Details

Time bar (total: 6.7s)

sample97.0ms

Algorithm
intervals
Results
51.0ms140×body1280valid
20.0ms23×body2560valid
13.0ms58×body640valid
3.0ms17×body320valid
2.0ms16×body160valid
0.0ms2×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

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: 41.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (cos (+ x eps)) (cos x))
3.8b
(cos (+ x eps))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt cos-sum add-cbrt-cube
1×associate--l- sub-neg flip3-- diff-log flip-- diff-cos distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
6.0ms
(- (cos (+ x eps)) (cos x))
4.0ms
(cos (+ x eps))

series69.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(- (cos (+ x eps)) (cos x))
15.0ms
(cos (+ x eps))

simplify115.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0134176
1281167
2840164
32958164
45002164

prune95.0ms

Filtered
30 candidates to 23 candidates (76.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New181230
Fresh000
Picked101
Done000
Total191231

Merged error: 16.9b

Counts
31 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (cos eps))
0.1b
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b
(* (sin x) (sin eps))
2.8b
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
6×associate-*r* associate-*l*
4×diff-log
3×sub-neg cos-mult sin-mult
2×flip3-- pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod unswap-sqr
1×associate--l- frac-sub distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 70
Calls
4 calls:
4.0ms
(* (cos x) (cos eps))
5.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms
(* (sin x) (sin eps))
9.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series295.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (cos x) (cos eps))
82.0ms
(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
48.0ms
(* (sin x) (sin eps))
126.0ms
(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify116.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0304632
11061601
24487583
35002583

prune244.0ms

Filtered
82 candidates to 56 candidates (68.3%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New681482
Fresh7411
Picked101
Done000
Total761894

Merged error: 16.7b

Counts
94 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
0.6b
(cbrt (sin x))
2.8b
(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt *-un-lft-identity add-log-exp
7×add-cube-cbrt
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3 diff-log
2×sub-neg associate--l+
1×associate--l- flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 51
Calls
4 calls:
1.0ms
(cbrt (sin x))
1.0ms
(cbrt (sin x))
1.0ms
(cbrt (sin x))
9.0ms
(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

series421.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (sin x))
96.0ms
(cbrt (sin x))
104.0ms
(cbrt (sin x))
124.0ms
(- (- (* (cos x) (cos eps)) (* (* (cbrt (sin x)) (cbrt (sin x))) (* (cbrt (sin x)) (sin eps)))) (cos x))

simplify61.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 3 (55.0ms)

IterNodesCost
0187622
1481552
21873502
35002476

prune238.0ms

Filtered
63 candidates to 47 candidates (74.6%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New62163
Fresh01717
Picked011
Done000
Total621981

Merged error: 16.7b

Counts
81 → 19

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b
(pow (cos x) 3)
0.5b
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
2.6b
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
22×*-un-lft-identity
18×unpow-prod-down cube-prod
16×difference-of-squares
11×add-log-exp
10×add-cube-cbrt sqr-pow
6×pow1 add-exp-log pow-unpow add-cbrt-cube
5×distribute-lft-out--
4×cube-div
2×cube-mult pow-to-exp sub-neg associate-+l+ flip3-- pow-pow diff-log unpow3 pow-exp sum-log cos-mult flip-- sin-mult rem-cube-cbrt
1×difference-cubes +-commutative associate-+l- flip3-+ frac-sub flip-+ distribute-lft-out sub-div
Counts
4 → 100
Calls
4 calls:
8.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.0ms
(pow (cos x) 3)
6.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
20.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series836.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
28.0ms
(pow (cos x) 3)
109.0ms
(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
600.0ms
(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify100.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
05991433
128891321
250021320

prune384.0ms

Filtered
112 candidates to 70 candidates (62.5%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New9913112
Fresh11617
Picked101
Done011
Total11120131

Merged error: 16.6b

Counts
131 → 20

regimes299.0ms

Accuracy

84% (1.6b remaining)

Error of 15.4b against oracle of 13.8b and baseline of 24.0b

bsearch122.0ms

Steps
ItersRangePoint
9
2.1164709868071477e-11
0.0002141056345597589
7.062983208410759e-09
7
-3.110173650790201e-07
-6.09662256770312e-09
-2.7905907270542693e-08

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05157
15357
25357

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.8s4531×body1280valid
536.0ms608×body2560valid
415.0ms1873×body640valid
91.0ms616×body320valid
38.0ms291×body160valid
4.0ms81×body80valid