Average Error: 12.8 → 0.5
Time: 5.0m
Precision: 64
Internal Precision: 384
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\frac{0.125 \cdot \left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right)}{\frac{1}{3 - \left(v + v\right)} - \frac{v}{\frac{3}{v} - 2}} \cdot \left(\sqrt[3]{1 + v} \cdot \sqrt[3]{1 + v}\right)\right) \cdot \sqrt[3]{1 + v}\right) - 4.5\]

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 flip--13.6

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

  4. Applied associate-/r/13.6

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

  5. Applied simplify5.6

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

  7. Applied add-cube-cbrt5.7

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

  8. Applied associate-*r*5.6

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

  10. Applied div-sub5.7

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

  11. Applied simplify0.5

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

Runtime

Time bar (total: 5.0m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(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))