Average Error: 12.6 → 0.3
Time: 45.9s
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{\left(3 + v \cdot -2\right) \cdot 0.125}{\left(1 - v\right) \cdot \frac{\frac{1}{w}}{r}} \cdot \left(w \cdot r\right)\]

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 12.6

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

  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

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

  5. Applied times-frac0.4

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

  7. Applied associate-/r*0.3

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

  9. Applied associate-/r*0.3

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

  11. Applied associate-*r/0.3

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

  12. Applied associate-/r/0.3

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

  13. Final simplification0.3

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

Runtime

Time bar (total: 45.9s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.30.30.10.20%
herbie shell --seed 2018285 
(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))