Details

analyze43.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	4×	body	80	invalid

simplify42.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	799	14
1	799	14

prune6.0ms (0.1%)

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: 0.2b

Counts

2 → 1

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
0.2b	(/ y (* 3.0 (sqrt x)))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(* 3.0 (sqrt x))

rewrite26.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
11×	`add-cube-cbrt`
9×	`add-log-exp`
6×	`pow1` `times-frac` `associate-r` `associate-/l*`
4×	`cbrt-undiv` `div-exp` `sqrt-prod`
3×	`diff-log` `associate-l` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `associate-/r*` `frac-sub` `flip--` `div-inv` `unswap-sqr`
1×	`associate--l-` `pow-prod-down` `associate--l+` `*-commutative` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

11.0ms	(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
5.0ms	(/ y (* 3.0 (sqrt x)))
5.0ms	(* 3.0 (sqrt x))
4.0ms	(/ 1.0 (* x 9.0))

series26.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ y (* 3.0 (sqrt x)))
9.0ms	(- (- 1.0 (/ 1.0 (* x 9.0))) (/ y (* 3.0 (sqrt x))))
4.0ms	(* 3.0 (sqrt x))
2.0ms	(/ 1.0 (* x 9.0))

simplify55.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4981	999
1	4981	999

prune199.0ms (4.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ 3.0 (/ y (sqrt x)))
0.3b	(/ y (sqrt x))
0.3b	(/ 1.0 (* x 9.0))
0.3b	(/ 1 (/ 3.0 (/ y (sqrt x))))

rewrite63.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

852×	`times-frac`
416×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
100×	`associate-/r*`
37×	`add-exp-log`
25×	`add-cbrt-cube`
24×	`div-inv`
21×	`div-exp`
12×	`cbrt-undiv` `associate-/l*`
6×	`associate-/r/`
5×	`pow1`
4×	`frac-2neg` `clear-num` `add-log-exp`
3×	`rec-exp` `1-exp`
1×	`pow-flip` `prod-exp` `cbrt-unprod` `inv-pow`

Counts

4 → 478

Calls

4 calls:

16.0ms	(/ 1 (/ 3.0 (/ y (sqrt x))))
7.0ms	(/ 3.0 (/ y (sqrt x)))
4.0ms	(/ 1.0 (* x 9.0))
4.0ms	(/ y (sqrt x))

series26.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 1 (/ 3.0 (/ y (sqrt x))))
8.0ms	(/ 3.0 (/ y (sqrt x)))
7.0ms	(/ y (sqrt x))
2.0ms	(/ 1.0 (* x 9.0))

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4960	6836
1	4960	6836

prune1.1s (27.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	487	3	490
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	491	10	501

Merged error: 0.0b

Counts

501 → 10

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (- 1.0 (/ 1.0 (* x 9.0))) (* 1 (/ (/ y (sqrt x)) 3.0)))
0.2b	(/ (/ y (sqrt x)) 3.0)
0.3b	(/ y (sqrt x))
0.3b	(/ 1.0 (* x 9.0))

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`times-frac`
99×	`*-un-lft-identity`
96×	`add-sqr-sqrt` `add-cube-cbrt`
48×	`sqrt-prod`
28×	`associate-/l*`
16×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
9×	`add-log-exp`
7×	`div-inv`
6×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `diff-log` `clear-num` `distribute-lft-out--`
2×	`sub-neg` `flip3--` `associate-*r/` `frac-sub` `flip--`
1×	`associate--l-` `prod-exp` `associate--l+` `cbrt-unprod` `associate-/l/`

Counts

4 → 184

Calls

4 calls:

8.0ms	(- (- 1.0 (/ 1.0 (* x 9.0))) (* 1 (/ (/ y (sqrt x)) 3.0)))
8.0ms	(/ (/ y (sqrt x)) 3.0)
4.0ms	(/ 1.0 (* x 9.0))
4.0ms	(/ y (sqrt x))

series29.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (- 1.0 (/ 1.0 (* x 9.0))) (* 1 (/ (/ y (sqrt x)) 3.0)))
8.0ms	(/ (/ y (sqrt x)) 3.0)
7.0ms	(/ y (sqrt x))
5.0ms	(/ 1.0 (* x 9.0))

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4967	2367
1	4967	2367

prune336.0ms (8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	196	10	206

Merged error: 0.0b

Counts

206 → 10

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(- (- 1.0 (/ 0.1111111111111111 x)) (/ 1 (/ 3.0 (/ y (sqrt x)))))
0.2b	(/ 3.0 (/ y (sqrt x)))
0.3b	(/ y (sqrt x))
0.3b	(/ 1 (/ 3.0 (/ y (sqrt x))))

rewrite137.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

867×	`times-frac`
446×	`add-sqr-sqrt`
426×	`*-un-lft-identity`
414×	`add-cube-cbrt`
158×	`sqrt-prod`
99×	`associate-/r*`
32×	`add-exp-log`
25×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp`
10×	`cbrt-undiv`
9×	`associate-/l*` `add-log-exp` `difference-of-squares`
6×	`associate-/r/` `distribute-lft-out--`
5×	`pow1`
3×	`rec-exp` `frac-2neg` `diff-log` `1-exp` `clear-num`
2×	`sub-neg` `flip3--` `frac-sub` `flip--`
1×	`associate--l-` `pow-flip` `associate--l+` `inv-pow`

Counts

4 → 486

Calls

4 calls:

78.0ms	(- (- 1.0 (/ 0.1111111111111111 x)) (/ 1 (/ 3.0 (/ y (sqrt x)))))
16.0ms	(/ 1 (/ 3.0 (/ y (sqrt x))))
7.0ms	(/ 3.0 (/ y (sqrt x)))
4.0ms	(/ y (sqrt x))

series39.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

13.0ms	(/ y (sqrt x))
9.0ms	(/ 3.0 (/ y (sqrt x)))
9.0ms	(/ 1 (/ 3.0 (/ y (sqrt x))))
9.0ms	(- (- 1.0 (/ 0.1111111111111111 x)) (/ 1 (/ 3.0 (/ y (sqrt x)))))

simplify110.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

498 → 498

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4963	7397
1	4963	7397

prune997.0ms (23.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	498	0	498
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	498	10	508

Merged error: 0.0b

Counts

508 → 10

regimes190.0ms (4.5%)

Accuracy

Total 0.2b remaining (85.9%)

Threshold costs 0.2b (85.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	14
1	79	14

end0.0ms (0%)

sample470.0ms (11.2%)

Algorithm

1×

intervals

Results

339.0ms	8000×	body	80	valid
3.0ms	81×	body	80	invalid

Details

analyze43.0ms (1%)

sample19.0ms (0.4%)

simplify42.0ms (1%)

prune6.0ms (0.1%)

localize10.0ms (0.2%)

rewrite26.0ms (0.6%)

series26.0ms (0.6%)

simplify55.0ms (1.3%)

prune199.0ms (4.7%)

localize11.0ms (0.3%)

rewrite63.0ms (1.5%)

series26.0ms (0.6%)

simplify110.0ms (2.6%)

prune1.1s (27.1%)

localize11.0ms (0.3%)

rewrite31.0ms (0.7%)

series29.0ms (0.7%)

simplify70.0ms (1.7%)

prune336.0ms (8%)

localize9.0ms (0.2%)

rewrite137.0ms (3.3%)

series39.0ms (0.9%)

simplify110.0ms (2.6%)

prune997.0ms (23.7%)

regimes190.0ms (4.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample470.0ms (11.2%)

Profiling