Average Error: 12.3 → 0.3
Time: 2.9m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \left(\left(\frac{3}{1 - v \cdot v} - \frac{2}{\frac{1}{v} - v}\right) \cdot \left(\left(\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) \cdot 0.125\right)\right) \cdot \left(1 + v\right)\right) - 4.5\]

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 12.3

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

  3. Applied flip--13.2

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

  4. Applied associate-/r/13.2

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

  5. Applied simplify5.5

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

  7. Applied div-inv5.5

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

  8. Applied times-frac5.5

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

  9. Applied simplify5.5

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

  11. Applied div-sub5.5

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

  12. Applied simplify0.3

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

Runtime

Time bar (total: 2.9m)Debug logProfile

herbie shell --seed 2019053 
(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))