Average Error: 0.0 → 0.0
Time: 29.8s
Precision: 64
Internal Precision: 384
\[\left(0.5 \cdot \cos re\right) \cdot \left(e^{-im} + e^{im}\right)\]
↓
\[\frac{\cos re}{e^{im}} \cdot 0.5 + e^{im} \cdot \left(0.5 \cdot \cos re\right)\]

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-rgt-in0.0

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

  4. Applied simplify0.0

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

Runtime

Time bar (total: 29.8s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (re im)
  :name "math.cos on complex, real part"
  (* (* 0.5 (cos re)) (+ (exp (- im)) (exp im))))