Error

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Derivation

1. Initial program 0.4

   \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
2. Using strategy rm

3. Applied add-sqr-sqrt0.4

   \[\leadsto \frac{\color{blue}{\sqrt{1 - 5 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 5 \cdot \left(v \cdot v\right)}}}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]

4. Applied times-frac0.4

   \[\leadsto \color{blue}{\frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}}\]

5. Simplified0.4

   \[\leadsto \color{blue}{\frac{\frac{\sqrt{1 + -5 \cdot \left(v \cdot v\right)}}{\pi \cdot t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]
6. Using strategy rm

7. Applied associate-/r*0.3

   \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt{1 + -5 \cdot \left(v \cdot v\right)}}{\pi}}{t}}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}} \cdot \frac{\sqrt{1 - 5 \cdot \left(v \cdot v\right)}}{1 - v \cdot v}\]

8. Final simplification0.3

   \[\leadsto \frac{\sqrt{1 - \left(v \cdot v\right) \cdot 5}}{1 - v \cdot v} \cdot \frac{\frac{\frac{\sqrt{1 + \left(v \cdot v\right) \cdot -5}}{\pi}}{t}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]

Reproduce

herbie shell --seed 2019008 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))

Details

Time bar (total: 35.6s)Debug log