Average Error: 0.0 → 0.0
Time: 20.5s
Precision: 64
Internal Precision: 576
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[{\left((\left(d + c\right) \cdot a + \left(b \cdot a\right))_*\right)}^{1}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

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

Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.5

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

  4. Applied associate-*r*0.6

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

  6. Applied pow10.6

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

  7. Applied pow10.6

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

  8. Applied pow-prod-down0.6

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

  9. Applied simplify0.0

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

Runtime

Time bar (total: 20.5s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +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)))