Average Error: 0.0 → 0.0
Time: 52.8s
Precision: 64
Internal Precision: 576
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\cos re \cdot \frac{0.5}{e^{im}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(0.5 \cdot \cos re\right) \cdot e^{-im} + \left(0.5 \cdot \cos re\right) \cdot e^{im}}\]

  4. Applied simplify0.0

    \[\leadsto \color{blue}{\cos re \cdot \frac{0.5}{e^{im}}} + \left(0.5 \cdot \cos re\right) \cdot e^{im}\]

Runtime

Time bar (total: 52.8s)Debug logProfile

herbie shell --seed '#(1071119240 1686926585 3481876196 78132896 2080707795 3185793749)' +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))