Average Error: 11.9 → 0.4
Time: 2.8m
Precision: 64
Internal Precision: 384
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + 3\right) - (\left(\frac{0.125}{1 - v} \cdot \left(\left(3 - v\right) - v\right)\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

Derivation

  1. Initial program 11.9

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

  2. Applied simplify0.4

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

  4. Applied associate-/r*0.4

    \[\leadsto \left(\color{blue}{\frac{\frac{2}{r}}{r}} + 3\right) - (\left(\frac{0.125}{1 - v} \cdot \left(\left(3 - v\right) - v\right)\right) \cdot \left(\left(w \cdot r\right) \cdot \left(w \cdot r\right)\right) + 4.5)_*\]
  5. Removed slow pow expressions.

Runtime

Time bar (total: 2.8m)Debug log

herbie shell --seed '#(1889797285 268396849 4100589100 2067516092 3019009300 3748763710)' +o rules:numerics
(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))