Details

sample99.0ms

Algorithm

intervals

Results

39.0ms	94×	body	1280	valid
22.0ms	25×	body	2560	valid
21.0ms	65×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	44×	body	80	valid
1.0ms	8×	body	160	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: 35.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
4.5b	(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))

series62.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify141.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (11.0ms)

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

prune75.0ms

Filtered

30 candidates to 23 candidates (76.7%)

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: 14.0b

Counts

31 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
1.7b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite24.0ms

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×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

5.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
9.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* (cos x) (sin eps)) (sin x))
41.0ms	(* (cos x) (sin eps))
48.0ms	(* (sin x) (cos eps))
111.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune202.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 0.6b

Counts

85 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
2.3b	(- (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)))
4.0ms	(* (cos x) (sin eps))
8.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(- (cos eps) 1)

series226.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
48.0ms	(* (cos x) (sin eps))
44.0ms	(* (sin x) (- (cos eps) 1))
24.0ms	(- (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

prune218.0ms

Filtered

89 candidates to 57 candidates (64.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	85	11	96

Merged error: 0.1b

Counts

96 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (log (exp (- (cos eps) 1))))
2.3b	(log (exp (- (cos eps) 1)))
2.3b	(- (cos eps) 1)

rewrite30.0ms

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:

4.0ms	(* (cos x) (sin eps))
9.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
5.0ms	(log (exp (- (cos eps) 1)))
8.0ms	(- (cos eps) 1)

series130.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
51.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
18.0ms	(log (exp (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)

simplify134.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	287	592
1	1034	493
2	4506	482
3	5002	482

prune232.0ms

Filtered

104 candidates to 66 candidates (63.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	104	11	115

Merged error: 0.1b

Counts

115 → 11

regimes101.0ms

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	16	8
1	16	8

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	3303×	body	1280	valid
560.0ms	614×	body	2560	valid
454.0ms	1831×	body	640	valid
124.0ms	780×	body	320	valid
57.0ms	1147×	body	80	valid
36.0ms	325×	body	160	valid