Average Error: 12.1 → 0.3
Time: 1.1m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\left(3 - v \cdot 2\right) \cdot 0.125}{\left(1 - v\right) \cdot {\left(w \cdot r\right)}^{\left(\left(-1\right) + \left(-1\right)\right)}}\]

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 12.1

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

  2. Initial simplification0.4

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

  4. Applied div-inv0.4

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

  6. Applied pow10.4

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

  7. Applied pow10.4

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

  8. Applied pow-prod-up0.4

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

  9. Applied pow-flip0.3

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

  10. Final simplification0.3

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018219 
(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))