Details

Time bar (total: 3.6s)

sample59.0ms

Algorithm
intervals
Results
29.0ms61×body2560valid
9.0ms38×body1280valid
8.0ms52×body640valid
2.0ms23×body320valid
2.0ms70×body80valid
1.0ms12×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: 33.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
18.0b
(/ (- 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))

series63.0ms

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

simplify60.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune111.0ms

Filtered
48 candidates to 34 candidates (70.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New39948
Fresh000
Picked101
Done000
Total40949

Merged error: 0.1b

Counts
49 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.8b
(- (+ (* 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
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)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(* 1/720 (pow x 4))
24.0ms
(* 1/24 (pow x 2))
46.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify40.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0268347
11132316
25001310

prune129.0ms

Filtered
75 candidates to 46 candidates (61.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh088
Picked011
Done000
Total75984

Merged error: 0.1b

Counts
84 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (* x x))
0.3b
(/ (cos x) (* x x))
19.4b
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
12×times-frac
11×*-un-lft-identity
7×add-cube-cbrt
6×associate-/l*
5×add-log-exp
4×cbrt-undiv div-exp div-inv difference-of-squares
3×pow1
2×frac-2neg prod-exp clear-num associate-/r* cbrt-unprod distribute-lft-out--
1×sub-neg flip3-- distribute-rgt-out-- diff-log frac-sub flip-- sub-div
Counts
3 → 63
Calls
3 calls:
4.0ms
(/ 1.0 (* x x))
5.0ms
(/ (cos x) (* x x))
8.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series129.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(/ 1.0 (* x x))
28.0ms
(/ (cos x) (* x x))
73.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify65.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0269413
1885365
23007362
35001362

prune118.0ms

Filtered
72 candidates to 53 candidates (73.6%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New71172
Fresh077
Picked011
Done011
Total711081

Merged error: 0.1b

Counts
81 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

13.6b
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
13.6b
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
19.4b
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))
19.4b
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
24×times-frac
22×*-un-lft-identity
20×sqrt-prod
16×difference-of-squares
8×sqrt-div div-inv distribute-lft-out-- add-log-exp
6×pow1 add-cube-cbrt
4×add-exp-log flip3-- distribute-rgt-out-- frac-sub add-cbrt-cube flip-- sub-div
2×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 90
Calls
4 calls:
9.0ms
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
9.0ms
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
9.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))
9.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
114.0ms
(sqrt (- (/ 1.0 (* x x)) (/ (cos x) (* x x))))
74.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))
75.0ms
(- (/ 1.0 (* x x)) (/ (cos x) (* x x)))

simplify81.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
02351010
1767946
22937938
35001934

prune263.0ms

Filtered
102 candidates to 88 candidates (86.3%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New993102
Fresh167
Picked011
Done022
Total10012112

Merged error: 0.1b

Counts
112 → 12

regimes99.0ms

Accuracy

99% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 32.2b

bsearch65.0ms

Steps
ItersRangePoint
8
6.042829624826513e-05
0.09081442282169057
0.03382973364614673
8
-6.238959787773506
-0.00010711273713490883
-0.03501152839106913

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04025
14025

end0.0ms

sample1.7s

Algorithm
intervals
Results
763.0ms1555×body2560valid
311.0ms1237×body1280valid
238.0ms1493×body640valid
108.0ms940×body320valid
81.0ms2291×body80valid
44.0ms484×body160valid

Profiling

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