Details

analyze2.0ms

Algorithm: search

sample101.0ms

Algorithm

intervals

Results

59.0ms	148×	body	1280	valid
16.0ms	17×	body	2560	valid
13.0ms	60×	body	640	valid
4.0ms	24×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 39.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.0b	(cos (+ 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` `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))

series15.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify110.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	134	176
1	281	167
2	840	164
3	2958	164
4	5002	164

prune83.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	17	13	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	13	31

Merged error: 16.8b

Counts

31 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin x) (sin eps))
1.9b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite24.0ms

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:

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

series60.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
10.0ms	(* (cos x) (cos eps))
9.0ms	(* (sin x) (sin eps))
24.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4488	582
3	5001	582

prune142.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	68	14	82
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	77	18	95

Merged error: 16.6b

Counts

95 → 18

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
1.9b	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
29.1b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
8×	`cbrt-prod` `add-cube-cbrt`
3×	`pow-unpow` `diff-log` `associate-r` `associate-l` `sin-mult`
2×	`cube-div` `cube-mult` `sub-neg` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `associate--l+` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `cbrt-div` `flip3--` `pow1/3` `*-commutative` `flip--` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
7.0ms	(pow (* (sin x) (sin eps)) 3)
10.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series58.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
16.0ms	(pow (* (sin x) (sin eps)) 3)
23.0ms	(- (- (* (cos x) (cos eps)) (cbrt (pow (* (sin x) (sin eps)) 3))) (cos x))
9.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	293	636
1	1142	582
2	5002	567

prune161.0ms

Filtered

59 candidates to 90 candidates (-52.5%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	17	17
Picked	0	1	1
Done	0	0	0
Total	89	19	108

Merged error: 16.6b

Counts

108 → 19

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 3)
0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
1.7b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite36.0ms

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:

2.0ms	(pow (cos x) 3)
8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
16.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series200.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos x) 3)
19.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
29.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
147.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify97.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	599	1456
1	2881	1337
2	5001	1328

prune154.0ms

Filtered

63 candidates to 112 candidates (-77.8%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	98	14	112
Fresh	11	6	17
Picked	1	0	1
Done	0	1	1
Total	110	21	131

Merged error: 16.5b

Counts

131 → 21

regimes328.0ms

Accuracy

84% (1.6b remaining)

Error of 16.3b against oracle of 14.7b and baseline of 24.6b

bsearch89.0ms

Steps

Iters	Range		Point
8	2.5317959361117113e-12	6.570653690111025e-10	3.2432813869765597e-10
8	-0.03626708378964699	-6.466156276620261e-06	-6.744781525222824e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	52
1	50	52
2	50	52

end0.0ms

analyze6.0ms

Algorithm: search

sample3.0s

Algorithm

intervals

Results

1.7s	4442×	body	1280	valid
595.0ms	630×	body	2560	valid
420.0ms	1858×	body	640	valid
125.0ms	740×	body	320	valid
28.0ms	252×	body	160	valid
4.0ms	78×	body	80	valid

Details

analyze2.0ms

sample101.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series15.0ms

simplify110.0ms

prune83.0ms

localize13.0ms

rewrite24.0ms

series60.0ms

simplify113.0ms

prune142.0ms

localize16.0ms

rewrite26.0ms

series58.0ms

simplify40.0ms

prune161.0ms

localize25.0ms

rewrite36.0ms

series200.0ms

simplify97.0ms

prune154.0ms

regimes328.0ms

bsearch89.0ms

simplify2.0ms

end0.0ms

analyze6.0ms

sample3.0s

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