Average Error: 12.1 → 1.9
Time: 4.1m
Precision: 64
Internal Precision: 576
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{\left(\sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}} \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}\right) \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}} \cdot \left(1 + v\right)\right) - 4.5 \le -1.5000000010109722:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(3 - 2 \cdot v\right) \cdot \left(w \cdot r\right)}{\frac{1 - v \cdot v}{0.125 \cdot \left(w \cdot r\right)}} \cdot \left(1 + v\right)\right) - 4.5\\ \mathbf{if}\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{\left(\sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}} \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}\right) \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}} \cdot \left(1 + v\right)\right) - 4.5 \le 8.428831695019834 \cdot 10^{+112}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{0.125 \cdot \left(3 - 2 \cdot v\right)}{\frac{1 - v}{\left(\left(w \cdot w\right) \cdot r\right) \cdot r}}\right) - 4.5\\ \mathbf{else}:\\ \;\;\;\;\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(r \cdot w\right) \cdot \left(r \cdot w\right)}{\left(\sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}} \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}\right) \cdot \sqrt[3]{\frac{\frac{1 - v \cdot v}{0.125}}{3 - 2 \cdot v}}} \cdot \left(1 + v\right)\right) - 4.5\\ \end{array}\]

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. Split input into 3 regimes

  2. if (- (- (+ 3 (/ 2 (* r r))) (* (/ (* (* r w) (* r w)) (* (* (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v))))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))))) (+ 1 v))) 4.5) < -1.5000000010109722

    1. Initial program 21.5

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

    3. Applied flip--21.5

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

    4. Applied associate-/r/21.6

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

    5. Applied simplify6.1

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

    7. Applied associate-/l*0.7

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

    9. Applied *-un-lft-identity0.7

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

    10. Applied associate-*r*0.7

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

    11. Applied simplify0.6

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

    if -1.5000000010109722 < (- (- (+ 3 (/ 2 (* r r))) (* (/ (* (* r w) (* r w)) (* (* (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v))))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))))) (+ 1 v))) 4.5) < 8.428831695019834e+112

    1. Initial program 8.4

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

    3. Applied associate-/l*2.6

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

    if 8.428831695019834e+112 < (- (- (+ 3 (/ 2 (* r r))) (* (/ (* (* r w) (* r w)) (* (* (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v))))) (cbrt (/ (/ (- 1 (* v v)) 0.125) (- 3 (* 2 v)))))) (+ 1 v))) 4.5)

    1. Initial program 9.6

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

    3. Applied flip--9.6

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

    4. Applied associate-/r/9.6

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

    5. Applied simplify3.8

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

    7. Applied associate-/l*1.8

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

    9. Applied add-cube-cbrt1.8

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

Runtime

Time bar (total: 4.1m)Debug logProfile

herbie shell --seed 2018207 
(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))