Details

Time bar (total: 4.8s)

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))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
4×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u sin-sum add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- diff-log diff-sin associate--l+ flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
7.0ms
(- (sin (+ x eps)) (sin x))
4.0ms
(sin (+ x eps))

series61.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (sin (+ x eps)) (sin x))
23.0ms
(sin (+ x eps))

simplify73.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0192386
1538285
22616275
35002220

prune104.0ms

Filtered
46 candidates to 31 candidates (67.4%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New361046
Fresh000
Picked101
Done000
Total371047

Merged error: 17.4b

Counts
47 → 10

localize13.0ms

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
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
11×add-log-exp
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u
3×fma-neg
2×diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
1×+-commutative sub-neg flip3-- fma-def flip3-+ associate--l+ sin-cos-mult flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 85
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))

series275.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (sin x) (cos eps))
84.0ms
(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
43.0ms
(* (cos x) (sin eps))
106.0ms
(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify49.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0373918
11424763
25002741

prune242.0ms

Filtered
97 candidates to 67 candidates (69.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New90797
Fresh909
Picked011
Done000
Total998107

Merged error: 0.4b

Counts
107 → 8

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
12×add-cube-cbrt
9×prod-diff
6×add-exp-log
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u fma-neg associate-*r* associate-*l* log1p-expm1-u
2×difference-of-squares
1×sub-neg expm1-def flip3-- diff-log difference-of-sqr-1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod fma-udef distribute-lft-out-- unswap-sqr
Counts
3 → 61
Calls
3 calls:
1.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
4.0ms
(* (cos x) (sin eps))
5.0ms
(- (cos eps) 1)

series172.0ms

Counts
3 → 9
Calls
3 calls:
107.0ms
(fma (sin x) (- (cos eps) 1) (* (cos x) (sin eps)))
42.0ms
(* (cos x) (sin eps))
23.0ms
(- (cos eps) 1)

simplify100.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (94.0ms)

IterNodesCost
0276442
1932347
23460325
35001303

prune182.0ms

Filtered
70 candidates to 45 candidates (64.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New61970
Fresh516
Picked101
Done011
Total671178

Merged error: 0.0b

Counts
78 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (cos x) (sin eps))
0.1b
(log1p (expm1 (* (cos x) (sin eps))))
0.1b
(expm1 (* (cos x) (sin eps)))
1.6b
(- (cos eps) 1)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cube-cbrt
9×prod-diff
7×add-exp-log
6×pow1 add-cbrt-cube add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u
3×fma-neg associate-*r* associate-*l*
2×difference-of-squares
1×sub-neg expm1-def log1p-udef expm1-log1p flip3-- diff-log difference-of-sqr-1 log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- expm1-udef unswap-sqr
Counts
4 → 73
Calls
4 calls:
4.0ms
(* (cos x) (sin eps))
3.0ms
(log1p (expm1 (* (cos x) (sin eps))))
1.0ms
(expm1 (* (cos x) (sin eps)))
5.0ms
(- (cos eps) 1)

series209.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (cos x) (sin eps))
76.0ms
(log1p (expm1 (* (cos x) (sin eps))))
71.0ms
(expm1 (* (cos x) (sin eps)))
18.0ms
(- (cos eps) 1)

simplify94.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 3 (87.0ms)

IterNodesCost
0271459
1898365
23240343
35001320

prune187.0ms

Filtered
85 candidates to 52 candidates (61.2%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New85085
Fresh099
Picked011
Done011
Total851196

Merged error: 0.0b

Counts
96 → 11

regimes96.0ms

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
0159
1159

end0.0ms

sample2.8s

Algorithm
intervals
Results
1.3s3237×body1280valid
577.0ms654×body2560valid
446.0ms1857×body640valid
133.0ms786×body320valid
63.0ms1120×body80valid
36.0ms346×body160valid

Profiling

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