Average Error: 14.3 → 3.0
Time: 28.8s
Precision: 64
Internal precision: 128
\[\sin x \cdot \frac{\sinh y}{y}\]
⬇
\[\sin x \cdot \left(\frac{1}{6} \cdot {y}^2 + \left(1 + \frac{1}{120} \cdot {y}^{4}\right)\right)\]

Error

Bits error versus x

Bits error versus y

Target

Original14.3
Comparison14.3
Herbie3.0
\[ \sin x \cdot \frac{\sinh y}{y} \]

Derivation

  1. Initial program 14.3

    \[\sin x \cdot \frac{\sinh y}{y}\]

  2. Applied taylor 3.0

    \[\leadsto \sin x \cdot \left(\frac{1}{6} \cdot {y}^2 + \left(1 + \frac{1}{120} \cdot {y}^{4}\right)\right)\]

  3. Taylor expanded around 0 3.0

    \[\leadsto \sin x \cdot \color{blue}{\left(\frac{1}{6} \cdot {y}^2 + \left(1 + \frac{1}{120} \cdot {y}^{4}\right)\right)}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 28.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(2980468976 1130065073 3885922468 4061911941 2684497215 2147217504)'
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"

  :target
  (* (sin x) (/ (sinh y) y))

  (* (sin x) (/ (sinh y) y)))