Details

sample97.0ms

Algorithm

intervals

Results

52.0ms	150×	body	1280	valid
18.0ms	21×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	5×	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: 39.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (cos (+ x eps)) (cos x))
3.3b	(cos (+ x eps))

rewrite11.0ms

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))

series20.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

simplify107.0ms

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

prune63.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 14.1b

Counts

31 → 9

localize13.0ms

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))
2.9b	(- (- (* (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:

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

8.0ms	(* (cos x) (cos eps))
18.0ms	(- (* (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))

simplify111.0ms

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

prune131.0ms

Filtered

57 candidates to 82 candidates (-43.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	75	16	91

Merged error: 14.0b

Counts

91 → 16

localize13.0ms

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))
2.9b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite26.0ms

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:

6.0ms	(* (cos x) (cos eps))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
8.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos x) (cos eps))
11.0ms	(+ (* (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 (34.0ms)

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

prune139.0ms

Filtered

53 candidates to 77 candidates (-45.3%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	73	20	93

Merged error: 13.9b

Counts

93 → 20

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (sin eps))
0.3b	(pow (* (sin x) (sin eps)) 3)
2.9b	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
26.3b	(cbrt (pow (* (sin x) (sin eps)) 3))

rewrite25.0ms

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)
11.0ms	(- (* (cos x) (cos eps)) (+ (cbrt (pow (* (sin x) (sin eps)) 3)) (cos x)))
3.0ms	(cbrt (pow (* (sin x) (sin eps)) 3))

series60.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (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))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

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

prune88.0ms

Filtered

58 candidates to 88 candidates (-51.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	18	19
Picked	0	1	1
Done	0	0	0
Total	87	21	108

Merged error: 13.9b

Counts

108 → 21

regimes272.0ms

Accuracy

81.7% (1.8b remaining)

Error of 16.3b against oracle of 14.5b and baseline of 24.3b

bsearch76.0ms

Steps

Iters	Range		Point
8	2.7788449623543706e-28	1.4606124828733529e-25	1.4423632138238029e-25
8	-0.0031172004064292094	-2.3041037433406002e-07	-2.6231847589922844e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	28
1	38	28

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4519×	body	1280	valid
561.0ms	658×	body	2560	valid
419.0ms	1804×	body	640	valid
95.0ms	639×	body	320	valid
34.0ms	287×	body	160	valid
5.0ms	93×	body	80	valid

Details

sample97.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series20.0ms

simplify107.0ms

prune63.0ms

localize13.0ms

rewrite24.0ms

series60.0ms

simplify111.0ms

prune131.0ms

localize13.0ms

rewrite26.0ms

series51.0ms

simplify41.0ms

prune139.0ms

localize17.0ms

rewrite25.0ms

series60.0ms

simplify50.0ms

prune88.0ms

regimes272.0ms

bsearch76.0ms

simplify1.0ms

end0.0ms

sample2.9s

Profiling