Average Error: 0.0 → 0.0
Time: 17.4s
Precision: 64
Internal Precision: 128
\[a \cdot \left(\left(b + c\right) + d\right)\]
↓
\[\left(\left(b + c\right) + d\right) \cdot a\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019004 +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: 16.6s)Debug log

sample54.0ms

Algorithm
intervals

simplify69.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

68.0ms
(* a (+ (+ b c) d))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Counts
1 → 17
Calls

1 calls. Slowest were:

4.0ms
(* a (+ (+ b c) d))

series33.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

33.0ms
(* a (+ (+ b c) d))

simplify319.0ms

Counts
10 → 20
Calls

10 calls. Slowest were:

143.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
74.0ms
(+ (* a d) (+ (* a b) (* a c)))
58.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune204.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Counts
2 → 30
Calls

2 calls. Slowest were:

8.0ms
(+ (* (+ b c) a) (* d a))
5.0ms
(* (+ b c) a)

series50.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

36.0ms
(+ (* (+ b c) a) (* d a))
15.0ms
(* (+ b c) a)

simplify445.0ms

Counts
13 → 36
Calls

13 calls. Slowest were:

208.0ms
(* (- (* b b) (* c c)) a)
88.0ms
(* (exp (* (+ b c) a)) (exp (* d a)))
55.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune308.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
0.3b
(* a (sqrt (+ (+ b c) d)))
0.0b
(sqrt (+ (+ b c) d))
0.0b
(sqrt (+ (+ b c) d))

rewrite55.0ms

Algorithm
rewrite-expression-head
Counts
4 → 78
Calls

4 calls. Slowest were:

29.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
9.0ms
(sqrt (+ (+ b c) d))
9.0ms
(* a (sqrt (+ (+ b c) d)))

series197.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

72.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
59.0ms
(* a (sqrt (+ (+ b c) d)))
36.0ms
(sqrt (+ (+ b c) d))
28.0ms
(sqrt (+ (+ b c) d))

simplify4.6s

Counts
53 → 90
Calls

53 calls. Slowest were:

635.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (pow (+ b c) 3) (pow d 3))))
544.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
501.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))

prune911.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ b c) d))
0.6b
(cbrt (+ (+ b c) d))
0.6b
(cbrt (+ (+ b c) d))
0.4b
(* (cbrt (+ (+ b c) d)) (cbrt (+ (+ b c) d)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Counts
4 → 83
Calls

4 calls. Slowest were:

11.0ms
(* (cbrt (+ (+ b c) d)) (cbrt (+ (+ b c) d)))
2.0ms
(cbrt (+ (+ b c) d))
2.0ms
(cbrt (+ (+ b c) d))

series639.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

190.0ms
(* (cbrt (+ (+ b c) d)) (cbrt (+ (+ b c) d)))
174.0ms
(cbrt (+ (+ b c) d))
142.0ms
(cbrt (+ (+ b c) d))
133.0ms
(cbrt (+ (+ b c) d))

simplify5.6s

Counts
59 → 95
Calls

59 calls. Slowest were:

781.0ms
(* (cbrt (+ (pow (+ b c) 3) (pow d 3))) (cbrt (+ (pow (+ b c) 3) (pow d 3))))
494.0ms
(* (cbrt (+ (pow (+ b c) 3) (pow d 3))) (cbrt (+ (+ b c) d)))
491.0ms
(cbrt (+ (pow (+ b c) 3) (pow d 3)))

prune1.5s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes524.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.0s

Algorithm
intervals