Details

Time bar (total: 3.1s)

analyze233.0ms

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

sample60.0ms

Algorithm
intervals
Results
29.0ms60×body2560valid
10.0ms59×body640valid
9.0ms34×body1280valid
3.0ms25×body320valid
2.0ms65×body80valid
1.0ms13×body160valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
05008
15008

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
17.3b
(/ (- 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 → 41
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))

simplify46.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
04894437
14894437

prune89.0ms

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

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New39847
Fresh000
Picked101
Done000
Total40848

Merged error: 0.2b

Counts
48 → 8

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)
1.5b
(- 1.0 (cos x))

rewrite26.0ms

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 → 146
Calls
3 calls:
8.0ms
(/ (/ (- 1.0 (cos x)) x) x)
5.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 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))

simplify57.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
054811984

prune163.0ms

Filtered
102 candidates to 155 candidates (-52.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1514155
Fresh257
Picked101
Done000
Total1549163

Merged error: 0.1b

Counts
163 → 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)
1.6b
(- (/ 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
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 → 117
Calls
3 calls:
15.0ms
(/ (- (/ 1.0 x) (/ (cos x) x)) x)
3.0ms
(/ (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))

simplify54.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
051741525

prune139.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1242126
Fresh178
Picked101
Done000
Total1269135

Merged error: 0.1b

Counts
135 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
0.1b
(/ (cos x) x)
1.6b
(- (/ 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-*r*
12×associate-*l*
10×add-cbrt-cube
distribute-lft-out-- difference-of-squares
div-inv
pow1 add-log-exp
frac-times associate-*l/ prod-exp
flip3-- div-exp associate-/r* frac-sub flip-- associate-/l* sub-div unswap-sqr
cbrt-undiv distribute-rgt-out-- cbrt-unprod
sub-neg rec-exp frac-2neg diff-log 1-exp associate-*r/ pow-prod-down clear-num un-div-inv *-commutative
Counts
3 → 102
Calls
3 calls:
20.0ms
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
4.0ms
(/ (cos x) x)
13.0ms
(- (/ 1.0 x) (/ (cos x) x))

series19.0ms

Counts
3 → 9
Calls
3 calls:
9.0ms
(* (- (/ 1.0 x) (/ (cos x) x)) (/ 1 x))
4.0ms
(/ (cos x) x)
6.0ms
(- (/ 1.0 x) (/ (cos x) x))

simplify56.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
049531117
149531117

prune106.0ms

Filtered
87 candidates to 111 candidates (-27.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1110111
Fresh088
Picked011
Done000
Total1119120

Merged error: 0.1b

Counts
120 → 9

regimes110.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 30.6b

bsearch29.0ms

Steps
ItersRangePoint
10
7.041687525152563e-14
5.868207604963725
0.03047569278769371
9
-4.642161588021477
-8.054016468356278e-06
-0.035212767529547204

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05134
15134

end0.0ms

sample1.8s

Algorithm
intervals
Results
837.0ms1661×body2560valid
315.0ms1211×body1280valid
252.0ms1515×body640valid
107.0ms893×body320valid
88.0ms2244×body80valid
42.0ms476×body160valid

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