Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
Internal precision: 128
\[\left(\frac{x}{2.0} + y \cdot x\right) + z\]
⬇
\[z + x \cdot \left(y + 0.5\right)\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.0
Comparison0.0
Herbie0.0
\[ \left(\frac{x}{2.0} + y \cdot x\right) + z \]

Derivation

  1. Initial program 0.0

    \[\left(\frac{x}{2.0} + y \cdot x\right) + z\]

  2. Applied taylor 0.0

    \[\leadsto \left(0.5 \cdot x + y \cdot x\right) + z\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot x + y \cdot x\right)} + z\]

  4. Applied simplify 0.0

    \[\leadsto \color{blue}{z + x \cdot \left(y + 0.5\right)}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 11.9s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3019856085 1220891216 2889477378 1800861212 720098821 4126260465)'
(FPCore (x y z)
  :name "Data.Histogram.Bin.BinF:$cfromIndex from histogram-fill-0.8.4.1"

  :target
  (+ (+ (/ x 2.0) (* y x)) z)

  (+ (+ (/ x 2.0) (* y x)) z))