Average Error: 0.2 → 0.2
Time: 13.8s
Precision: 64
Internal Precision: 576
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} - \frac{x}{\tan B}\]

Error

Bits error versus B

Bits error versus x

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Results

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Derivation

  1. Initial program 0.2

    \[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]

  2. Initial simplification0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x}{\tan B}\]
  3. Using strategy rm

  4. Applied clear-num0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{\frac{1}{\frac{\tan B}{x}}}\]
  5. Using strategy rm

  6. Applied *-un-lft-identity0.2

    \[\leadsto \frac{1}{\sin B} - \color{blue}{1 \cdot \frac{1}{\frac{\tan B}{x}}}\]

  7. Applied div-inv0.2

    \[\leadsto \color{blue}{1 \cdot \frac{1}{\sin B}} - 1 \cdot \frac{1}{\frac{\tan B}{x}}\]

  8. Applied distribute-lft-out--0.2

    \[\leadsto \color{blue}{1 \cdot \left(\frac{1}{\sin B} - \frac{1}{\frac{\tan B}{x}}\right)}\]

  9. Simplified0.2

    \[\leadsto 1 \cdot \color{blue}{\left(\frac{1}{\sin B} - \frac{x}{\tan B}\right)}\]

  10. Final simplification0.2

    \[\leadsto \frac{1}{\sin B} - \frac{x}{\tan B}\]

Runtime

Time bar (total: 13.8s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))