Details

Time bar (total: 3.5s)

sample51.0ms

Algorithm
intervals
Results
24.0ms54×body2560valid
8.0ms37×body1280valid
7.0ms52×body640valid
3.0ms29×body320valid
2.0ms71×body80valid
1.0ms13×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b
(- 1.0 (cos x))
16.0b
(/ (- 1.0 (cos x)) (* x x))

rewrite12.0ms

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:
2.0ms
(- 1.0 (cos x))
9.0ms
(/ (- 1.0 (cos x)) (* x x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
47.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify63.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune106.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (- 1.0 (cos x))) x)
0.2b
(/ (sqrt (- 1.0 (cos x))) x)
1.2b
(- 1.0 (cos x))
1.2b
(- 1.0 (cos x))

rewrite26.0ms

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
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r*
4×pow1 flip3-- sqrt-div flip-- associate-/l/
2×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
4 → 126
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
2.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

series219.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (sqrt (- 1.0 (cos x))) x)
90.0ms
(/ (sqrt (- 1.0 (cos x))) x)
22.0ms
(- 1.0 (cos x))
18.0ms
(- 1.0 (cos x))

simplify99.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
02421020
1706972
22968960
35002960

prune296.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- 1.0 (cos x)))
1.2b
(- 1.0 (cos x))
1.2b
(- 1.0 (cos x))
1.2b
(- 1.0 (cos x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
5×cbrt-prod add-cube-cbrt
4×pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
3×sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 57
Calls
4 calls:
2.0ms
(cbrt (- 1.0 (cos x)))
3.0ms
(- 1.0 (cos x))
2.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

series182.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(cbrt (- 1.0 (cos x)))
18.0ms
(- 1.0 (cos x))
17.0ms
(- 1.0 (cos x))
22.0ms
(- 1.0 (cos x))

simplify53.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0150361
1391327
21222320
35001309

prune182.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- 1.0 (cos x))
1.2b
(- 1.0 (cos x))
1.2b
(- 1.0 (cos x))
1.3b
(log (exp (- 1.0 (cos x))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
10×add-log-exp
6×add-cube-cbrt log-pow
5×pow1 log-prod exp-prod
4×add-exp-log sub-neg add-cbrt-cube distribute-lft-out-- difference-of-squares
3×flip3-- diff-log flip--
2×exp-sum
1×log-div exp-diff rem-log-exp
Counts
4 → 62
Calls
4 calls:
2.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))
2.0ms
(- 1.0 (cos x))
8.0ms
(log (exp (- 1.0 (cos x))))

series76.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- 1.0 (cos x))
22.0ms
(- 1.0 (cos x))
17.0ms
(- 1.0 (cos x))
19.0ms
(log (exp (- 1.0 (cos x))))

simplify124.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0127319
1313294
2787294
33371294
45002294

prune202.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 0.1b

regimes65.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 30.6b

bsearch70.0ms

Steps
ItersRangePoint
10
3.2824798326487284e-15
0.08347146558812443
0.03157722500580303
9
-5.7596417613087905
-6.7357437175194845e-09
-0.03315307006442389

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03121
13121

end0.0ms

sample1.5s

Algorithm
intervals
Results
689.0ms1570×body2560valid
291.0ms1251×body1280valid
214.0ms1507×body640valid
90.0ms935×body320valid
74.0ms2289×body80valid
31.0ms448×body160valid