Details

Time bar (total: 4.9s)

sample93.0ms

Algorithm
intervals
Results
40.0ms101×body1280valid
25.0ms29×body2560valid
12.0ms52×body640valid
4.0ms23×body320valid
2.0ms36×body80valid
2.0ms15×body160valid

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: 38.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (sin (+ x eps)) (sin x))
2.9b
(sin (+ x eps))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt sin-sum add-cbrt-cube
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
11.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series58.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (sin (+ x eps)) (sin x))
19.0ms
(sin (+ x eps))

simplify142.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0133175
1301166
2937164
33445164
45001164

prune83.0ms

Filtered
30 candidates to 23 candidates (76.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831

Merged error: 17.5b

Counts
31 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin x) (cos eps))
0.1b
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b
(* (cos x) (sin eps))
3.5b
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite26.0ms

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*
2×diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-- flip3-+ associate--l+ sin-cos-mult flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 64
Calls
4 calls:
4.0ms
(* (sin x) (cos eps))
6.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms
(* (cos x) (sin eps))
9.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series283.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sin x) (cos eps))
85.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
46.0ms
(* (cos x) (sin eps))
111.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify38.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0308589
11168555
25001543

prune185.0ms

Filtered
76 candidates to 53 candidates (69.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New69776
Fresh707
Picked101
Done000
Total77784

Merged error: 0.4b

Counts
84 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b
(* (sin x) (- (cos eps) 1))
0.1b
(* (cos x) (sin eps))
1.6b
(- (cos eps) 1)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×*-un-lft-identity
10×associate-*r*
8×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
6×associate-*l*
5×sub-neg
4×distribute-rgt-in associate-+l+ distribute-lft-in difference-of-squares
2×flip3-- difference-of-sqr-1 associate-*r/ pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- unswap-sqr
1×+-commutative flip3-+ diff-log sum-log flip-+
Counts
4 → 77
Calls
4 calls:
8.0ms
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
8.0ms
(* (sin x) (- (cos eps) 1))
4.0ms
(* (cos x) (sin eps))
4.0ms
(- (cos eps) 1)

series214.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
47.0ms
(* (sin x) (- (cos eps) 1))
41.0ms
(* (cos x) (sin eps))
22.0ms
(- (cos eps) 1)

simplify41.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0337548
11280501
25001499

prune207.0ms

Filtered
89 candidates to 57 candidates (64.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New82789
Fresh156
Picked101
Done000
Total841296

Merged error: 0.0b

Counts
96 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos x))
0.3b
(cbrt (cos x))
0.3b
(cbrt (cos x))
1.6b
(- (cos eps) 1)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity
9×cbrt-prod
7×add-cube-cbrt
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
2×difference-of-squares
1×sub-neg flip3-- diff-log difference-of-sqr-1 flip-- distribute-lft-out--
Counts
4 → 49
Calls
4 calls:
1.0ms
(cbrt (cos x))
1.0ms
(cbrt (cos x))
1.0ms
(cbrt (cos x))
4.0ms
(- (cos eps) 1)

series352.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(cbrt (cos x))
94.0ms
(cbrt (cos x))
138.0ms
(cbrt (cos x))
19.0ms
(- (cos eps) 1)

simplify56.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0141258
1453233
21469226
35002226

prune156.0ms

Filtered
61 candidates to 45 candidates (73.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New59261
Fresh01111
Picked101
Done000
Total601373

Merged error: 0.0b

Counts
73 → 13

regimes114.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02623
12623

end0.0ms

sample2.7s

Algorithm
intervals
Results
1.3s3237×body1280valid
579.0ms654×body2560valid
438.0ms1857×body640valid
124.0ms786×body320valid
54.0ms1120×body80valid
42.0ms346×body160valid

Profiling

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