Average Error: 0.0 → 0.1
Time: 35.4s
Precision: 64
Internal Precision: 320
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{f + n}{f - n}} \cdot \left(\left(\sqrt[3]{\frac{\sqrt[3]{f + n} \cdot \sqrt[3]{f + n}}{\sqrt[3]{f - n} \cdot \sqrt[3]{f - n}}} \cdot \left(-\sqrt[3]{\frac{f + n}{f - n}}\right)\right) \cdot \sqrt[3]{\frac{\sqrt[3]{f + n}}{\sqrt[3]{f - n}}}\right)\]

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. Initial simplification0.0

    \[\leadsto -\frac{n + f}{f - n}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.1

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

  6. Applied add-cube-cbrt0.3

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied times-frac0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied associate-*r*0.1

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

  11. Final simplification0.1

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

Runtime

Time bar (total: 35.4s)Debug logProfile

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