Average Error: 12.7 → 0.3
Time: 1.2m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \left(\left(3 + v \cdot -2\right) \cdot 0.125\right) \cdot \left(\frac{r \cdot w}{1 - v} \cdot \left(r \cdot w\right)\right)\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.7

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

  2. Initial simplification0.4

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

  4. Applied *-un-lft-identity0.4

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

  5. Applied times-frac0.4

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

  6. Simplified0.4

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

  8. Applied div-inv0.4

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

  9. Applied associate-*r*0.4

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

  10. Simplified0.4

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

  12. Applied *-un-lft-identity0.4

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

  13. Applied times-frac0.3

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

  14. Simplified0.3

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

  16. Applied associate-/r*0.3

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

  17. Final simplification0.3

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018249 
(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))