Average Error: 0.4 → 0.4
Time: 1.2m
Precision: 64
Internal Precision: 576
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - \left(v \cdot v\right) \cdot 5}{\left(\left(t \cdot \sqrt{\left(1 - \left(v \cdot v\right) \cdot 3\right) \cdot 2}\right) \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}\]

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 associate-*l*0.4

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

  4. Final simplification0.4

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018219 
(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)))))