Details

analyze228.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

sample60.0ms

Algorithm

intervals

Results

28.0ms	55×	body	2560	valid
9.0ms	35×	body	1280	valid
9.0ms	53×	body	640	valid
3.0ms	30×	body	320	valid
3.0ms	71×	body	80	valid
1.0ms	12×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	500	8
1	500	8

prune7.0ms

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: 33.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b	(- 1.0 (cos x))
15.3b	(/ (- 1.0 (cos x)) (* x x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-exp-log` `add-cbrt-cube`
5×	`times-frac` `associate-/l*`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

2 → 41

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
7.0ms	(/ (- 1.0 (cos x)) (* x x))

series9.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(- 1.0 (cos x))
6.0ms	(/ (- 1.0 (cos x)) (* x x))

simplify48.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4894	437
1	4894	437

prune80.0ms

Filtered

34 candidates to 47 candidates (-38.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	40	7	47
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Merged error: 0.1b

Counts

48 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (* x -1/24))
0.1b	(* (pow x 4) 1/720)
0.3b	(* x -1/24)
12.0b	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log`
13×	`associate-l` `add-cbrt-cube`
11×	`pow1`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
7×	`associate-r` `prod-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `pow-prod-down` `unswap-sqr`
3×	`sum-log` `*-commutative`
2×	`sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(* x (* x -1/24))
5.0ms	(* (pow x 4) 1/720)
3.0ms	(* x -1/24)
7.0ms	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

series13.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* x (* x -1/24))
4.0ms	(* (pow x 4) 1/720)
2.0ms	(* x -1/24)
5.0ms	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))

simplify41.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4973	646
1	4973	646

prune109.0ms

Filtered

53 candidates to 86 candidates (-62.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	85	9	94

Merged error: 0.1b

Counts

94 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

12.0b	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))
12.8b	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
12.8b	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
12.8b	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`pow1/3` `sum-log`
1×	`+-commutative` `associate-+r+`

Counts

4 → 52

Calls

4 calls:

7.0ms	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))
6.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
6.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
6.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24))))
13.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
13.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))
16.0ms	(cbrt (+ (* (pow x 4) 1/720) (+ 1/2 (* x (* x -1/24)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5300	1343

prune223.0ms

Filtered

53 candidates to 64 candidates (-20.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
0.1b	(/ (- 1.0 (cos x)) x)
2.0b	(- 1.0 (cos x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`add-exp-log`
19×	`associate-r`
17×	`add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
6×	`unswap-sqr`
5×	`pow1` `cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`cbrt-unprod`
3×	`associate-/r*` `div-inv`
2×	`rec-exp` `flip3--` `1-exp` `flip--` `associate-/l/`
1×	`frac-times` `sub-neg` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 113

Calls

3 calls:

15.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
4.0ms	(- 1.0 (cos x))

series13.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (/ 1 x) (/ (- 1.0 (cos x)) x))
5.0ms	(/ (- 1.0 (cos x)) x)
3.0ms	(- 1.0 (cos x))

simplify43.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5658	1207

prune109.0ms

Filtered

79 candidates to 122 candidates (-54.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	3	2	5
Picked	1	0	1
Done	0	3	3
Total	119	12	131

Merged error: 0.1b

Counts

131 → 12

regimes162.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 31.1b

bsearch27.0ms

Steps

Iters	Range		Point
9	8.066580626132822e-07	1806.8211942563867	0.028650006657888936
8	-19.596719073147515	-0.015015160328561981	-0.033404312087007934

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	67
1	75	67

end0.0ms

sample1.8s

Algorithm

intervals

Results

811.0ms	1605×	body	2560	valid
324.0ms	1231×	body	1280	valid
250.0ms	1500×	body	640	valid
106.0ms	868×	body	320	valid
91.0ms	2293×	body	80	valid
46.0ms	503×	body	160	valid

Details

analyze228.0ms

sample60.0ms

simplify20.0ms

prune7.0ms

localize6.0ms

rewrite11.0ms

series9.0ms

simplify48.0ms

prune80.0ms

localize10.0ms

rewrite21.0ms

series13.0ms

simplify41.0ms

prune109.0ms

localize14.0ms

rewrite26.0ms

series47.0ms

simplify83.0ms

prune223.0ms

localize7.0ms

rewrite29.0ms

series13.0ms

simplify43.0ms

prune109.0ms

regimes162.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling