Details

Time bar (total: 3.3s)

sample59.0ms

Algorithm
intervals
Results
28.0ms58×body2560valid
11.0ms45×body1280valid
6.0ms41×body640valid
3.0ms31×body320valid
3.0ms66×body80valid
1.0ms15×body160valid

simplify7.0ms

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: 32.8b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b
(- 1.0 (cos x))
16.4b
(/ (- 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))

series64.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(- 1.0 (cos x))
46.0ms
(/ (- 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

prune109.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New361248
Fresh000
Picked101
Done000
Total371249

Merged error: 0.1b

Counts
49 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
10.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite21.0ms

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)))

series145.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(* 1/720 (pow x 4))
40.0ms
(* 1/24 (pow x 2))
56.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify40.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0268345
11132313
25001307

prune129.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New74175
Fresh11011
Picked101
Done000
Total761187

Merged error: 0.1b

Counts
87 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1/2 (* 1/24 (pow x 2)))
0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
10.8b
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
15×associate-*r*
14×add-exp-log
11×add-log-exp
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 sqr-pow
2×pow-to-exp sub-neg associate-+r+ diff-log pow-exp sum-log *-commutative cbrt-unprod unpow2
1×+-commutative associate-+r- flip3-- flip3-+ flip-- flip-+
Counts
4 → 79
Calls
4 calls:
2.0ms
(- 1/2 (* 1/24 (pow x 2)))
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
6.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

series160.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(- 1/2 (* 1/24 (pow x 2)))
39.0ms
(* 1/720 (pow x 4))
23.0ms
(* 1/24 (pow x 2))
45.0ms
(+ (* 1/720 (pow x 4)) (- 1/2 (* 1/24 (pow x 2))))

simplify45.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0314411
11275380
25001378

prune162.0ms

Filtered
91 candidates to 57 candidates (62.6%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New91091
Fresh01010
Picked011
Done000
Total9111102

Merged error: 0.1b

Counts
102 → 11

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)
1.8b
(- 1.0 (cos x))

rewrite24.0ms

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:
8.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series107.0ms

Counts
3 → 9
Calls
3 calls:
42.0ms
(/ (/ (- 1.0 (cos x)) x) x)
46.0ms
(/ (- 1.0 (cos x)) x)
19.0ms
(- 1.0 (cos x))

simplify58.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05311270
118991197
250011186

prune206.0ms

Filtered
156 candidates to 103 candidates (66.0%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New1515156
Fresh369
Picked011
Done011
Total15413167

Merged error: 0.1b

Counts
167 → 13

regimes100.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.2b

bsearch66.0ms

Steps
ItersRangePoint
9
0.004314681149180372
39972.03059165128
0.034588668937196705
9
-2.6022242175013632
-1.4174312616962401e-08
-0.03062216897551053

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02910
12910

end0.0ms

sample1.6s

Algorithm
intervals
Results
748.0ms1604×body2560valid
316.0ms1250×body1280valid
224.0ms1431×body640valid
101.0ms922×body320valid
82.0ms2284×body80valid
39.0ms509×body160valid

Profiling

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