Details

Time bar (total: 3.4s)

analyze226.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
50%50%0%3
75%25%0%4
75%25%0%5
75%25%0%6
78.1%21.9%0%7
78.1%21.9%0%8
78.1%21.9%0%9
78.1%21.9%0%10
78.1%21.9%0%11
78.1%21.9%0%12
78.1%21.9%0%13
78.1%21.8%0%14

sample55.0ms

Algorithm
intervals
Results
22.0ms46×body2560valid
10.0ms38×body1280valid
8.0ms52×body640valid
4.0ms39×body320valid
2.0ms70×body80valid
1.0ms11×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
05008
15008

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.5b

Counts
2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
14.4b
(/ (- 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 → 41
Calls
2 calls:
4.0ms
(- 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))

simplify46.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04894437
14894437

prune90.0ms

Filtered
34 candidates to 47 candidates (-38.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New371047
Fresh000
Picked101
Done000
Total381048

Merged error: 0.3b

Counts
48 → 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)
1.7b
(- 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 → 146
Calls
3 calls:
9.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series13.0ms

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))

simplify56.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
054811984

prune166.0ms

Filtered
100 candidates to 155 candidates (-55.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1496155
Fresh459
Picked101
Done000
Total15411165

Merged error: 0.2b

Counts
165 → 11

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
0.1b
(/ (cos x) x)
1.6b
(- (/ 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
7×add-exp-log add-cbrt-cube
6×associate-/r*
5×distribute-rgt-out-- add-log-exp
4×associate-/l/
3×pow1
2×cbrt-undiv flip3-- frac-2neg div-exp clear-num frac-sub flip-- sub-div
1×sub-neg diff-log div-sub
Counts
3 → 117
Calls
3 calls:
15.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
3.0ms
(/ (cos x) x)
15.0ms
(- (/ 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))

simplify53.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
051741525

prune152.0ms

Filtered
96 candidates to 126 candidates (-31.3%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1224126
Fresh1910
Picked011
Done000
Total12314137

Merged error: 0.2b

Counts
137 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
32×*-un-lft-identity
28×cbrt-prod
12×add-cube-cbrt cbrt-div
11×pow1
10×swap-sqr add-log-exp
9×flip3-- flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log pow1/3
4×frac-times add-cbrt-cube unswap-sqr
3×sub-neg diff-log
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
10.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series35.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (cbrt (- 1.0 (cos x))) (cbrt (- 1.0 (cos x))))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))
5.0ms
(- 1.0 (cos x))

simplify36.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
051281093

prune163.0ms

Filtered
72 candidates to 107 candidates (-48.6%)
Pruning

16 alts after pruning (14 fresh and 2 done)

PrunedKeptTotal
New1025107
Fresh3912
Picked011
Done011
Total10516121

Merged error: 0.2b

Counts
121 → 16

regimes95.0ms

Accuracy

99% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.0b

bsearch38.0ms

Steps
ItersRangePoint
10
1.2242921435180001e-09
9.201970846692953
0.03592992967463037
11
-959731.2497518875
-5.210873737169412e-18
-0.03375314859115401

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
06549
16549

end0.0ms

sample1.9s

Algorithm
intervals
Results
826.0ms1574×body2560valid
493.0ms1284×body1280valid
247.0ms1434×body640valid
113.0ms947×body320valid
94.0ms2307×body80valid
38.0ms454×body160valid

Profiling

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