Details

Time bar (total: 3.1s)

sample62.0ms

Algorithm
intervals
Results
29.0ms60×body2560valid
10.0ms40×body1280valid
8.0ms48×body640valid
3.0ms24×body320valid
2.0ms66×body80valid
1.0ms18×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0134
1214
2264
3284
4284

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.0b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b
(- 1.0 (cos x))
18.5b
(/ (- 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:
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))

simplify60.0ms

Algorithm
egg-herbie
Counts
48 → 48
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0221271
1735239
22396239
35002239

prune100.0ms

Filtered
48 candidates to 34 candidates (29.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New371148
Fresh000
Picked101
Done000
Total381149

Merged error: 0.1b

Counts
49 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.2b
(* 1/24 (pow x 2))
11.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×associate-*r*
13×add-exp-log
9×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-log-exp
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
4×sqr-pow
3×pow1
2×pow-to-exp diff-log pow-exp *-commutative cbrt-unprod unpow2
1×sub-neg flip3-- associate--l+ sum-log flip--
Counts
3 → 66
Calls
3 calls:
5.0ms
(* 1/720 (pow x 4))
5.0ms
(* 1/24 (pow x 2))
7.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series14.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(* 1/720 (pow x 4))
3.0ms
(* 1/24 (pow x 2))
5.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0268345
11132313
25001307

prune123.0ms

Filtered
75 candidates to 46 candidates (38.7%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New75075
Fresh01010
Picked011
Done000
Total751186

Merged error: 0.1b

Counts
86 → 11

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)
1.9b
(- 1.0 (cos x))
1.9b
(- 1.0 (cos x))

rewrite24.0ms

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:
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
6.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))

series23.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ (sqrt (- 1.0 (cos x))) x)
9.0ms
(/ (sqrt (- 1.0 (cos x))) x)
3.0ms
(- 1.0 (cos x))
3.0ms
(- 1.0 (cos x))

simplify102.0ms

Algorithm
egg-herbie
Counts
138 → 138
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
02421020
1706972
22954960
35002960

prune210.0ms

Filtered
138 candidates to 92 candidates (33.3%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1353138
Fresh189
Picked101
Done011
Total13712149

Merged error: 0.1b

Counts
149 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
1.9b
(- 1.0 (cos x))
1.9b
(- 1.0 (cos x))
2.0b
(log (exp (- 1.0 (cos x))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt *-un-lft-identity
36×times-frac sqrt-prod
31×add-cube-cbrt
30×log-pow
25×exp-prod
12×associate-/l*
9×pow1
8×add-log-exp
7×distribute-lft-out-- difference-of-squares
6×add-exp-log add-cbrt-cube
5×log-prod
3×sub-neg associate-/r*
2×flip3-- diff-log exp-sum flip--
1×cbrt-undiv log-div frac-2neg exp-diff div-exp rem-log-exp clear-num div-inv
Counts
4 → 111
Calls
4 calls:
10.0ms
(/ (sqrt (log (exp (- 1.0 (cos x))))) x)
3.0ms
(- 1.0 (cos x))
4.0ms
(- 1.0 (cos x))
5.0ms
(log (exp (- 1.0 (cos x))))

series18.0ms

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

simplify106.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
0305911
1837822
23341790
35002789

prune179.0ms

Filtered
123 candidates to 80 candidates (35.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1203123
Fresh3710
Picked101
Done011
Total12411135

Merged error: 0.1b

Counts
135 → 11

regimes172.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.7b

bsearch35.0ms

Steps
ItersRangePoint
10
1.6467731241392944e-08
62869179882.65231
0.03474969771455722
9
-3.3701171682469404
-2.708263725627834e-09
-0.03257779273637018

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04640
14640

end0.0ms

sample1.8s

Algorithm
intervals
Results
787.0ms1577×body2560valid
320.0ms1257×body1280valid
250.0ms1501×body640valid
118.0ms902×body320valid
82.0ms2279×body80valid
41.0ms484×body160valid

Profiling

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