Details

analyze829.0ms (14.7%)

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
12.5%	87.4%	0.1%	5
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample113.0ms (2%)

Algorithm

1×

intervals

Results

52.0ms	114×	body	8192	exit
20.0ms	216×	body	128	valid
6.0ms	26×	body	256	valid
3.0ms	13×	body	512	valid
1.0ms	1×	body	1024	valid
0.0ms	3×	body	128	invalid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

568×	`neg-mul-1_binary64`
503×	`fma-def_binary64`
491×	`fma-neg_binary64`
484×	`div-sub_binary64`
416×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	22	23
2	58	23
3	152	21
4	338	18
5	1090	18
6	2902	18
7	3695	18
8	4706	18
9	4881	18

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

11.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	11.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	11.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	5.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite66.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
49×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`

Counts

3 → 100

Calls

3 calls:

28.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
23.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
5.0ms	(/.f64 x (exp.f64 wj))

series152.0ms (2.7%)

Counts

3 → 52

Calls

3 calls:

60.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
47.0ms	(/.f64 x (exp.f64 wj))
45.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

simplify211.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-neg_binary64`
444×	`fma-def_binary64`
331×	`distribute-rgt-in_binary64`
292×	`associate--l+_binary64`
278×	`distribute-lft-in_binary64`

Counts

152 → 235

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	228	3154
1	583	3016
2	1604	2995
3	4798	2993
4	5298	2993

prune178.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	234	3	237

Error

0.0b

Counts

237 → 3

Alt Table

Status	Error	Program
✓	11.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	6.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
▶	0.7b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))

Compiler

Compiled 3212 to 1388 computations (56.8% saved)

localize18.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2)))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

5.0ms

(*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))

series75.0ms (1.3%)

Counts

1 → 24

Calls

1 calls:

75.0ms

(*.f64 x (fma.f64 5/2 (*.f64 wj wj) (*.f64 wj -2)))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

850×	`distribute-rgt-in_binary64`
840×	`distribute-lft-in_binary64`
345×	`fma-def_binary64`
239×	`associate-l_binary64`
199×	`associate-r_binary64`

Counts

46 → 88

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	55	753
1	110	653
2	317	569
3	1046	569
4	5151	569

prune63.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	88	3	91

Error

0.0b

Counts

91 → 3

Alt Table

Status	Error	Program
✓	11.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	6.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	0.7b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))

Compiler

Compiled 917 to 460 computations (49.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (exp.f64 wj) wj)
✓	0.0b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	0.0b	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 65

Calls

3 calls:

11.0ms	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
7.0ms	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))
6.0ms	(*.f64 (exp.f64 wj) wj)

series91.0ms (1.6%)

Counts

3 → 22

Calls

3 calls:

71.0ms	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
12.0ms	(*.f64 (exp.f64 wj) wj)
8.0ms	(+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj))

simplify152.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

785×	`times-frac_binary64`
488×	`fma-neg_binary64`
456×	`cancel-sign-sub-inv_binary64`
412×	`fma-def_binary64`
311×	`associate-l_binary64`

Counts

87 → 158

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	145	1458
1	337	1367
2	954	1338
3	3010	1323
4	4869	1323
5	4897	1323

prune164.0ms (2.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	158	3	161

Error

0.0b

Counts

161 → 3

Alt Table

Status	Error	Program
✓	11.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	6.3b	(/.f64 x (+.f64 (*.f64 (exp.f64 wj) wj) (exp.f64 wj)))
✓	0.7b	(+.f64 (fma.f64 wj wj x) (.f64 x (fma.f64 5/2 (.f64 wj wj) (*.f64 wj -2))))

Compiler

Compiled 2242 to 627 computations (72% saved)

regimes212.0ms (3.8%)

Accuracy

Total 1.6b remaining (85.1%)

Threshold costs 0b (0%)

Compiler

Compiled 1590 to 999 computations (37.2% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	28
1	25	28
2	33	28
3	43	28
4	50	28
5	55	28
6	57	28
7	56	28

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample3.0s (54%)

Algorithm

1×

intervals

Results

1.6s	3832×	body	8192	exit
474.0ms	6535×	body	128	valid
160.0ms	689×	body	512	valid
118.0ms	751×	body	256	valid
9.0ms	25×	body	1024	valid
6.0ms	77×	body	128	invalid
1.0ms	15×	body	128	overflowed

Compiler

Compiled 84 to 51 computations (39.3% saved)

Details

analyze829.0ms (14.7%)

sample113.0ms (2%)

simplify103.0ms (1.8%)

prune6.0ms (0.1%)

localize17.0ms (0.3%)

rewrite66.0ms (1.2%)

series152.0ms (2.7%)

simplify211.0ms (3.8%)

prune178.0ms (3.2%)

localize18.0ms (0.3%)

rewrite7.0ms (0.1%)

series75.0ms (1.3%)

simplify79.0ms (1.4%)

prune63.0ms (1.1%)

localize10.0ms (0.2%)

rewrite29.0ms (0.5%)

series91.0ms (1.6%)

simplify152.0ms (2.7%)

prune164.0ms (2.9%)

regimes212.0ms (3.8%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample3.0s (54%)

Profiling