Details

Time bar (total: 3.3s)

analyze228.0ms

Algorithm
search

sample69.0ms

Algorithm
intervals
Results
34.0ms58×body2560valid
11.0ms42×body1280valid
8.0ms48×body640valid
4.0ms33×body320valid
3.0ms62×body80valid
1.0ms13×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: 33.2b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.8b
(- 1.0 (cos x))
17.2b
(/ (- 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 (5.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune89.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New39948
Fresh000
Picked011
Done000
Total391049

Merged error: 0.1b

Counts
49 → 10

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.6b
(- (+ (* 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
(* 1/720 (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)))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268345
11132313
25001307

prune116.0ms

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

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New75075
Fresh088
Picked011
Done011
Total751085

Merged error: 0.1b

Counts
85 → 10

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)
1.8b
(- 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*
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:
16.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series13.0ms

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

simplify63.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0521814
12334726
25001690

prune128.0ms

Filtered
81 candidates to 123 candidates (-51.9%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1212123
Fresh257
Picked011
Done022
Total12310133

Merged error: 0.1b

Counts
133 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
0.1b
(/ (cos x) x)
1.9b
(- (/ 1.0 x) (/ (cos x) x))

rewrite41.0ms

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
distribute-lft-out-- difference-of-squares
div-inv
pow1 add-log-exp
frac-times associate-*r/ prod-exp
sub-neg flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in cbrt-unprod
rec-exp frac-2neg diff-log 1-exp pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 106
Calls
3 calls:
20.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
4.0ms
(/ (cos x) x)
14.0ms
(- (/ 1.0 x) (/ (cos x) x))

series19.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(* (/ 1 x) (- (/ 1.0 x) (/ (cos x) x)))
3.0ms
(/ (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

prune109.0ms

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

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New1141115
Fresh156
Picked011
Done033
Total11510125

Merged error: 0.1b

Counts
125 → 10

regimes147.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.8b

bsearch48.0ms

Steps
ItersRangePoint
9
0.000116853398397054
21.564460051137775
0.03128874894178308
11
-87937235.23723643
-3.929523802944544e-14
-0.03294833675977308

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03411
13411

end0.0ms

analyze221.0ms

Algorithm
search

sample1.8s

Algorithm
intervals
Results
836.0ms1613×body2560valid
332.0ms1244×body1280valid
244.0ms1481×body640valid
118.0ms923×body320valid
80.0ms2285×body80valid
38.0ms454×body160valid

Profiling

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