Average Error: 12.8 → 0.4
Time: 2.4m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(\frac{2}{r \cdot r} + 3\right) - 4.5\right) - \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot \frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

Derivation

  1. Initial program 12.8

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

  3. Applied *-un-lft-identity12.8

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

  4. Applied associate-/r*12.8

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

  5. Applied simplify6.6

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

  7. Applied associate-*l*6.6

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

  8. Taylor expanded around inf 6.6

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

  9. Applied simplify6.6

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

  11. Applied *-un-lft-identity6.6

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

  12. Applied times-frac0.4

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

  13. Applied simplify0.4

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

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed '#(1071501266 3581234924 1086666455 2685055582 1243441566 1802958749)' 
(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))