Average Error: 0.2 → 0.2
Time: 50.7s
Precision: 64
Internal Precision: 576
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
↓
\[\frac{1}{\sin B} + \frac{x}{\sin B} \cdot \left(-\cos B\right)\]

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. Taylor expanded around inf 0.2

    \[\leadsto \left(-\color{blue}{\frac{\cos B \cdot x}{\sin B}}\right) + \frac{1}{\sin B}\]
  3. Using strategy rm

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

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

  5. Applied times-frac0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Runtime

Time bar (total: 50.7s)Debug logProfile

herbie shell --seed 2018214 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))