Details

Time bar (total: 2.0s)

sample10.0ms

Algorithm
intervals
Results
3.0ms256×body80valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
072
1102
2122
3132
4132

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ x y) x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity add-log-exp
3×sum-log distribute-lft-out
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+l+ flip3-+ add-cbrt-cube flip-+
Counts
1 → 15
Calls
1 calls:
8.0ms
(+ (+ x y) x)

series22.0ms

Counts
1 → 3
Calls
1 calls:
22.0ms
(+ (+ x y) x)

simplify103.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (30.0ms)

IterNodesCost
08265
124160
285458
3453553
4500253

prune23.0ms

Filtered
18 candidates to 10 candidates (55.6%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ x y) x)
0.0b
(+ (+ x y) x)
0.3b
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
38×sqrt-prod
30×distribute-lft-out
23×add-sqr-sqrt
18×pow1
16×swap-sqr
13×add-log-exp
12×sqrt-div
11×add-cube-cbrt
8×sqrt-pow1 flip3-+ pow1/2 associate-*r* associate-*l* flip-+
6×sum-log
5×add-exp-log pow-prod-up add-cbrt-cube
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative associate-+l+ associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
3 → 99
Calls
3 calls:
5.0ms
(+ (+ x y) x)
6.0ms
(+ (+ x y) x)
18.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series85.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (+ x y) x)
22.0ms
(+ (+ x y) x)
35.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0204509
1838459
25001444

prune131.0ms

Filtered
108 candidates to 46 candidates (42.6%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ (+ x y) x)))
0.1b
(sqrt (sqrt (+ (+ x y) x)))
0.1b
(* (sqrt (sqrt (+ (+ x y) x))) (pow (sqrt (sqrt (+ (+ x y) x))) 3))
0.4b
(pow (sqrt (sqrt (+ (+ x y) x))) 3)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
135×sqrt-prod
74×add-sqr-sqrt
60×*-un-lft-identity
36×sqrt-div
31×unpow-prod-down cube-prod
28×associate-*r*
25×add-cube-cbrt
24×unswap-sqr
21×distribute-lft-out
12×pow1 sqrt-pow1
11×associate-*l*
10×add-exp-log
9×flip3-+ flip-+
8×cube-div
7×add-cbrt-cube
6×pow1/2
5×pow-pow sqr-pow
4×frac-times rem-sqrt-square add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 associate-*r/ associate-*l/ pow-exp
1×*-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 176
Calls
4 calls:
6.0ms
(sqrt (sqrt (+ (+ x y) x)))
6.0ms
(sqrt (sqrt (+ (+ x y) x)))
27.0ms
(* (sqrt (sqrt (+ (+ x y) x))) (pow (sqrt (sqrt (+ (+ x y) x))) 3))
9.0ms
(pow (sqrt (sqrt (+ (+ x y) x))) 3)

series783.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(sqrt (sqrt (+ (+ x y) x)))
241.0ms
(sqrt (sqrt (+ (+ x y) x)))
39.0ms
(* (sqrt (sqrt (+ (+ x y) x))) (pow (sqrt (sqrt (+ (+ x y) x))) 3))
259.0ms
(pow (sqrt (sqrt (+ (+ x y) x))) 3)

simplify88.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
05162008
123791440
250021284

prune336.0ms

Filtered
188 candidates to 88 candidates (46.8%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune1.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
072
172

end0.0ms

sample237.0ms

Algorithm
intervals
Results
114.0ms8005×body80valid