Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[(a \cdot \left(b + c\right) + \left(d \cdot a\right))_*\]

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 distribute-lft-in0.0

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

  5. Applied fma-def0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019008 +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)))

Details

Time bar (total: 3.8s)Debug log

sample57.0ms

Algorithm
intervals

simplify60.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

59.0ms
(* a (+ (+ b c) d))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 1 expressions with local error:

0.1b
(* a (+ (+ b c) d))

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

5.0ms
(* a (+ (+ b c) d))

series21.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

21.0ms
(* a (+ (+ b c) d))

simplify374.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

181.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
77.0ms
(+ (* a d) (+ (* a b) (* a c)))
62.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune186.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma a (+ d b) (* c a))

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma a (+ d b) (* c a))

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(fma a (+ d b) (* c a))

simplify91.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

53.0ms
(+ (* a d) (+ (* a b) (* a c)))
37.0ms
(+ (* a d) (+ (* a b) (* a c)))
0.0ms
0

prune539.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b
(* a (+ b c))
0.0b
(+ (* a (+ b c)) (* a d))

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 34
Calls

2 calls. Slowest were:

6.0ms
(+ (* a (+ b c)) (* a d))
2.0ms
(* a (+ b c))

series68.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(+ (* a (+ b c)) (* a d))
27.0ms
(* a (+ b c))

simplify324.0ms

Counts
17 → 40
Calls

17 calls. Slowest were:

108.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
68.0ms
(+ (* a d) (+ (* a b) (* a c)))
61.0ms
(+ (* b b) (- (* c c) (* b c)))

prune389.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(fma a (+ b c) (* a d))

rewrite0.0ms

Algorithm
rewrite-expression-head
Counts
1 → 10
Calls

1 calls. Slowest were:

0.0ms
(fma a (+ b c) (* a d))

series24.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

24.0ms
(fma a (+ b c) (* a d))

simplify127.0ms

Counts
3 → 13
Calls

3 calls. Slowest were:

65.0ms
(+ (* a d) (+ (* a b) (* a c)))
61.0ms
(+ (* a d) (+ (* a b) (* a c)))
0.0ms
0

prune106.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes208.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals