Details

Time bar (total: 4.3s)

sample103.0ms

Algorithm
intervals
Results
45.0ms101×body1280valid
22.0ms24×body2560valid
18.0ms69×body640valid
4.0ms21×body320valid
2.0ms30×body80valid
1.0ms11×body160valid

simplify12.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (7.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.4b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (sin (+ x eps)) (sin x))
3.7b
(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))

series14.0ms

Counts
2 → 6
Calls
2 calls:
8.0ms
(- (sin (+ x eps)) (sin x))
6.0ms
(sin (+ x eps))

simplify140.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0133175
1301165
2937164
33445164
45001164

prune64.0ms

Filtered
30 candidates to 23 candidates (23.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831

Merged error: 16.7b

Counts
31 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sin x) (cos eps))
0.1b
(- (* (cos x) (sin eps)) (sin x))
0.1b
(* (cos x) (sin eps))
2.7b
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite23.0ms

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:
5.0ms
(* (sin x) (cos eps))
4.0ms
(- (* (cos x) (sin eps)) (sin x))
4.0ms
(* (cos x) (sin eps))
8.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series52.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin x) (cos eps))
11.0ms
(- (* (cos x) (sin eps)) (sin x))
9.0ms
(* (cos x) (sin eps))
23.0ms
(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0348614
11352580
25002565

prune119.0ms

Filtered
78 candidates to 55 candidates (29.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New671178
Fresh707
Picked101
Done000
Total751186

Merged error: 0.2b

Counts
86 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b
(* (cos x) (sin eps))
0.2b
(* (sin x) (- (cos eps) 1))
2.3b
(- (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)))
4.0ms
(* (cos x) (sin eps))
7.0ms
(* (sin x) (- (cos eps) 1))
4.0ms
(- (cos eps) 1)

series42.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
9.0ms
(* (cos x) (sin eps))
10.0ms
(* (sin x) (- (cos eps) 1))
3.0ms
(- (cos eps) 1)

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0337546
11279498
25002497

prune135.0ms

Filtered
89 candidates to 56 candidates (37.1%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New82789
Fresh3710
Picked101
Done000
Total8614100

Merged error: 0.1b

Counts
100 → 14

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos eps) (cos eps))
0.3b
(pow (cos eps) 3)
0.3b
(+ (* 1 1) (* (cos eps) 1))
2.2b
(- (pow (cos eps) 3) 1)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
17×*-un-lft-identity
12×pow1
11×add-cube-cbrt
8×add-log-exp difference-of-squares
7×add-exp-log add-cbrt-cube
6×unpow-prod-down cube-prod
4×difference-of-sqr-1 sqr-pow
3×pow-unpow swap-sqr associate-*r* associate-*l*
1×+-commutative pow2 cube-mult pow-to-exp sub-neg sqr-cos distribute-rgt-out flip3-- pow-pow flip3-+ pow-plus diff-log unpow3 pow-prod-down pow-exp prod-exp sum-log pow-sqr cos-mult *-commutative pow-prod-up flip-- cbrt-unprod flip-+ distribute-lft-out-- rem-cube-cbrt unswap-sqr
Counts
4 → 87
Calls
4 calls:
4.0ms
(* (cos eps) (cos eps))
2.0ms
(pow (cos eps) 3)
5.0ms
(+ (* 1 1) (* (cos eps) 1))
7.0ms
(- (pow (cos eps) 3) 1)

series16.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* (cos eps) (cos eps))
5.0ms
(pow (cos eps) 3)
2.0ms
(+ (* 1 1) (* (cos eps) 1))
7.0ms
(- (pow (cos eps) 3) 1)

simplify64.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0337404
11642366
25002345

prune103.0ms

Filtered
99 candidates to 56 candidates (43.4%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New98199
Fresh01313
Picked011
Done000
Total9815113

Merged error: 0.1b

Counts
113 → 15

regimes180.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02717
13217
23217

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.5s3292×body1280valid
573.0ms622×body2560valid
495.0ms1847×body640valid
131.0ms754×body320valid
72.0ms1103×body80valid
45.0ms382×body160valid

Profiling

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