Average Error: 0.1 → 0.2
Time: 46.2s
Precision: 64
Internal Precision: 576
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\sqrt[3]{1 - m \cdot m} \cdot \sqrt[3]{1 - m \cdot m}}{\sqrt[3]{1 + m} \cdot \sqrt[3]{1 + m}} \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \sqrt[3]{1 - m}\]

Error

Bits error versus m

Bits error versus v

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

    \[\leadsto \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \color{blue}{\left(\left(\sqrt[3]{1 - m} \cdot \sqrt[3]{1 - m}\right) \cdot \sqrt[3]{1 - m}\right)}\]

  4. Applied associate-*r*0.2

    \[\leadsto \color{blue}{\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt[3]{1 - m} \cdot \sqrt[3]{1 - m}\right)\right) \cdot \sqrt[3]{1 - m}}\]
  5. Using strategy rm

  6. Applied flip--0.2

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

  7. Applied cbrt-div0.2

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

  8. Applied flip--0.2

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

  9. Applied cbrt-div0.2

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

  10. Applied frac-times0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

    \[\leadsto \left(\frac{\sqrt[3]{1 - m \cdot m} \cdot \sqrt[3]{1 - m \cdot m}}{\sqrt[3]{1 + m} \cdot \sqrt[3]{1 + m}} \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)\right) \cdot \sqrt[3]{1 - m}\]

Runtime

Time bar (total: 46.2s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))