Details

Time bar (total: 3.4s)

analyze230.0ms

Algorithm
search

sample63.0ms

Algorithm
intervals
Results
24.0ms48×body2560valid
10.0ms36×body1280valid
8.0ms49×body640valid
8.0ms73×body80valid
4.0ms31×body320valid
2.0ms19×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: 31.9b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

3.0b
(- 1.0 (cos x))
14.6b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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))

series10.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(- 1.0 (cos x))
7.0ms
(/ (- 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

prune97.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New381048
Fresh000
Picked101
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
12.4b
(- (+ (* 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
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series12.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(* 1/720 (pow x 4))
3.0ms
(* 1/24 (pow x 2))
5.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0268345
11132313
25001307

prune123.0ms

Filtered
46 candidates to 75 candidates (-63.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New74175
Fresh189
Picked011
Done000
Total751085

Merged error: 0.1b

Counts
85 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
0.3b
(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
12.4b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
12×add-cube-cbrt *-un-lft-identity
9×add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×log-prod associate-*l* prod-exp
5×pow1
4×log-pow sqr-pow
3×exp-prod exp-sum
2×pow-to-exp sub-neg diff-log pow-exp associate--l+ *-commutative cbrt-unprod unpow2
1×log-div flip3-- exp-diff rem-log-exp sum-log flip--
Counts
4 → 85
Calls
4 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
6.0ms
(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series16.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* 1/720 (pow x 4))
3.0ms
(* 1/24 (pow x 2))
5.0ms
(log (exp (- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))))
5.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0303533
11254479
25001473

prune170.0ms

Filtered
60 candidates to 97 candidates (-61.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New97097
Fresh088
Picked011
Done011
Total9710107

Merged error: 0.1b

Counts
107 → 10

localize6.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- 1.0 (cos x)) x) x)
0.1b
(/ (- 1.0 (cos x)) x)
3.0b
(- 1.0 (cos x))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
132×times-frac
103×add-sqr-sqrt *-un-lft-identity
69×add-cube-cbrt
24×associate-/l*
17×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg diff-log
Counts
3 → 147
Calls
3 calls:
9.0ms
(/ (/ (- 1.0 (cos x)) x) x)
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series16.0ms

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

simplify52.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05311270
118991197
250011186

prune141.0ms

Filtered
104 candidates to 156 candidates (-50.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1515156
Fresh257
Picked101
Done022
Total15412166

Merged error: 0.1b

Counts
166 → 12

regimes141.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.4b

bsearch36.0ms

Steps
ItersRangePoint
6
0.008350854801249755
0.04423768339840673
0.0282905967055219
9
-0.8362751047506872
-2.781472463626374e-06
-0.03330074166064683

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03011
13011

end0.0ms

analyze232.0ms

Algorithm
search

sample1.8s

Algorithm
intervals
Results
834.0ms1598×body2560valid
349.0ms1300×body1280valid
259.0ms1462×body640valid
118.0ms937×body320valid
90.0ms2197×body80valid
43.0ms506×body160valid

Profiling

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