Average Error: 0.0 → 0.0
Time: 15.4s
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 
(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: 14.6s)Debug log

sample46.0ms

Algorithm
intervals

simplify48.0ms

Counts
1 → 1
Calls

1 calls. Slowest were:

48.0ms
(* a (+ (+ b c) d))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
1 → 15
Calls

1 calls. Slowest were:

7.0ms
(* a (+ (+ b c) d))

series32.0ms

Counts
1 → 3
Calls

1 calls. Slowest were:

32.0ms
(* a (+ (+ b c) d))

simplify265.0ms

Counts
10 → 18
Calls

10 calls. Slowest were:

159.0ms
(+ (* (+ b c) (+ b c)) (- (* d d) (* (+ b c) d)))
32.0ms
(+ (* a d) (+ (* a b) (* a c)))
23.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune200.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm
rewrite-expression-head
Counts
2 → 29
Calls

2 calls. Slowest were:

5.0ms
(+ (* a (+ b c)) (* a d))
2.0ms
(* a (+ b c))

series69.0ms

Counts
2 → 6
Calls

2 calls. Slowest were:

41.0ms
(+ (* a (+ b c)) (* a d))
28.0ms
(* a (+ b c))

simplify296.0ms

Counts
17 → 35
Calls

17 calls. Slowest were:

126.0ms
(* (exp (* a (+ b c))) (exp (* a d)))
62.0ms
(+ (* b b) (- (* c c) (* b c)))
24.0ms
(+ (* a d) (+ (* a b) (* a c)))

prune359.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize17.0ms

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))

rewrite50.0ms

Algorithm
rewrite-expression-head
Counts
4 → 70
Calls

4 calls. Slowest were:

28.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
9.0ms
(* a (sqrt (+ (+ b c) d)))
6.0ms
(sqrt (+ (+ b c) d))

series197.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

75.0ms
(* (* a (sqrt (+ (+ b c) d))) (sqrt (+ (+ b c) d)))
54.0ms
(* a (sqrt (+ (+ b c) d)))
41.0ms
(sqrt (+ (+ b c) d))
27.0ms
(sqrt (+ (+ b c) d))

simplify3.8s

Counts
53 → 82
Calls

53 calls. Slowest were:

442.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))
431.0ms
(* (* a (sqrt (+ (pow (+ b c) 3) (pow d 3)))) (sqrt (+ (+ b c) d)))
363.0ms
(sqrt (+ (pow (+ b c) 3) (pow d 3)))

prune865.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize29.0ms

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)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Counts
4 → 75
Calls

4 calls. Slowest were:

18.0ms
(* (cbrt (+ (+ b c) d)) (cbrt (+ (+ b c) d)))
3.0ms
(cbrt (+ (+ b c) d))
3.0ms
(cbrt (+ (+ b c) d))

series754.0ms

Counts
4 → 12
Calls

4 calls. Slowest were:

255.0ms
(* (cbrt (+ (+ b c) d)) (cbrt (+ (+ b c) d)))
187.0ms
(cbrt (+ (+ b c) d))
156.0ms
(cbrt (+ (+ b c) d))
156.0ms
(cbrt (+ (+ b c) d))

simplify4.3s

Counts
59 → 87
Calls

59 calls. Slowest were:

419.0ms
(cbrt (+ (pow (+ b c) 3) (pow d 3)))
381.0ms
(cbrt (+ (pow (+ b c) 3) (pow d 3)))
370.0ms
(* (cbrt (+ (pow (+ b c) 3) (pow d 3))) (cbrt (+ (+ b c) d)))

prune1.8s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes393.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.1s

Algorithm
intervals