Details

analyze2.0ms

Algorithm

Search

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

sample97.0ms

Algorithm

intervals

Results

52.0ms	116×	body	1280	valid
15.0ms	57×	body	640	valid
14.0ms	15×	body	2560	valid
4.0ms	22×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	12×	body	160	valid

simplify3.0ms

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: 37.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
4.1b	(sin (+ x eps))

rewrite17.0ms

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:

7.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4933	268
1	4933	268

prune48.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	4	30

Merged error: 0.2b

Counts

30 → 4

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))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
4.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite26.0ms

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))

series32.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* 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))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4990	887
1	4990	887

prune136.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	68	8	76

Merged error: 0.2b

Counts

76 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (sin (/ eps 2)))
0.0b	(+ x (+ x eps))
0.2b	(* (* 2 (sin (/ eps 2))) (cos (/ (+ x (+ x eps)) 2)))
4.2b	(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-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:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 2 (sin (/ eps 2)))
4.0ms	(+ x (+ x eps))
12.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (+ x (+ x eps)) 2)))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify40.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4934	700
1	4934	700

prune295.0ms

Filtered

48 candidates to 70 candidates (-45.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	72	6	78

Merged error: 0.2b

Counts

78 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.4b	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
0.5b	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
4.2b	(cos (/ (+ x (+ x eps)) 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
2.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
2.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
9.0ms	(cos (/ (+ x (+ x eps)) 2))

series34.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
6.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
12.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5226	1255

prune132.0ms

Filtered

59 candidates to 97 candidates (-64.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	97	6	103

Merged error: 0.2b

Counts

103 → 6

regimes128.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.7b

bsearch113.0ms

Steps

Iters	Range		Point
10	3.14523817394636e-14	52.849086929477764	6.897912047083434e-09
9	-4.978065389594377e-07	-1.8958666446607609e-16	-9.845370976900334e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	51
1	35	51

end0.0ms

analyze1.0ms

Algorithm

Search

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

sample3.2s

Algorithm

intervals

Results

1.6s	3341×	body	1280	valid
644.0ms	655×	body	2560	valid
512.0ms	1807×	body	640	valid
146.0ms	766×	body	320	valid
64.0ms	1066×	body	80	valid
47.0ms	365×	body	160	valid

Details

analyze2.0ms

sample97.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite17.0ms

series13.0ms

simplify38.0ms

prune48.0ms

localize13.0ms

rewrite26.0ms

series32.0ms

simplify40.0ms

prune136.0ms

localize13.0ms

rewrite25.0ms

series25.0ms

simplify40.0ms

prune295.0ms

localize16.0ms

rewrite24.0ms

series34.0ms

simplify53.0ms

prune132.0ms

regimes128.0ms

bsearch113.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample3.2s

Profiling