Details

sample97.0ms

Algorithm

intervals

Results

42.0ms	100×	body	1280	valid
21.0ms	23×	body	2560	valid
18.0ms	57×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	21×	body	160	valid
2.0ms	30×	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 (0.0%)

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: 40.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.8b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ 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` `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))

series63.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify140.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune82.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 16.8b

Counts

31 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
4.2b	(- (+ (* (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:

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

series489.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin x) (cos eps))
88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
244.0ms	(* (cos x) (sin eps))
114.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune219.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	72	12	84

Merged error: 0.3b

Counts

84 → 12

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))
2.1b	(- (cos eps) 1)

rewrite26.0ms

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)

series221.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (- (cos eps) 1))
47.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify45.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune237.0ms

Filtered

89 candidates to 55 candidates (61.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	86	15	101

Merged error: 0.0b

Counts

101 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (log (exp (- (cos eps) 1))))
0.2b	(* (cos x) (sin eps))
2.1b	(- (cos eps) 1)
2.2b	(log (exp (- (cos eps) 1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

9.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)
5.0ms	(log (exp (- (cos eps) 1)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
43.0ms	(* (cos x) (sin eps))
18.0ms	(- (cos eps) 1)
22.0ms	(log (exp (- (cos eps) 1)))

simplify135.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	287	592
1	1044	493
2	4516	482
3	5002	482

prune239.0ms

Filtered

104 candidates to 67 candidates (64.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	104	15	119

Merged error: 0.0b

Counts

119 → 15

regimes128.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3326×	body	1280	valid
555.0ms	608×	body	2560	valid
480.0ms	1878×	body	640	valid
133.0ms	739×	body	320	valid
60.0ms	1106×	body	80	valid
40.0ms	343×	body	160	valid