Average Error: 0.0 → 0.1
Time: 51.5s
Precision: 64
Internal Precision: 320
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{\frac{\sqrt[3]{\left(-n\right) - f} \cdot \sqrt[3]{\left(-n\right) - f}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}}}{\frac{f - n}{n + f}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\left(-n\right) - f}}{\sqrt[3]{f - n}}}{\frac{f - n}{n + f}}}\]

Error

Bits error versus f

Bits error versus n

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube41.0

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

  4. Applied add-cbrt-cube41.2

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

  5. Applied cbrt-undiv41.2

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

  6. Simplified0.0

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

  8. Applied add-cube-cbrt0.3

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

  9. Applied add-cube-cbrt0.0

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

  10. Applied times-frac0.1

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

  11. Applied times-frac0.0

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

  12. Applied cbrt-prod0.1

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

  13. Final simplification0.1

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

Runtime

Time bar (total: 51.5s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))