Average Error: 12.9 → 0.4
Time: 3.5m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - 0.125 \cdot \frac{3 - v \cdot 2}{\frac{1 - v}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}\right) - 4.5\]

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.9

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

  3. Applied *-un-lft-identity12.9

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

  4. Applied associate-/r*12.9

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

  5. Applied simplify6.7

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

  7. Applied add-cube-cbrt6.8

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

  8. Applied associate-*r*6.8

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

  10. Applied *-un-lft-identity6.8

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

  11. Applied times-frac6.8

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

  12. Applied simplify6.8

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

  13. Applied simplify0.4

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

Runtime

Time bar (total: 3.5m)Debug logProfile

herbie shell --seed 2018195 
(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))