Details

Time bar (total: 4.8s)

sample807.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 78.161621%

Results
25.0ms49×body2560valid
14.0ms50×body1280valid
7.0ms42×body640valid
3.0ms28×body320valid
3.0ms76×body80valid
1.0ms11×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.9b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b
(- 1.0 (cos x))
14.9b
(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
7×add-exp-log add-cbrt-cube
5×times-frac associate-/l*
4×add-cube-cbrt add-log-exp
3×distribute-lft-out-- difference-of-squares
2×pow1 cbrt-undiv flip3-- div-exp flip-- associate-/l/
1×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))

simplify62.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune104.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New351348
Fresh000
Picked101
Done000
Total361349

Merged error: 0.1b

Counts
49 → 13

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)
1.2b
(- 1.0 (cos x))

rewrite29.0ms

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*
9×div-exp
8×prod-exp distribute-lft-out-- difference-of-squares
6×unswap-sqr
5×pow1 cbrt-undiv associate-/l* add-log-exp
4×cbrt-unprod
3×associate-/r* div-inv
2×rec-exp flip3-- 1-exp flip-- associate-/l/
1×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:
14.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
5.0ms
(- 1.0 (cos x))

series15.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0521814
12334726
25001690

prune148.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1212123
Fresh3912
Picked011
Done000
Total12412136

Merged error: 0.1b

Counts
136 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.1b
(/ (cos x) x)
1.4b
(- (/ 1.0 x) (/ (cos x) x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×*-un-lft-identity times-frac
23×add-cube-cbrt
14×add-exp-log
13×associate-*l*
12×associate-*r*
10×add-cbrt-cube
8×distribute-lft-out-- difference-of-squares
6×div-inv
5×pow1 add-log-exp
4×frac-times associate-*r/ prod-exp
3×sub-neg flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
2×cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in cbrt-unprod
1×rec-exp frac-2neg diff-log 1-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 106
Calls
3 calls:
21.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
4.0ms
(/ (cos x) x)
13.0ms
(- (/ 1.0 x) (/ (cos x) x))

series22.0ms

Counts
3 → 9
Calls
3 calls:
12.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
4.0ms
(/ (cos x) x)
6.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify58.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0478762
12181681
25001665

prune143.0ms

Filtered
86 candidates to 115 candidates (-33.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1141115
Fresh1910
Picked011
Done011
Total11512127

Merged error: 0.1b

Counts
127 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
1.3b
(- (/ 1.0 (cbrt x)) (/ (cos x) (cbrt x)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
25×*-un-lft-identity
24×times-frac
21×cbrt-prod
11×add-cube-cbrt
9×difference-of-squares
7×distribute-lft-out--
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
2×div-inv
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
4 → 64
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
27.0ms
(- (/ 1.0 (cbrt x)) (/ (cos x) (cbrt x)))

series122.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt x)
22.0ms
(cbrt x)
24.0ms
(cbrt x)
54.0ms
(- (/ 1.0 (cbrt x)) (/ (cos x) (cbrt x)))

simplify69.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (62.0ms)

IterNodesCost
0287574
1670506
22014482
35002479

prune93.0ms

Filtered
64 candidates to 76 candidates (-18.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New74276
Fresh189
Picked101
Done022
Total761288

Merged error: 0.1b

Counts
88 → 12

regimes135.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.1b

bsearch53.0ms

Steps
ItersRangePoint
10
1.2024928942441805e-18
0.16745856168064865
0.027397043128647394
10
-0.11587461641624221
-1.292522413854792e-16
-0.030269514238490947

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03411
13411

end0.0ms

sample2.7s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 78.161621%

Results
801.0ms1540×body2560valid
360.0ms1348×body1280valid
257.0ms1528×body640valid
106.0ms884×body320valid
86.0ms2233×body80valid
44.0ms467×body160valid

Profiling

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