Average Error: 12.3 → 0.4
Time: 3.3m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(\frac{2}{r \cdot r} + 3\right) - \frac{0.125}{\frac{1 - v}{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}} \cdot \left(3 - v \cdot 2\right)\right) - 4.5\]

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 add-exp-log23.7

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

  4. Applied add-exp-log24.3

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

  5. Applied div-exp24.3

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

  6. Simplified2.1

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

  8. Applied rem-exp-log0.4

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

  10. Applied *-un-lft-identity0.4

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

  11. Applied times-frac0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Runtime

Time bar (total: 3.3m)Debug logProfile

herbie shell --seed 2018214 +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))