Details

analyze2.0ms

Algorithm: search

sample102.0ms

Algorithm

intervals

Results

47.0ms	130×	body	1280	valid
27.0ms	26×	body	2560	valid
16.0ms	69×	body	640	valid
3.0ms	20×	body	320	valid
1.0ms	9×	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: 41.8b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
5.7b	(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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify110.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

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

prune77.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	19	11	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	11	31

Merged error: 15.5b

Counts

31 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.3b	(* (sin x) (sin eps))
2.4b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos 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×	`cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip--` `sin-mult` `associate--r+`

Counts

4 → 65

Calls

4 calls:

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

series53.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cos x) (cos eps))
10.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	332	607
1	1284	574
2	5002	565

prune138.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	63	14	77
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	68	20	88

Merged error: 15.3b

Counts

88 → 20

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.3b	(* (sin x) (sin eps))
2.4b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite22.0ms

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:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cos x) (cos eps))
23.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
24.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify167.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	304	633
1	1061	601
2	4487	582
3	5002	582

prune200.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	84	18	102

Merged error: 15.3b

Counts

102 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.4b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
27.9b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

5.0ms	(* (sin x) (sin eps))
5.0ms	(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))

series55.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
15.0ms	(pow (* (sin x) (sin eps)) 3)
22.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
9.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	374	684
1	1626	609
2	5001	596

prune86.0ms

Filtered

58 candidates to 88 candidates (-51.7%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	88	18	106

Merged error: 15.3b

Counts

106 → 18

regimes258.0ms

Accuracy

83.5% (1.6b remaining)

Error of 16.1b against oracle of 14.5b and baseline of 24.2b

bsearch103.0ms

Steps

Iters	Range		Point
9	4.299395115198124e-15	4.175266024993839e-08	3.184154944205606e-09
9	-2014.1507951608808	-6.901433889594804e-06	-7.006329774326013e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

analyze1.0ms

Algorithm: search

sample3.0s

Algorithm

intervals

Results

1.6s	4408×	body	1280	valid
585.0ms	635×	body	2560	valid
440.0ms	1885×	body	640	valid
105.0ms	674×	body	320	valid
36.0ms	315×	body	160	valid
5.0ms	83×	body	80	valid

Details

analyze2.0ms

sample102.0ms

simplify4.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify110.0ms

prune77.0ms

localize14.0ms

rewrite23.0ms

series53.0ms

simplify42.0ms

prune138.0ms

localize14.0ms

rewrite22.0ms

series66.0ms

simplify167.0ms

prune200.0ms

localize19.0ms

rewrite24.0ms

series55.0ms

simplify53.0ms

prune86.0ms

regimes258.0ms

bsearch103.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.0s

Profiling