Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample99.0ms

Algorithm

intervals

Results

57.0ms	161×	body	1280	valid
14.0ms	15×	body	2560	valid
12.0ms	55×	body	640	valid
6.0ms	7×	body	160	valid
2.0ms	14×	body	320	valid
0.0ms	4×	body	80	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune3.0ms

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: 37.6b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
4.0b	(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 → 23

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))

simplify60.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4816	270
1	4816	270

prune63.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	21	8	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	8	30

Merged error: 0.4b

Counts

30 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
4.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

10.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
5.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
8.0ms	(sin (/ (+ x (+ x eps)) 2))

series35.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms	(+ x (+ x eps))
12.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4847	891
1	4847	891

prune163.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	65	15	80

Merged error: 0.3b

Counts

80 → 15

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sin (/ eps 2)) -2)
0.0b	(+ x (+ x eps))
0.3b	(* (* (sin (/ eps 2)) -2) (sin (/ (+ x (+ x eps)) 2)))
4.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

4.0ms	(* (sin (/ eps 2)) -2)
5.0ms	(+ x (+ x eps))
12.0ms	(* (* (sin (/ eps 2)) -2) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

series27.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sin (/ eps 2)) -2)
4.0ms	(+ x (+ x eps))
14.0ms	(* (* (sin (/ eps 2)) -2) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5630	699

prune140.0ms

Filtered

48 candidates to 70 candidates (-45.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	70	15	85

Merged error: 0.3b

Counts

85 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
4.0b	(sin (/ (+ x (+ x eps)) 2))
4.0b	(sin (/ (+ x (+ x eps)) 2))
4.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

5.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

series38.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify57.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4907	469
1	4907	469

prune123.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	44	15	59

Merged error: 0.3b

Counts

59 → 15

regimes312.0ms

Accuracy

93.6% (0.9b remaining)

Error of 1.3b against oracle of 0.4b and baseline of 14.7b

bsearch95.0ms

Steps

Iters	Range		Point
10	3.14523817394636e-14	52.849086929477764	2.9676922165611374e-05
7	-2.3599329975581476e+28	-1.328589091502893e+26	-1.35117877873764e+26

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample3.0s

Algorithm

intervals

Results

1.7s	4467×	body	1280	valid
616.0ms	655×	body	2560	valid
430.0ms	1825×	body	640	valid
105.0ms	676×	body	320	valid
37.0ms	291×	body	160	valid
5.0ms	86×	body	80	valid

Details

analyze2.0ms

sample99.0ms

simplify2.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify60.0ms

prune63.0ms

localize13.0ms

rewrite35.0ms

series35.0ms

simplify58.0ms

prune163.0ms

localize13.0ms

rewrite30.0ms

series27.0ms

simplify52.0ms

prune140.0ms

localize20.0ms

rewrite25.0ms

series38.0ms

simplify57.0ms

prune123.0ms

regimes312.0ms

bsearch95.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.0s

Profiling