Average Error: 14.1 → 0.2
Time: 42.7s
Precision: 64
Internal Precision: 384
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]

Error

Bits error versus x

Bits error versus y

Target

Original14.1
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.1

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied associate-/l*0.7

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied div-inv0.8

    \[\leadsto \color{blue}{\sin x \cdot \frac{1}{\frac{x}{\sinh y}}}\]

  6. Applied simplify0.2

    \[\leadsto \sin x \cdot \color{blue}{\frac{\sinh y}{x}}\]
  7. Removed slow pow expressions.

Runtime

Time bar (total: 42.7s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

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

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