Details

Time bar (total: 3.6s)

analyze225.0ms

Algorithm
search

sample60.0ms

Algorithm
intervals
Results
20.0ms41×body2560valid
14.0ms57×body640valid
11.0ms44×body1280valid
4.0ms31×body320valid
3.0ms71×body80valid
1.0ms12×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: 30.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b
(- 1.0 (cos x))
12.9b
(/ (- 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 → 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))

simplify59.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune98.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New361248
Fresh000
Picked101
Done000
Total371249

Merged error: 0.0b

Counts
49 → 12

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))

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 → 147
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))

simplify53.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
05311270
118991197
250011186

prune171.0ms

Filtered
101 candidates to 156 candidates (-54.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1542156
Fresh2911
Picked011
Done000
Total15612168

Merged error: 0.0b

Counts
168 → 12

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)
1.7b
(- 1.0 (cos x))

rewrite28.0ms

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:
14.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
6.0ms
(/ (- 1.0 (cos x)) x)
4.0ms
(- 1.0 (cos x))

series14.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms
(/ (- 1.0 (cos x)) x)
3.0ms
(- 1.0 (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0521814
12334726
25001690

prune139.0ms

Filtered
78 candidates to 123 candidates (-57.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1221123
Fresh1910
Picked011
Done011
Total12312135

Merged error: 0.0b

Counts
135 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- 1.0 (cos x))) x)
0.1b
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
1.7b
(- 1.0 (cos x))
1.7b
(- 1.0 (cos x))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
167×add-sqr-sqrt
156×times-frac
143×*-un-lft-identity
104×sqrt-prod
89×add-cube-cbrt
40×swap-sqr
28×associate-*r* associate-*l*
24×distribute-lft-out--
18×add-exp-log add-cbrt-cube difference-of-squares
11×pow1
unswap-sqr
associate-/l* add-log-exp
cbrt-undiv div-exp div-inv
prod-exp cbrt-unprod
flip3-- associate-/r* flip--
sub-neg sqrt-div diff-log associate-/l/
pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr *-commutative pow-prod-up
Counts
4 → 206
Calls
4 calls:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
25.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
4.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series24.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(* (/ (sqrt (- 1.0 (cos x))) x) (/ (sqrt (- 1.0 (cos x))) x))
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify90.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
06672403
133402087
250011922

prune270.0ms

Filtered
122 candidates to 218 candidates (-78.7%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New2162218
Fresh279
Picked011
Done022
Total21812230

Merged error: 0.0b

Counts
230 → 12

regimes77.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.0b

bsearch53.0ms

Steps
ItersRangePoint
10
1.8304015800755974e-11
5978.515960881942
0.027140316278725395
10
-53500635.28645546
-5.972664956026343e-06
-0.032022030743945114

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03215
13215

end0.0ms

analyze221.0ms

Algorithm
search

sample1.8s

Algorithm
intervals
Results
803.0ms1580×body2560valid
347.0ms1292×body1280valid
266.0ms1560×body640valid
105.0ms839×body320valid
79.0ms2266×body80valid
43.0ms463×body160valid

Profiling

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