Details

analyze2.0s (21.2%)

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
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample142.0ms (1.5%)

Algorithm

1×

intervals

Results

61.0ms	64×	body	1280	valid
27.0ms	42×	body	640	valid
19.0ms	120×	body	80	valid
8.0ms	18×	body	320	valid
4.0ms	12×	body	160	valid
3.0ms	20×	body	80	invalid
1.0ms	5×	body	80	nan

simplify466.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune14.0ms (0.1%)

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: 15.7b

Counts

2 → 1

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0))))
18.8b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0)))

rewrite62.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

30.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0)))
14.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0))))
7.0ms	(* x (/ 1.0 (tan B)))
4.0ms	(/ 1.0 (tan B))

series136.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0))))
33.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (neg (/ 1.0 2.0)))
26.0ms	(* x (/ 1.0 (tan B)))
11.0ms	(/ 1.0 (tan B))

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5069	2444

prune489.0ms (5.2%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	147	20	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	148	20	168

Merged error: 11.2b

Counts

168 → 20

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
18.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`times-frac`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
6×	`associate-l`
5×	`pow-neg` `associate-*r/` `div-exp` `unswap-sqr`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `pow-exp` `associate-/r*` `associate-/l/` `pow-sub` `sqr-pow`
2×	`un-div-inv` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 133

Calls

4 calls:

13.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))
7.0ms	(* x (/ 1.0 (tan B)))

series136.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
31.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
23.0ms	(* x (/ 1.0 (tan B)))
23.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4949	2252
1	4949	2252

prune428.0ms (4.5%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	5	14	19
Picked	1	0	1
Done	0	0	0
Total	143	22	165

Merged error: 11.2b

Counts

165 → 22

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
0.4b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
18.8b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))

rewrite39.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`pow-unpow`
27×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`times-frac`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`unpow-prod-down` `associate-r` `prod-exp`
6×	`div-exp` `associate-/r*`
5×	`pow1` `pow-neg`
4×	`cbrt-undiv` `associate-*r/` `div-inv` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `associate-l` `pow-exp` `cbrt-unprod` `associate-/l/` `pow-sub` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `un-div-inv` `associate-/l*`
1×	`tan-quot` `neg-mul-1` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
10.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
10.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))
4.0ms	(/ (* x 1.0) (tan B))

series138.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))) (sin B))
32.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))
25.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0)))
23.0ms	(/ (* x 1.0) (tan B))

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4964	2169
1	4964	2169

prune385.0ms (4.1%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	4	17	21
Picked	1	0	1
Done	0	0	0
Total	136	20	156

Merged error: 11.2b

Counts

156 → 20

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B))
0.3b	(/ F (* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B)))
18.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-exp-log`
24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`pow-unpow`
7×	`unpow-prod-down` `associate-l` `prod-exp`
6×	`div-exp`
5×	`pow1`
4×	`cbrt-undiv` `associate-/r` `associate-/l` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 97

Calls

4 calls:

10.0ms	(* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B))
10.0ms	(/ F (* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B)))
9.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))
4.0ms	(/ (* x 1.0) (tan B))

series204.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ F (* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B)))
63.0ms	(* (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)) (sin B))
24.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))
23.0ms	(/ (* x 1.0) (tan B))

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4976	1813
1	4976	1813

prune237.0ms (2.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	6	13	19
Picked	1	0	1
Done	0	0	0
Total	111	18	129

Merged error: 11.2b

Counts

129 → 18

regimes379.0ms (4%)

Accuracy

Total 0.4b remaining (3.6%)

Threshold costs 0.4b (3.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	28
1	67	28

end0.0ms (0%)

sample3.8s (39.8%)

Algorithm

1×

intervals

Results

1.6s	1689×	body	1280	valid
837.0ms	1353×	body	640	valid
562.0ms	3904×	body	80	valid
303.0ms	700×	body	320	valid
105.0ms	354×	body	160	valid
94.0ms	618×	body	80	invalid
11.0ms	102×	body	80	nan
1.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	320	invalid

Details

analyze2.0s (21.2%)

sample142.0ms (1.5%)

simplify466.0ms (4.9%)

prune14.0ms (0.1%)

localize27.0ms (0.3%)

rewrite62.0ms (0.7%)

series136.0ms (1.4%)

simplify91.0ms (1%)

prune489.0ms (5.2%)

localize24.0ms (0.2%)

rewrite44.0ms (0.5%)

series136.0ms (1.4%)

simplify63.0ms (0.7%)

prune428.0ms (4.5%)

localize24.0ms (0.2%)

rewrite39.0ms (0.4%)

series138.0ms (1.5%)

simplify48.0ms (0.5%)

prune385.0ms (4.1%)

localize22.0ms (0.2%)

rewrite36.0ms (0.4%)

series204.0ms (2.2%)

simplify44.0ms (0.5%)

prune237.0ms (2.5%)

regimes379.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.8s (39.8%)

Profiling