Average Error: 0.0 → 0.3
Time: 29.2s
Precision: 64
Internal Precision: 576
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\log_* (1 + (e^{(\left(b + c\right) \cdot a + \left(d \cdot a\right))_*} - 1)^*)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original0.0
Target0.0
Herbie0.3
\[a \cdot b + a \cdot \left(c + d\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot \left(\left(b + c\right) + d\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{a \cdot \left(b + c\right) + a \cdot d}\]
  4. Using strategy rm

  5. Applied log1p-expm1-u0.3

    \[\leadsto \color{blue}{\log_* (1 + (e^{a \cdot \left(b + c\right) + a \cdot d} - 1)^*)}\]

  6. Applied simplify0.3

    \[\leadsto \log_* (1 + \color{blue}{(e^{(\left(b + c\right) \cdot a + \left(d \cdot a\right))_*} - 1)^*})\]

Runtime

Time bar (total: 29.2s)Debug logProfile

herbie shell --seed 2018193 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))