Details

sample96.0ms

Algorithm

intervals

Results

45.0ms	110×	body	1280	valid
15.0ms	16×	body	2560	valid
14.0ms	56×	body	640	valid
6.0ms	45×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	11×	body	160	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

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: 34.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ 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` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify134.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	133	175
1	301	165
2	937	164
3	3445	164
4	5001	164

prune58.0ms

Filtered

30 candidates to 23 candidates (23.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 13.0b

Counts

31 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
1.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin 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`
2×	`diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate--l+` `sin-cos-mult` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
8.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series59.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
9.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (cos eps))
23.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	554
2	5001	543

prune119.0ms

Filtered

76 candidates to 54 candidates (28.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	6	0	6
Picked	0	1	1
Done	0	0	0
Total	70	13	83

Merged error: 0.2b

Counts

83 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
1.9b	(- (cos eps) 1)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

8.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
7.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series44.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
9.0ms	(* (sin x) (- (cos eps) 1))
9.0ms	(* (cos x) (sin eps))
3.0ms	(- (cos eps) 1)

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	337	546
1	1279	498
2	5002	497

prune143.0ms

Filtered

89 candidates to 56 candidates (37.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	5	6	11
Picked	1	0	1
Done	1	0	1
Total	87	15	102

Merged error: 0.1b

Counts

102 → 15

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (sin x) (- (* (cos eps) (cos eps)) 1)) (+ (cos eps) 1))
0.3b	(* (cos eps) (cos eps))
0.4b	(+ (cos eps) 1)
1.9b	(- (* (cos eps) (cos eps)) 1)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
8×	`add-log-exp`
4×	`times-frac` `associate-/r*`
3×	`swap-sqr` `associate-r` `associate-l` `distribute-lft-out`
2×	`cbrt-undiv` `sqr-cos` `flip3--` `flip3-+` `associate-*r/` `div-exp` `prod-exp` `sub-1-cos` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/` `difference-of-squares`
1×	`+-commutative` `pow2` `sub-neg` `frac-2neg` `pow-plus` `diff-log` `difference-of-sqr-1` `distribute-frac-neg` `pow-prod-down` `associate--l+` `clear-num` `sum-log` `pow-sqr` `cos-mult` `-commutative` `pow-prod-up` `distribute-rgt-neg-out` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(/ (* (sin x) (- (* (cos eps) (cos eps)) 1)) (+ (cos eps) 1))
4.0ms	(* (cos eps) (cos eps))
4.0ms	(+ (cos eps) 1)
5.0ms	(- (* (cos eps) (cos eps)) 1)

series37.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* (sin x) (- (* (cos eps) (cos eps)) 1)) (+ (cos eps) 1))
3.0ms	(* (cos eps) (cos eps))
2.0ms	(+ (cos eps) 1)
5.0ms	(- (* (cos eps) (cos eps)) 1)

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	400	630
1	1943	515
2	5001	507

prune101.0ms

Filtered

96 candidates to 68 candidates (29.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	97	14	111

Merged error: 0.1b

Counts

111 → 14

regimes173.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	13
1	31	13
2	32	13
3	32	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3284×	body	1280	valid
571.0ms	621×	body	2560	valid
460.0ms	1802×	body	640	valid
136.0ms	800×	body	320	valid
57.0ms	1106×	body	80	valid
42.0ms	387×	body	160	valid

Details

sample96.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify134.0ms

prune58.0ms

localize16.0ms

rewrite24.0ms

series59.0ms

simplify38.0ms

prune119.0ms

localize15.0ms

rewrite25.0ms

series44.0ms

simplify42.0ms

prune143.0ms

localize17.0ms

rewrite27.0ms

series37.0ms

simplify55.0ms

prune101.0ms

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.9s

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