Details

sample99.0ms

Algorithm

intervals

Results

47.0ms	132×	body	1280	valid
16.0ms	19×	body	2560	valid
16.0ms	72×	body	640	valid
3.0ms	21×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	4×	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

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: 42.5b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.7b	(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))

simplify113.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

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

prune76.0ms

Filtered

30 candidates to 23 candidates (23.3%)

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: 15.0b

Counts

31 → 11

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))
3.3b	(- (- (* (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))
4.0ms	(- (* (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))
18.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
9.0ms	(* (sin x) (sin eps))
23.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify114.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (31.0ms)

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

prune133.0ms

Filtered

82 candidates to 56 candidates (31.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	69	13	82
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	78	15	93

Merged error: 14.8b

Counts

93 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
0.4b	(pow (cos x) 3)
0.5b	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
3.1b	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

rewrite34.0ms

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:

8.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
2.0ms	(pow (cos x) 3)
6.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
15.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

series196.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))
5.0ms	(pow (cos x) 3)
27.0ms	(pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3)
145.0ms	(- (pow (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) 3) (pow (cos x) 3))

simplify98.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	599	1433
1	2889	1321
2	5002	1280

prune241.0ms

Filtered

112 candidates to 63 candidates (43.8%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	97	15	112
Fresh	5	9	14
Picked	1	0	1
Done	0	0	0
Total	103	24	127

Merged error: 14.7b

Counts

127 → 24

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin eps))
0.4b	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
0.4b	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
3.3b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (sin x) (sin eps))
9.0ms	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
9.0ms	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
8.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series98.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin x) (sin eps))
24.0ms	(cbrt (pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3))
41.0ms	(pow (- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x))) 3)
24.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	439	1402
1	1856	1327
2	5003	1321

prune109.0ms

Filtered

99 candidates to 62 candidates (37.4%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	6	17	23
Picked	1	0	1
Done	0	0	0
Total	100	23	123

Merged error: 14.6b

Counts

123 → 23

regimes318.0ms

Accuracy

86.1% (1.4b remaining)

Error of 16.0b against oracle of 14.5b and baseline of 25.0b

bsearch68.0ms

Steps

Iters	Range		Point
7	1.2210739837988395e-17	1.9304018642174603e-15	1.8795608205420914e-15
8	-0.043109630562856945	-6.874330246037776e-05	-8.749548452425656e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	77
1	55	77

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	4374×	body	1280	valid
560.0ms	649×	body	2560	valid
421.0ms	1886×	body	640	valid
106.0ms	725×	body	320	valid
29.0ms	291×	body	160	valid
4.0ms	75×	body	80	valid

Details

sample99.0ms

simplify5.0ms

prune3.0ms

localize9.0ms

rewrite10.0ms

series14.0ms

simplify113.0ms

prune76.0ms

localize14.0ms

rewrite22.0ms

series58.0ms

simplify114.0ms

prune133.0ms

localize27.0ms

rewrite34.0ms

series196.0ms

simplify98.0ms

prune241.0ms

localize17.0ms

rewrite33.0ms

series98.0ms

simplify59.0ms

prune109.0ms

regimes318.0ms

bsearch68.0ms

simplify2.0ms

end0.0ms

sample2.9s

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