Details

sample88.0ms

Algorithm

intervals

Results

48.0ms	144×	body	1280	valid
14.0ms	17×	body	2560	valid
13.0ms	64×	body	640	valid
3.0ms	18×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	6×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 40.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
2.2b	(cos (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `cos-sum` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `+-commutative` `associate--l-` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify107.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	134	187
1	274	178
2	810	175
3	2813	175
4	5001	175

prune85.0ms

Filtered

32 candidates to 24 candidates (25.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	21	11	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	11	33

Merged error: 16.3b

Counts

33 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin eps) (sin x)) (cos x))
0.1b	(* (cos x) (cos eps))
0.2b	(* (sin eps) (sin x))
3.6b	(- (* (cos x) (cos eps)) (+ (* (sin eps) (sin x)) (cos x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
12×	`associate-l`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `distribute-lft-out` `distribute-lft-out--`
3×	`cos-mult` `unswap-sqr`
2×	`+-commutative` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `associate--r+` `difference-of-squares`
1×	`sub-neg` `flip3--` `flip--` `sin-mult`

Counts

4 → 76

Calls

4 calls:

10.0ms	(+ (* (sin eps) (sin x)) (cos x))
4.0ms	(* (cos x) (cos eps))
5.0ms	(* (sin eps) (sin x))
18.0ms	(- (* (cos x) (cos eps)) (+ (* (sin eps) (sin x)) (cos x)))

series295.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (* (sin eps) (sin x)) (cos x))
45.0ms	(* (cos x) (cos eps))
46.0ms	(* (sin eps) (sin x))
137.0ms	(- (* (cos x) (cos eps)) (+ (* (sin eps) (sin x)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	345	722
1	1305	690
2	5002	673

prune406.0ms

Filtered

88 candidates to 59 candidates (33.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	89	10	99

Merged error: 0.3b

Counts

99 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
0.1b	(* (cos x) (- (cos eps) 1))
0.2b	(* (sin eps) (sin x))
1.6b	(- (cos eps) 1)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
10×	`associate-r` `associate-l`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
6×	`sub-neg` `distribute-lft-out--` `unswap-sqr`
4×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*r/` `associate--l+` `flip--`
3×	`sin-mult`
2×	`diff-log` `difference-of-sqr-1` `pow-prod-down` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod`

Counts

4 → 89

Calls

4 calls:

21.0ms	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
7.0ms	(* (cos x) (- (cos eps) 1))
7.0ms	(* (sin eps) (sin x))
4.0ms	(- (cos eps) 1)

series264.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
67.0ms	(* (cos x) (- (cos eps) 1))
48.0ms	(* (sin eps) (sin x))
20.0ms	(- (cos eps) 1)

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	353	727
1	1310	682
2	5002	675

prune247.0ms

Filtered

101 candidates to 65 candidates (35.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	95	16	111

Merged error: 0.1b

Counts

111 → 16

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos eps) (cos eps))
0.3b	(+ (* 1 1) (* (cos eps) 1))
0.3b	(pow (cos eps) 3)
1.4b	(- (pow (cos eps) 3) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
12×	`pow1` `add-cube-cbrt` `associate-r` `distribute-lft-out`
10×	`associate-l` `*-commutative`
8×	`distribute-rgt-out` `add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `difference-of-squares`
4×	`sqr-pow`
3×	`pow-unpow` `difference-of-sqr-1` `swap-sqr`
1×	`+-commutative` `pow2` `pow-to-exp` `sub-neg` `sqr-cos` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

5.0ms	(* (cos eps) (cos eps))
17.0ms	(+ (* 1 1) (* (cos eps) 1))
2.0ms	(pow (cos eps) 3)
6.0ms	(- (pow (cos eps) 3) 1)

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (cos eps) (cos eps))
11.0ms	(+ (* 1 1) (* (cos eps) 1))
29.0ms	(pow (cos eps) 3)
51.0ms	(- (pow (cos eps) 3) 1)

simplify55.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	356	416
1	1684	375
2	5003	355

prune238.0ms

Filtered

111 candidates to 57 candidates (48.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	2	13	15
Picked	1	0	1
Done	0	0	0
Total	110	17	127

Merged error: 0.1b

Counts

127 → 17

regimes192.0ms

Accuracy

93.4% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 6.5b

bsearch150.0ms

Steps

Iters	Range		Point
9	0.0004381094517774334	45.72067326335533	0.03378383009651785
10	-69.11608992374592	-3.290670417289015e-13	-0.03371359321114002

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	37
1	60	37
2	60	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4435×	body	1280	valid
527.0ms	610×	body	2560	valid
428.0ms	1890×	body	640	valid
100.0ms	688×	body	320	valid
31.0ms	301×	body	160	valid
4.0ms	76×	body	80	valid