Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{{\left(\left(-\left(f + n\right)\right) \cdot \frac{1}{f - n}\right)}^{3}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{{\left(\left(-\left(f + n\right)\right) \cdot \frac{1}{f - n}\right)}^{3}}
double f(double f, double n) {
        double r14039 = f;
        double r14040 = n;
        double r14041 = r14039 + r14040;
        double r14042 = -r14041;
        double r14043 = r14039 - r14040;
        double r14044 = r14042 / r14043;
        return r14044;
}
↓
double f(double f, double n) {
        double r14045 = f;
        double r14046 = n;
        double r14047 = r14045 + r14046;
        double r14048 = -r14047;
        double r14049 = 1.0;
        double r14050 = r14045 - r14046;
        double r14051 = r14049 / r14050;
        double r14052 = r14048 * r14051;
        double r14053 = 3.0;
        double r14054 = pow(r14052, r14053);
        double r14055 = cbrt(r14054);
        return r14055;
}

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-cbrt-cube41.5

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

  4. Applied add-cbrt-cube42.3

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

  5. Applied cbrt-undiv42.3

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

  6. Simplified0.0

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

  8. Applied div-inv0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))