Average Error: 0.2 → 0.2

Time: 22.3s

Precision: 64

Ground Truth: 128

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

⬇

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

Error

The X axis may use a short exponential scale — Bits error versus B

The X axis may use a short exponential scale — Bits error versus B

The X axis may use a short exponential scale — Bits error versus x

The X axis may use a short exponential scale — Bits error versus x

Derivation

Initial program 0.2
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{1}{\sin B}\]
Applied simplify 0.2
\[\leadsto \color{blue}{\frac{1}{\sin B} + \frac{-x}{\tan B}}\]
Using strategy rm
Applied div-inv 0.2
\[\leadsto \frac{1}{\sin B} + \color{blue}{\left(-x\right) \cdot \frac{1}{\tan B}}\]
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie --seed '#(1541929771 1968859716 3884739687 3170354870 1260142310 618757016)'
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  (+ (- (* x (/ 1 (tan B)))) (/ 1 (sin B))))