Average Error: 12.0 → 0.4
Time: 58.4s
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(3 + \frac{2}{r \cdot r}\right) - \left(4.5 + \left(\sqrt[3]{{\left(\frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}\right)}^{3}} \cdot \left(r \cdot w\right)\right) \cdot \left(r \cdot w\right)\right)\]

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 12.0

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

  2. Initial simplification0.4

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

  4. Applied fma-udef0.4

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

  6. Applied associate-*r*0.3

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

  8. Applied add-cbrt-cube7.2

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

  9. Applied add-cbrt-cube21.5

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

  10. Applied cbrt-undiv21.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Runtime

Time bar (total: 58.4s)Debug logProfile

herbie shell --seed 2018225 +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))