Average Error: 1.0 → 0.0
Time: 5.2m
Precision: 64
Internal Precision: 128
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{\frac{\frac{4}{3}}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{1 - v \cdot v}}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]

Error

Bits error versus v

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  2. Initial simplification0.0

    \[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{1 - v \cdot v}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

    \[\leadsto \frac{\frac{\frac{\frac{4}{3}}{\pi}}{\color{blue}{\sqrt{1 - v \cdot v} \cdot \sqrt{1 - v \cdot v}}}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}\]

  5. Applied associate-/r*0.0

    \[\leadsto \frac{\color{blue}{\frac{\frac{\frac{\frac{4}{3}}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{1 - v \cdot v}}}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}\]

  6. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{\frac{\frac{4}{3}}{\pi}}{\sqrt{1 - v \cdot v}}}{\sqrt{1 - v \cdot v}}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]

Runtime

Time bar (total: 5.2m)Debug logProfile

herbie shell --seed 2018285 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))