Details

Time bar (total: 1.4s)

analyze53.0ms

Algorithm
search

sample10.0ms

Algorithm
intervals
Results
4.0ms256×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
072
1102
2122
3132
4132

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.0b

Counts
2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ (+ x y) x)

rewrite6.0ms

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:
6.0ms
(+ (+ x y) x)

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(+ (+ x y) x)

simplify97.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
08265
124160
285458
3453553
4500253

prune18.0ms

Filtered
10 candidates to 18 candidates (-80.0%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New17118
Fresh000
Picked011
Done000
Total17219

Merged error: 0.0b

Counts
19 → 2

localize6.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
43×sqrt-prod
33×distribute-lft-out
26×add-sqr-sqrt
20×pow1
16×swap-sqr
14×sqrt-div add-log-exp
13×add-cube-cbrt
9×sqrt-pow1 flip3-+ pow1/2 flip-+
8×associate-*r* associate-*l*
6×add-exp-log sum-log add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×+-commutative associate-+l+ associate-*r/ associate-*l/
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 116
Calls
4 calls:
5.0ms
(sqrt (+ (+ x y) x))
6.0ms
(+ (+ x y) x)
5.0ms
(+ (+ x y) x)
15.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

series22.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(sqrt (+ (+ x y) x))
4.0ms
(+ (+ x y) x)
4.0ms
(+ (+ x y) x)
7.0ms
(* (sqrt (+ (+ x y) x)) (sqrt (+ (+ x y) x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0253621
11103568
25002554

prune81.0ms

Filtered
60 candidates to 128 candidates (-113.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1262128
Fresh000
Picked011
Done011
Total1264130

Merged error: 0.0b

Counts
130 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x))))
0.3b
(* (sqrt (+ (+ x y) x)) (* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x)))))
0.5b
(cbrt (+ (+ x y) x))
0.5b
(cbrt (+ (+ x y) x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
18×add-sqr-sqrt
16×cbrt-prod
15×sqrt-prod
14×sqrt-div
12×add-cube-cbrt cbrt-div associate-*r* distribute-lft-out
11×pow1 add-exp-log associate-*l* add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times pow-prod-down prod-exp cbrt-unprod add-log-exp
3×unswap-sqr
2×pow1/3 associate-*l/ *-commutative
Counts
4 → 91
Calls
4 calls:
10.0ms
(* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x))))
17.0ms
(* (sqrt (+ (+ x y) x)) (* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x)))))
5.0ms
(cbrt (+ (+ x y) x))
6.0ms
(cbrt (+ (+ x y) x))

series173.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x))))
56.0ms
(* (sqrt (+ (+ x y) x)) (* (fabs (cbrt (+ (+ x y) x))) (sqrt (cbrt (+ (+ x y) x)))))
30.0ms
(cbrt (+ (+ x y) x))
34.0ms
(cbrt (+ (+ x y) x))

simplify62.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
05621352
118551255
250021238

prune128.0ms

Filtered
77 candidates to 103 candidates (-33.8%)
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New1030103
Fresh011
Picked011
Done022
Total1034107

Merged error: 0.0b

Counts
107 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ x y) (+ x y))
2.2b
(- (+ x y) x)
13.9b
(/ (- (* (+ x y) (+ x y)) (* x x)) (- (+ x y) x))
17.6b
(- (* (+ x y) (+ x y)) (* x x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
34×add-sqr-sqrt
24×times-frac
20×add-cube-cbrt
14×difference-of-squares
12×distribute-lft-out distribute-lft-out--
11×pow1 add-log-exp
8×add-exp-log add-cbrt-cube
6×flip3-+ swap-sqr associate-/r* flip-+
4×frac-times flip3-- associate-*r* associate-*l* flip-- associate-/l*
3×diff-log associate--l+
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus div-sub div-exp pow-prod-down prod-exp clear-num sum-log pow-sqr *-commutative pow-prod-up cbrt-unprod div-inv unswap-sqr
Counts
4 → 123
Calls
4 calls:
8.0ms
(* (+ x y) (+ x y))
6.0ms
(- (+ x y) x)
16.0ms
(/ (- (* (+ x y) (+ x y)) (* x x)) (- (+ x y) x))
8.0ms
(- (* (+ x y) (+ x y)) (* x x))

series27.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (+ x y) (+ x y))
5.0ms
(- (+ x y) x)
10.0ms
(/ (- (* (+ x y) (+ x y)) (* x x)) (- (+ x y) x))
8.0ms
(- (* (+ x y) (+ x y)) (* x x))

simplify75.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
04451043
12238933
25001917

prune96.0ms

Filtered
84 candidates to 135 candidates (-60.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1341135
Fresh000
Picked101
Done303
Total1381139

Merged error: 0b

Counts
139 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072
172

end0.0ms

analyze50.0ms

Algorithm
search

sample248.0ms

Algorithm
intervals
Results
133.0ms8000×body80valid
0.0ms3×body80invalid

Profiling

Loading profile data...