Average Error: 1.0 → 0.0
Time: 4.5m
Precision: 64
Internal Precision: 320
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\sqrt[3]{\frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}} \cdot \left(\frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}} \cdot \frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}}\right)}\]

Error

Bits error versus v

Try it out

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

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

  4. Applied add-cbrt-cube0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 4.5m)Debug logProfile

herbie shell --seed 2018242 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))