Details

Time bar (total: 5.0s)

sample833.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
30.0ms50×body2560valid
11.0ms38×body1280valid
9.0ms53×body640valid
3.0ms26×body320valid
3.0ms74×body80valid
1.0ms15×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.1b
(- 1.0 (cos x))
14.8b
(/ (- 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))

series9.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
6.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify61.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune105.0ms

Filtered
34 candidates to 48 candidates (-41.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New361248
Fresh000
Picked101
Done000
Total371249

Merged error: 0.1b

Counts
49 → 12

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b
(/ (- 1.0 (cos x)) x)
2.1b
(- 1.0 (cos x))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
47×*-un-lft-identity
46×times-frac
29×add-cube-cbrt
27×add-exp-log
19×associate-*r*
17×add-cbrt-cube
13×associate-*l*
div-exp
prod-exp distribute-lft-out-- difference-of-squares
unswap-sqr
pow1 cbrt-undiv associate-/l* add-log-exp
cbrt-unprod
associate-/r* div-inv
rec-exp flip3-- 1-exp flip-- associate-/l/
frac-times sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 114
Calls
3 calls:
13.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

series16.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0521814
12334726
25001690

prune156.0ms

Filtered
80 candidates to 123 candidates (-53.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1212123
Fresh01111
Picked101
Done000
Total12213135

Merged error: 0.1b

Counts
135 → 13

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
2.1b
(- 1.0 (cos x))
2.1b
(- 1.0 (cos x))

rewrite25.0ms

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)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series23.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
9.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify100.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
02421020
1706972
22954960
35002960

prune227.0ms

Filtered
92 candidates to 138 candidates (-50.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1371138
Fresh3912
Picked011
Done000
Total14011151

Merged error: 0.1b

Counts
151 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
2.1b
(- 1.0 (cos x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
cbrt-prod add-sqr-sqrt *-un-lft-identity
add-cube-cbrt
add-log-exp
pow1 add-exp-log add-cbrt-cube
pow1/3
sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 47
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
3.0ms
(- 1.0 (cos x))

series71.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(cbrt x)
21.0ms
(cbrt x)
23.0ms
(cbrt x)
3.0ms
(- 1.0 (cos x))

simplify202.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (33.0ms)

IterNodesCost
0146229
1325212
2891182
34788179
45002179

prune63.0ms

Filtered
45 candidates to 59 candidates (-31.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New59059
Fresh099
Picked011
Done011
Total591170

Merged error: 0.1b

Counts
70 → 11

regimes138.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.9b

bsearch44.0ms

Steps
ItersRangePoint
9
7.898238664675696e-07
16.9978394737498
0.03365495782702641
8
-1.501420303203214
-0.00023605401382188195
-0.032112897762436775

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13015

end0.0ms

sample2.7s

Algorithm
intervals
sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results
848.0ms1623×body2560valid
337.0ms1237×body1280valid
256.0ms1488×body640valid
244.0ms2247×body80valid
117.0ms922×body320valid
41.0ms483×body160valid

Profiling

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