Details

Time bar (total: 4.3s)

sample99.0ms

Algorithm
intervals
Results
43.0ms99×body1280valid
22.0ms20×body2560valid
15.0ms61×body640valid
4.0ms21×body320valid
2.0ms46×body80valid
1.0ms9×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

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:

1.6b
(- (sin (+ x eps)) (sin x))
3.2b
(sin (+ x eps))

rewrite10.0ms

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:
6.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series13.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(- (sin (+ x eps)) (sin x))
5.0ms
(sin (+ x eps))

simplify139.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (9.0ms)

IterNodesCost
0133175
1301165
2937164
33445164
45001164

prune64.0ms

Filtered
23 candidates to 30 candidates (-30.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831

Merged error: 14.4b

Counts
31 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin x) (cos eps))
0.2b
(* (cos x) (sin eps))
0.2b
(- (* (cos x) (sin eps)) (sin x))
3.0b
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
11×add-log-exp
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
3×sin-cos-mult
2×sub-neg associate-+r+ flip3-- diff-log pow-prod-down frac-add prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
1×+-commutative associate-+r- flip3-+ flip-+
Counts
4 → 66
Calls
4 calls:
4.0ms
(* (sin x) (cos eps))
4.0ms
(* (cos x) (sin eps))
4.0ms
(- (* (cos x) (sin eps)) (sin x))
8.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series49.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (sin x) (cos eps))
8.0ms
(* (cos x) (sin eps))
11.0ms
(- (* (cos x) (sin eps)) (sin x))
21.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify42.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0348614
11352580
25002565

prune124.0ms

Filtered
55 candidates to 78 candidates (-41.8%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New671178
Fresh707
Picked101
Done000
Total751186

Merged error: 0.3b

Counts
86 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos x) (sin eps))
0.2b
(* (sin x) (- (cos eps) 1))
0.2b
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
2.5b
(- (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:
4.0ms
(* (cos x) (sin eps))
8.0ms
(* (sin x) (- (cos eps) 1))
8.0ms
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms
(- (cos eps) 1)

series40.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (cos x) (sin eps))
8.0ms
(* (sin x) (- (cos eps) 1))
20.0ms
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
3.0ms
(- (cos eps) 1)

simplify42.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0337546
11279498
25001497

prune139.0ms

Filtered
56 candidates to 89 candidates (-58.9%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New82789
Fresh4610
Picked101
Done000
Total8713100

Merged error: 0.1b

Counts
100 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin x) (- (cos eps) 1))
0.2b
(+ (log (exp (* (sin x) (- (cos eps) 1)))) (* (cos x) (sin eps)))
2.5b
(- (cos eps) 1)
3.1b
(log (exp (* (sin x) (- (cos eps) 1))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×log-prod *-un-lft-identity
8×add-cube-cbrt exp-sum add-log-exp
7×pow1 sub-neg associate-+l+ associate-*r*
6×add-exp-log distribute-rgt-in distribute-lft-in add-cbrt-cube
4×difference-of-squares
3×associate-*l* log-pow
2×flip3-- difference-of-sqr-1 associate-*r/ flip-- distribute-lft-out--
1×+-commutative exp-prod exp-to-pow flip3-+ diff-log rem-log-exp pow-prod-down prod-exp sum-log *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 80
Calls
4 calls:
8.0ms
(* (sin x) (- (cos eps) 1))
6.0ms
(+ (log (exp (* (sin x) (- (cos eps) 1)))) (* (cos x) (sin eps)))
4.0ms
(- (cos eps) 1)
3.0ms
(log (exp (* (sin x) (- (cos eps) 1))))

series43.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(* (sin x) (- (cos eps) 1))
21.0ms
(+ (log (exp (* (sin x) (- (cos eps) 1)))) (* (cos x) (sin eps)))
3.0ms
(- (cos eps) 1)
11.0ms
(log (exp (* (sin x) (- (cos eps) 1))))

simplify41.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0316627
11122561
25001560

prune102.0ms

Filtered
60 candidates to 92 candidates (-53.3%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh01212
Picked011
Done000
Total9213105

Merged error: 0.1b

Counts
105 → 13

regimes163.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01810
11810

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s3259×body1280valid
585.0ms647×body2560valid
476.0ms1820×body640valid
132.0ms759×body320valid
63.0ms1157×body80valid
57.0ms358×body160valid

Profiling

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