Average Error: 11.9 → 0.5
Time: 1.8m
Precision: 64
Internal Precision: 128
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\left(3 + v \cdot -2\right) \cdot 0.125}{\frac{\sqrt[3]{1 - v} \cdot \sqrt[3]{1 - v}}{r \cdot w} \cdot \frac{\sqrt[3]{1 - v}}{r \cdot w}}\]

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 11.9

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

  2. Initial simplification0.4

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

  4. Applied add-cube-cbrt0.5

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

  5. Applied times-frac0.5

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

  6. Final simplification0.5

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed 2018348 
(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))