Details

analyze950.0ms (19.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

sample66.0ms (1.3%)

Algorithm

1×

intervals

Results

25.0ms	54×	body	1280	valid
12.0ms	43×	body	640	valid
9.0ms	122×	body	80	valid
4.0ms	20×	body	320	valid
2.0ms	17×	body	160	valid
0.0ms	3×	body	80	invalid

simplify422.0ms (8.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	382	11
1	382	11

prune24.0ms (0.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (tan B))
0.2b	(/ 1.0 (sin B))
0.2b	(* x (/ 1.0 (tan B)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 100

Calls

4 calls:

9.0ms	(* x (/ 1.0 (tan B)))
6.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
3.0ms	(/ 1.0 (tan B))
3.0ms	(/ 1.0 (sin B))

series82.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(* x (/ 1.0 (tan B)))
33.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
10.0ms	(/ 1.0 (tan B))
5.0ms	(/ 1.0 (sin B))

simplify47.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5054	989

prune207.0ms (4.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ 1.0 (sin B))

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

10.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ (* x 1.0) (tan B))
3.0ms	(/ 1.0 (sin B))

series57.0ms (1.2%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
24.0ms	(/ (* x 1.0) (tan B))
4.0ms	(/ 1.0 (sin B))

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5045	732

prune126.0ms (2.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 0.0b

Counts

81 → 7

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* 1.0 x))))
0.1b	(/ (tan B) (* 1.0 x))
0.2b	(/ 1.0 (sin B))
0.3b	(/ 1 (/ (tan B) (* 1.0 x)))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac`
47×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`prod-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`tan-quot` `sub-neg` `flip3--` `pow-flip` `diff-log` `associate-/r/` `frac-sub` `flip--` `associate-/l/` `inv-pow`

Counts

4 → 126

Calls

4 calls:

19.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* 1.0 x))))
6.0ms	(/ 1 (/ (tan B) (* 1.0 x)))
4.0ms	(/ (tan B) (* 1.0 x))
3.0ms	(/ 1.0 (sin B))

series65.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* 1.0 x))))
21.0ms	(/ 1 (/ (tan B) (* 1.0 x)))
13.0ms	(/ (tan B) (* 1.0 x))
4.0ms	(/ 1.0 (sin B))

simplify54.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4942	1464
1	4942	1464

prune227.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	137	8	145

Merged error: 0.0b

Counts

145 → 8

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ 1 (* (tan B) (/ 1 (* 1.0 x)))))
0.2b	(/ 1.0 (sin B))
0.3b	(/ 1 (* (tan B) (/ 1 (* 1.0 x))))
0.3b	(* (tan B) (/ 1 (* 1.0 x)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

93×	`add-exp-log`
40×	`prod-exp`
33×	`div-exp`
29×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`rec-exp` `times-frac` `1-exp`
9×	`pow1` `cbrt-undiv`
8×	`cbrt-unprod`
7×	`associate-r`
6×	`associate-/l*` `add-log-exp`
4×	`tan-quot` `associate-/r*` `associate-/r/` `div-inv`
3×	`associate-l`
2×	`frac-times` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `*-commutative` `frac-sub` `flip--` `inv-pow` `unswap-sqr`

Counts

4 → 129

Calls

4 calls:

13.0ms	(- (/ 1.0 (sin B)) (/ 1 (* (tan B) (/ 1 (* 1.0 x)))))
10.0ms	(* (tan B) (/ 1 (* 1.0 x)))
9.0ms	(/ 1 (* (tan B) (/ 1 (* 1.0 x))))
3.0ms	(/ 1.0 (sin B))

series66.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 (sin B)) (/ 1 (* (tan B) (/ 1 (* 1.0 x)))))
19.0ms	(/ 1 (* (tan B) (/ 1 (* 1.0 x))))
14.0ms	(* (tan B) (/ 1 (* 1.0 x)))
4.0ms	(/ 1.0 (sin B))

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4956	1204
1	4956	1204

prune198.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	141	8	149

Merged error: 0.0b

Counts

149 → 8

regimes123.0ms (2.5%)

Accuracy

Total 0.2b remaining (79.2%)

Threshold costs 0.2b (79.2%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	13
1	33	13

end0.0ms (0%)

sample1.9s (38.7%)

Algorithm

1×

intervals

Results

807.0ms	1791×	body	1280	valid
410.0ms	1411×	body	640	valid
275.0ms	3716×	body	80	valid
146.0ms	726×	body	320	valid
52.0ms	356×	body	160	valid
11.0ms	168×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze950.0ms (19.4%)

sample66.0ms (1.3%)

simplify422.0ms (8.6%)

prune24.0ms (0.5%)

localize14.0ms (0.3%)

rewrite26.0ms (0.5%)

series82.0ms (1.7%)

simplify47.0ms (1%)

prune207.0ms (4.2%)

localize11.0ms (0.2%)

rewrite19.0ms (0.4%)

series57.0ms (1.2%)

simplify43.0ms (0.9%)

prune126.0ms (2.6%)

localize13.0ms (0.3%)

rewrite37.0ms (0.8%)

series65.0ms (1.3%)

simplify54.0ms (1.1%)

prune227.0ms (4.6%)

localize14.0ms (0.3%)

rewrite40.0ms (0.8%)

series66.0ms (1.4%)

simplify66.0ms (1.3%)

prune198.0ms (4%)

regimes123.0ms (2.5%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (38.7%)

Profiling