Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
Internal Precision: 384
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[(a \cdot \left(d + b\right) + \left(a \cdot c\right))_*\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

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

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube16.9

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a \cdot \left(\left(b + c\right) + d\right)\right) \cdot \left(a \cdot \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a \cdot \left(\left(b + c\right) + d\right)\right)}}\]

  4. Applied simplify16.9

    \[\leadsto \sqrt[3]{\color{blue}{{\left((a \cdot \left(b + c\right) + \left(a \cdot d\right))_*\right)}^{3}}}\]

  5. Taylor expanded around inf 16.9

    \[\leadsto \sqrt[3]{{\color{blue}{\left(c \cdot a + \left(b \cdot a + d \cdot a\right)\right)}}^{3}}\]

  6. Applied simplify0.0

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

Runtime

Time bar (total: 9.2s)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' +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)))