Average Error: 12.6 → 0.4
Time: 2.2m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[(\left(\sqrt[3]{{\left(\frac{3 - 2 \cdot v}{\frac{1 - v}{0.125}}\right)}^{3}}\right) \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + 0\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

Derivation

  1. Initial program 12.6

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

  2. Applied simplify0.4

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

  4. Applied add-sqr-sqrt1.0

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

  5. Applied add-sqr-sqrt1.0

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

  6. Applied prod-diff1.0

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

  7. Applied simplify0.4

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

  8. Applied simplify0.4

    \[\leadsto (\left(\frac{3 - v \cdot 2}{\frac{1 - v}{0.125}}\right) \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + \color{blue}{0}\]
  9. Using strategy rm

  10. Applied add-cbrt-cube7.4

    \[\leadsto (\left(\frac{3 - v \cdot 2}{\color{blue}{\sqrt[3]{\left(\frac{1 - v}{0.125} \cdot \frac{1 - v}{0.125}\right) \cdot \frac{1 - v}{0.125}}}}\right) \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + 0\]

  11. Applied add-cbrt-cube21.2

    \[\leadsto (\left(\frac{\color{blue}{\sqrt[3]{\left(\left(3 - v \cdot 2\right) \cdot \left(3 - v \cdot 2\right)\right) \cdot \left(3 - v \cdot 2\right)}}}{\sqrt[3]{\left(\frac{1 - v}{0.125} \cdot \frac{1 - v}{0.125}\right) \cdot \frac{1 - v}{0.125}}}\right) \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + 0\]

  12. Applied cbrt-undiv21.1

    \[\leadsto (\color{blue}{\left(\sqrt[3]{\frac{\left(\left(3 - v \cdot 2\right) \cdot \left(3 - v \cdot 2\right)\right) \cdot \left(3 - v \cdot 2\right)}{\left(\frac{1 - v}{0.125} \cdot \frac{1 - v}{0.125}\right) \cdot \frac{1 - v}{0.125}}}\right)} \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + 0\]

  13. Applied simplify0.4

    \[\leadsto (\left(\sqrt[3]{\color{blue}{{\left(\frac{3 - 2 \cdot v}{\frac{1 - v}{0.125}}\right)}^{3}}}\right) \cdot \left(-\left(r \cdot w\right) \cdot \left(r \cdot w\right)\right) + \left(\left(\left(-4.5\right) + 3\right) + \frac{2}{r \cdot r}\right))_* + 0\]

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +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))