Details

Time bar (total: 3.7s)

sample59.0ms

Algorithm
intervals
Results
26.0ms56×body2560valid
10.0ms43×body1280valid
7.0ms46×body640valid
3.0ms23×body320valid
2.0ms73×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

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.3b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
15.8b
(/ (- 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))

series14.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(- 1.0 (cos x))
11.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune145.0ms

Filtered
48 candidates to 34 candidates (29.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New371148
Fresh000
Picked101
Done000
Total381149

Merged error: 0.1b

Counts
49 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(* 1/24 (pow x 2))
0.3b
(* 1/720 (pow x 4))
12.8b
(- (+ (* 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)))

series12.0ms

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

simplify42.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268345
11132313
25001307

prune214.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh01010
Picked011
Done000
Total751186

Merged error: 0.1b

Counts
86 → 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)
1.9b
(- 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
associate-/r* div-inv
add-log-exp
cbrt-undiv div-exp
pow1 div-sub associate-/l/
flip3-- frac-2neg clear-num flip--
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)
3.0ms
(- 1.0 (cos x))

series14.0ms

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

simplify54.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05311270
118991197
250011186

prune541.0ms

Filtered
156 candidates to 103 candidates (34.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1542156
Fresh369
Picked101
Done011
Total1589167

Merged error: 0.1b

Counts
167 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.9b
(- (/ 1.0 x) (/ (cos x) x))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
95×times-frac
78×*-un-lft-identity
38×add-cube-cbrt
20×distribute-lft-out-- difference-of-squares
15×associate-/l*
12×div-inv
add-exp-log add-cbrt-cube
associate-/r*
distribute-rgt-out-- add-log-exp
associate-/l/
pow1
cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
sub-neg diff-log div-sub
Counts
3 → 118
Calls
3 calls:
18.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
4.0ms
(/ (cos x) x)
12.0ms
(- (/ 1.0 x) (/ (cos x) x))

series19.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
3.0ms
(/ (cos x) x)
6.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify45.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04631015
11518940
25002936

prune547.0ms

Filtered
127 candidates to 101 candidates (20.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1261127
Fresh077
Picked011
Done011
Total12610136

Merged error: 0.1b

Counts
136 → 10

regimes72.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.5b

bsearch79.0ms

Steps
ItersRangePoint
10
4.00241138285282e-13
41.84587058567329
0.03303919024481564
7
-0.4867936294477796
-0.0038973504402139516
-0.03324940555921645

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03011
13011

end0.0ms

sample1.7s

Algorithm
intervals
Results
772.0ms1635×body2560valid
298.0ms1222×body1280valid
235.0ms1493×body640valid
106.0ms927×body320valid
74.0ms2259×body80valid
35.0ms464×body160valid

Profiling

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