Details

sample108.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

57.0ms	139×	body	1280	valid
21.0ms	22×	body	2560	valid
15.0ms	66×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

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: 41.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
2.5b	(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))

simplify109.0ms

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

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	20	10	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	10	31

Merged error: 16.1b

Counts

31 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
3.8b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite23.0ms

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))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (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))

simplify113.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	304	632
1	1061	600
2	4487	582
3	5002	582

prune147.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	75	17	92

Merged error: 15.9b

Counts

92 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
3.8b	(- (* (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:

8.0ms	(* (cos x) (cos eps))
13.0ms	(+ (* (sin x) (sin eps)) (cos x))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (35.0ms)

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

prune148.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	75	19	94

Merged error: 15.9b

Counts

94 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
0.2b	(* (cos x) (cos x))
0.3b	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
4.5b	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
18×	`pow-prod-down`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
7×	`cos-mult` `associate-/l/`
6×	`add-log-exp`
5×	`pow-sqr` `pow-prod-up`
4×	`swap-sqr` `associate-r` `associate-l` `frac-sub` `associate-/l*` `difference-of-squares`
3×	`flip3--` `pow-plus` `associate-r/` `associate-l/` `associate-/r*` `flip--`
2×	`pow2` `frac-times` `div-sub` `associate-/r/` `*-commutative` `sub-div`
1×	`cbrt-undiv` `sub-neg` `sqr-cos` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv` `associate--r-` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

19.0ms	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
5.0ms	(* (cos x) (cos x))
9.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
14.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

series130.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x)))
3.0ms	(* (cos x) (cos x))
16.0ms	(* (* (sin x) (sin eps)) (* (sin x) (sin eps)))
72.0ms	(- (* (cos x) (cos eps)) (/ (- (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (cos x) (cos x))) (- (* (sin x) (sin eps)) (cos x))))

simplify88.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	557	1733
1	2820	1445
2	5001	1407

prune133.0ms

Filtered

85 candidates to 131 candidates (-54.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	124	7	131
Fresh	1	17	18
Picked	1	0	1
Done	0	0	0
Total	126	24	150

Merged error: 15.9b

Counts

150 → 24

regimes337.0ms

Accuracy

84.7% (1.6b remaining)

Error of 15.9b against oracle of 14.4b and baseline of 24.6b

bsearch87.0ms

Steps

Iters	Range		Point
5	1.270496468348448e-09	2.9622670384345826e-09	2.9265808001381974e-09
9	-0.00023605401382188198	-1.5850919254858696e-12	-6.660131394398538e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	17
1	36	17

end0.0ms

sample3.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0.097632%

Space saved by search: 0.097632%

Guaranteed chance to sample good point: 0%

Results

1.7s	4336×	body	1280	valid
609.0ms	663×	body	2560	valid
486.0ms	1958×	body	640	valid
112.0ms	689×	body	320	valid
37.0ms	276×	body	160	valid
5.0ms	78×	body	80	valid

Details

sample108.0ms

simplify5.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify109.0ms

prune77.0ms

localize17.0ms

rewrite23.0ms

series58.0ms

simplify113.0ms

prune147.0ms

localize14.0ms

rewrite23.0ms

series53.0ms

simplify41.0ms

prune148.0ms

localize18.0ms

rewrite50.0ms

series130.0ms

simplify88.0ms

prune133.0ms

regimes337.0ms

bsearch87.0ms

simplify1.0ms

end0.0ms

sample3.1s

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