Average Error: 12.3 → 0.4
Time: 5.0m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\frac{\frac{2}{r}}{r} + 3\right) - \left(4.5 + \sqrt{\frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{\frac{1 - v}{w \cdot r}}{w \cdot r}}} \cdot \sqrt{\frac{0.125 \cdot \left(3 - v \cdot 2\right)}{\frac{\frac{1 - v}{w \cdot r}}{w \cdot r}}}\right)\]

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 12.3

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

  2. Initial simplification0.3

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

  4. Applied add-sqr-sqrt0.4

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

  5. Final simplification0.4

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

Runtime

Time bar (total: 5.0m)Debug logProfile

herbie shell --seed 2018214 
(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))