Details

Time bar (total: 3.1s)

sample58.0ms

Algorithm
intervals
Results
30.0ms64×body2560valid
9.0ms39×body1280valid
6.0ms41×body640valid
3.0ms26×body320valid
2.0ms71×body80valid
1.0ms15×body160valid

simplify7.0ms

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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.5b
(- 1.0 (cos x))
17.7b
(/ (- 1.0 (cos x)) (* x x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
2×flip3-- associate-/r* flip-- associate-/l/
1×sub-neg frac-2neg div-sub clear-num *-commutative div-inv
Counts
2 → 12
Calls
2 calls:
2.0ms
(- 1.0 (cos x))
8.0ms
(/ (- 1.0 (cos x)) (* x x))

series63.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(- 1.0 (cos x))
44.0ms
(/ (- 1.0 (cos x)) (* x x))

simplify156.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
012481
139681
2105081
3420080
4500180

prune50.0ms

Filtered
18 candidates to 13 candidates (72.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New11718
Fresh000
Picked011
Done000
Total11819

Merged error: 0.2b

Counts
19 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 1/720 (pow x 4))
0.1b
(* 1/24 (pow x 2))
12.8b
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r*
2×associate--l+ *-commutative sqr-pow
1×+-commutative sub-neg flip3-- flip-- unpow2
Counts
3 → 11
Calls
3 calls:
2.0ms
(* 1/720 (pow x 4))
2.0ms
(* 1/24 (pow x 2))
5.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

series109.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(* 1/720 (pow x 4))
25.0ms
(* 1/24 (pow x 2))
46.0ms
(- (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))

simplify76.0ms

Algorithm
egg-herbie
Counts
20 → 20
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
09492
135390
2171786
3500186

prune39.0ms

Filtered
20 candidates to 10 candidates (50.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New19120
Fresh066
Picked011
Done011
Total19928

Merged error: 0.2b

Counts
28 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/24 (pow x 2))
0.1b
(* 1/24 (pow x 2))
19.2b
(- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3))
22.9b
(/ (- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3)) (+ (* (+ (* 1/720 (pow x 4)) 1/2) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))) (* (pow x 4) 1/576)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
6×sqr-pow
4×associate-*r*
2×difference-cubes flip3-- associate-/r/ *-commutative flip-- associate-/l/ associate-/l* unpow2 difference-of-squares
1×sub-neg frac-2neg flip3-+ div-sub clear-num flip-+ div-inv
Counts
4 → 22
Calls
4 calls:
3.0ms
(* 1/24 (pow x 2))
3.0ms
(* 1/24 (pow x 2))
8.0ms
(- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3))
22.0ms
(/ (- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3)) (+ (* (+ (* 1/720 (pow x 4)) 1/2) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))) (* (pow x 4) 1/576)))

series307.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 1/24 (pow x 2))
25.0ms
(* 1/24 (pow x 2))
101.0ms
(- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3))
153.0ms
(/ (- (pow (+ (* 1/720 (pow x 4)) 1/2) 3) (pow (* 1/24 (pow x 2)) 3)) (+ (* (+ (* 1/720 (pow x 4)) 1/2) (+ (+ (* 1/720 (pow x 4)) 1/2) (* 1/24 (pow x 2)))) (* (pow x 4) 1/576)))

simplify39.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0236396
11010392
25002392

prune116.0ms

Filtered
34 candidates to 23 candidates (67.6%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New34034
Fresh066
Picked011
Done022
Total34943

Merged error: 0.2b

Counts
43 → 9

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))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-/l/
3×flip3-- frac-2neg div-sub clear-num flip-- div-inv
1×sub-neg associate-/l*
Counts
3 → 20
Calls
3 calls:
4.0ms
(/ (/ (- 1.0 (cos x)) x) x)
3.0ms
(/ (- 1.0 (cos x)) x)
2.0ms
(- 1.0 (cos x))

series111.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(/ (/ (- 1.0 (cos x)) x) x)
47.0ms
(/ (- 1.0 (cos x)) x)
20.0ms
(- 1.0 (cos x))

simplify60.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0163118
1458117
21640115
35001114

prune46.0ms

Filtered
29 candidates to 19 candidates (65.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New25429
Fresh415
Picked101
Done033
Total30838

Merged error: 0.1b

Counts
38 → 8

regimes71.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.9b

bsearch56.0ms

Steps
ItersRangePoint
6
0.018000635171863108
0.09117784756913819
0.03010910821075468
10
-1421.6155834850151
-1.485944467815708e-07
-0.03323288645356819

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03411
13411

end0.0ms

sample1.6s

Algorithm
intervals
Results
780.0ms1643×body2560valid
292.0ms1221×body1280valid
225.0ms1450×body640valid
104.0ms914×body320valid
79.0ms2291×body80valid
36.0ms481×body160valid