
        return r26936;
}
↓
double f(double f, double n) {
        double r26937 = n;
        double r26938 = f;
        double r26939 = r26937 + r26938;
        double r26940 = r26938 - r26937;
        double r26941 = r26939 / r26940;
        double r26942 = 2.0;
        double r26943 = pow(r26941, r26942);
        double r26944 = 3.0;
        double r26945 = pow(r26941, r26944);
        double r26946 = cbrt(r26945);
        double r26947 = r26943 * r26946;
        double r26948 = -r26947;
        double r26949 = cbrt(r26948);
        return r26949;
}

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 *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot \frac{-\left(f + n\right)}{f - n}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube41.7

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

  6. Applied add-cbrt-cube42.6

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

  7. Applied cbrt-undiv42.6

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

  8. Simplified0.0

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

  10. Applied add-log-exp0.0

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

  11. Simplified0.0

    \[\leadsto 1 \cdot \sqrt[3]{-\log \color{blue}{\left(e^{{\left(\frac{n + f}{f - n}\right)}^{3}}\right)}}\]
  12. Using strategy rm

  13. Applied add-cube-cbrt0.0

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

  14. Applied exp-prod0.0

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

  15. Applied log-pow0.0

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

  16. Simplified0.0

    \[\leadsto 1 \cdot \sqrt[3]{-\sqrt[3]{{\left(\frac{n + f}{f - n}\right)}^{3}} \cdot \color{blue}{{\left(\frac{f + n}{f - n}\right)}^{2}}}\]

  17. Final simplification0.0

    \[\leadsto \sqrt[3]{-{\left(\frac{n + f}{f - n}\right)}^{2} \cdot \sqrt[3]{{\left(\frac{n + f}{f - n}\right)}^{3}}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))