Details

analyze1.0ms

Algorithm

Search

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

sample106.0ms

Algorithm

intervals

Results

48.0ms	97×	body	1280	valid
25.0ms	27×	body	2560	valid
16.0ms	56×	body	640	valid
6.0ms	32×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 38.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

2.1b	(- (sin (+ x eps)) (sin x))
2.4b	(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 → 23

Calls

2 calls:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify42.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5348	268

prune45.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.4b

Counts

30 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite25.0ms

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-cos-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

7.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
5.0ms	(+ x (+ x eps))
5.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series34.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2))))
4.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5222	886

prune139.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	9	75

Merged error: 0.3b

Counts

75 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ x (+ x eps)) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
0.5b	(log (exp (cos (/ (+ x (+ x eps)) 2))))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

7.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
14.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
7.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series30.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (cos (/ (+ x (+ x eps)) 2)))
10.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ x (+ x eps)) 2)))))
5.0ms	(log (exp (cos (/ (+ x (+ x eps)) 2))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5064	940

prune156.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	73	9	82

Merged error: 0.3b

Counts

82 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
0.4b	(* (sin (/ eps 2)) (sqrt 2))
0.5b	(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
2.3b	(cos (/ (+ x (+ x eps)) 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-r`
7×	`sqrt-prod`
4×	`add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`

Counts

4 → 71

Calls

4 calls:

7.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
6.0ms	(* (sin (/ eps 2)) (sqrt 2))
10.0ms	(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series49.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2)))
5.0ms	(* (sin (/ eps 2)) (sqrt 2))
20.0ms	(* (sqrt 2) (* (cos (/ (+ x (+ x eps)) 2)) (* (sin (/ eps 2)) (sqrt 2))))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4927	1100
1	4927	1100

prune144.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	82	10	92

Merged error: 0.3b

Counts

92 → 10

regimes172.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.2b

bsearch27.0ms

Steps

Iters	Range		Point
1	2.120527876560294e-10	2.1947139214049714e-10	2.176167410193802e-10
5	-2.6358487214306052e-08	-1.0900084561437634e-08	-1.135616610718635e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	3292×	body	1280	valid
606.0ms	634×	body	2560	valid
501.0ms	1845×	body	640	valid
153.0ms	753×	body	320	valid
72.0ms	1122×	body	80	valid
44.0ms	354×	body	160	valid

Details

analyze1.0ms

sample106.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series12.0ms

simplify42.0ms

prune45.0ms

localize13.0ms

rewrite25.0ms

series34.0ms

simplify45.0ms

prune139.0ms

localize17.0ms

rewrite37.0ms

series30.0ms

simplify46.0ms

prune156.0ms

localize14.0ms

rewrite31.0ms

series49.0ms

simplify53.0ms

prune144.0ms

regimes172.0ms

bsearch27.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling