Details

Time bar (total: 3.4s)

analyze230.0ms

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

sample64.0ms

Algorithm
intervals
Results
29.0ms45×body2560valid
12.0ms43×body1280valid
7.0ms45×body640valid
4.0ms32×body320valid
3.0ms76×body80valid
1.0ms15×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: 29.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- 1.0 (cos x))
14.2b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:
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))

simplify49.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04894437
14894437

prune92.0ms

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: 0.1b

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)
2.0b
(- 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:
9.0ms
(/ (/ (- 1.0 (cos x)) x) x)
6.0ms
(/ (- 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))

simplify60.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
054811984

prune183.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1523155
Fresh279
Picked011
Done000
Total15411165

Merged error: 0.1b

Counts
165 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(/ (sqrt (- 1.0 (cos x))) x)
2.0b
(- 1.0 (cos x))
2.0b
(- 1.0 (cos x))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
58×add-sqr-sqrt *-un-lft-identity
48×times-frac
40×sqrt-prod
38×add-cube-cbrt
16×associate-/l*
10×distribute-lft-out-- difference-of-squares
add-exp-log add-cbrt-cube add-log-exp
associate-/r*
pow1 flip3-- sqrt-div flip-- associate-/l/
cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 124
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(- 1.0 (cos x))
10.0ms
(- 1.0 (cos x))

series23.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify46.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049801524
149801524

prune236.0ms

Filtered
92 candidates to 136 candidates (-47.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1342136
Fresh189
Picked011
Done011
Total13512147

Merged error: 0.1b

Counts
147 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (log (exp (- 1.0 (cos x)))) x)
0.1b
(exp (- 1.0 (cos x)))
2.0b
(- 1.0 (cos x))
2.2b
(log (exp (- 1.0 (cos x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
30×exp-prod log-pow
27×times-frac
25×add-cube-cbrt
pow1 associate-/l* add-log-exp
distribute-lft-out-- difference-of-squares
add-exp-log add-cbrt-cube
log-prod
sub-neg exp-diff associate-/r*
log-div diff-log exp-sum rem-exp-log
cbrt-undiv flip3-- frac-2neg div-sub div-exp rem-log-exp clear-num flip-- div-inv
Counts
4 → 100
Calls
4 calls:
8.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
5.0ms
(exp (- 1.0 (cos x)))
4.0ms
(- 1.0 (cos x))
5.0ms
(log (exp (- 1.0 (cos x))))

series19.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ (log (exp (- 1.0 (cos x)))) x)
7.0ms
(exp (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))
3.0ms
(log (exp (- 1.0 (cos x))))

simplify110.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (99.0ms)

IterNodesCost
04873974
14873974

prune115.0ms

Filtered
77 candidates to 112 candidates (-45.5%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1120112
Fresh099
Picked011
Done022
Total11212124

Merged error: 0.1b

Counts
124 → 12

regimes131.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 31.3b

bsearch31.0ms

Steps
ItersRangePoint
9
5.9190591704608434e-05
119.09567283585568
0.03110119868356473
10
-1051704.1093901352
-9.596635463168939e-08
-0.0302754788051601

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04239
14239

end0.0ms

sample1.8s

Algorithm
intervals
Results
850.0ms1669×body2560valid
325.0ms1250×body1280valid
250.0ms1466×body640valid
121.0ms924×body320valid
78.0ms2229×body80valid
43.0ms462×body160valid

Profiling

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