Details

Time bar (total: 3.5s)

sample53.0ms

Algorithm
intervals
Results
21.0ms46×body2560valid
10.0ms41×body1280valid
8.0ms54×body640valid
4.0ms37×body320valid
2.0ms67×body80valid
1.0ms11×body160valid

simplify8.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.8b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.3b
(- 1.0 (cos x))
13.5b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
add-exp-log add-cbrt-cube
times-frac associate-/l*
add-cube-cbrt add-log-exp
distribute-lft-out-- difference-of-squares
pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
sub-neg frac-2neg diff-log div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
2 → 42
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 1.0 (cos x)) (* x x))

series71.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(- 1.0 (cos x))
48.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify72.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune103.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New39948
Fresh000
Picked101
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 1/24 (pow x 2))
0.3b
(* 1/720 (pow x 4))
11.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
add-cube-cbrt *-un-lft-identity
unpow-prod-down add-log-exp
add-cbrt-cube unswap-sqr
associate-*l* prod-exp
sqr-pow
pow1
pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/24 (pow x 2))
5.0ms
(* 1/720 (pow x 4))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series111.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(* 1/24 (pow x 2))
36.0ms
(* 1/720 (pow x 4))
46.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268345
11132313
25001307

prune133.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh088
Picked011
Done000
Total75984

Merged error: 0.1b

Counts
84 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(/ (sqrt (- 1.0 (cos x))) x)
2.3b
(- 1.0 (cos x))
2.3b
(- 1.0 (cos x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
add-exp-log add-cbrt-cube add-log-exp
associate-/r*
pow1 flip3-- sqrt-div flip-- associate-/l/
cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series223.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (sqrt (- 1.0 (cos x))) x)
93.0ms
(/ (sqrt (- 1.0 (cos x))) x)
18.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify108.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
02421020
1706972
22954960
35002960

prune265.0ms

Filtered
138 candidates to 92 candidates (66.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1344138
Fresh167
Picked101
Done011
Total13611147

Merged error: 0.1b

Counts
147 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 (cos x)))
2.3b
(- 1.0 (cos x))
2.3b
(- 1.0 (cos x))
2.3b
(- 1.0 (cos x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
cbrt-prod add-cube-cbrt
pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
sub-neg diff-log
cbrt-div
pow1/3
Counts
4 → 57
Calls
4 calls:
3.0ms
(cbrt (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series181.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(cbrt (- 1.0 (cos x)))
23.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))
19.0ms
(- 1.0 (cos x))

simplify52.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (47.0ms)

IterNodesCost
0150361
1391327
21222319
35001309

prune181.0ms

Filtered
69 candidates to 50 candidates (72.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New66369
Fresh189
Picked101
Done011
Total681280

Merged error: 0.1b

Counts
80 → 12

regimes61.0ms

Accuracy

98.9% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 32.2b

bsearch81.0ms

Steps
ItersRangePoint
10
2.2826621327002547e-07
125321.6248081686
0.0299856578793022
9
-0.06461929534003709
-4.410039720853989e-10
-0.030425877078950985

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04732
14732

end0.0ms

sample1.6s

Algorithm
intervals
Results
731.0ms1545×body2560valid
305.0ms1228×body1280valid
233.0ms1521×body640valid
111.0ms935×body320valid
76.0ms2270×body80valid
38.0ms501×body160valid

Profiling

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