Average Error: 12.4 → 2.5
Time: 33.1s
Precision: 64
Internal Precision: 128
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \sqrt{\frac{\frac{2}{r}}{r}} \cdot \sqrt{\frac{\frac{2}{r}}{r}}\right) - \left(\left(3 + v \cdot -2\right) \cdot 0.125\right) \cdot \frac{r \cdot \left(\left(r \cdot w\right) \cdot w\right)}{1 - v}\right) - 4.5\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.4

    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
  2. Using strategy rm

  3. Applied associate-*l*7.6

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\color{blue}{\left(w \cdot \left(w \cdot r\right)\right)} \cdot r\right)}{1 - v}\right) - 4.5\]
  4. Using strategy rm

  5. Applied *-un-lft-identity7.6

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(w \cdot \left(w \cdot r\right)\right) \cdot r\right)}{\color{blue}{1 \cdot \left(1 - v\right)}}\right) - 4.5\]

  6. Applied times-frac2.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{1} \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}}\right) - 4.5\]

  7. Simplified2.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - \color{blue}{\left(0.125 \cdot \left(v \cdot -2 + 3\right)\right)} \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\]
  8. Using strategy rm

  9. Applied associate-/r*2.4

    \[\leadsto \left(\left(3 + \color{blue}{\frac{\frac{2}{r}}{r}}\right) - \left(0.125 \cdot \left(v \cdot -2 + 3\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt2.5

    \[\leadsto \left(\left(3 + \color{blue}{\sqrt{\frac{\frac{2}{r}}{r}} \cdot \sqrt{\frac{\frac{2}{r}}{r}}}\right) - \left(0.125 \cdot \left(v \cdot -2 + 3\right)\right) \cdot \frac{\left(w \cdot \left(w \cdot r\right)\right) \cdot r}{1 - v}\right) - 4.5\]

  12. Final simplification2.5

    \[\leadsto \left(\left(3 + \sqrt{\frac{\frac{2}{r}}{r}} \cdot \sqrt{\frac{\frac{2}{r}}{r}}\right) - \left(\left(3 + v \cdot -2\right) \cdot 0.125\right) \cdot \frac{r \cdot \left(\left(r \cdot w\right) \cdot w\right)}{1 - v}\right) - 4.5\]

Reproduce

herbie shell --seed 2019026 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))