Details

analyze395.0ms (5.5%)

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)

sample138.0ms (1.9%)

Algorithm

1×

intervals

Results

29.0ms	121×	body	8192	exit
9.0ms	205×	body	128	valid
5.0ms	23×	body	512	valid
2.0ms	26×	body	256	valid
0.0ms	2×	body	1024	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify80.0ms (1.1%)

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

prune3.0ms (0%)

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

14.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	14.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	14.6b	(-.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)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
✓	0.0b	(*.f64 wj (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
✓	4.9b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

series54.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

28.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
21.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
3.0ms	(*.f64 wj (exp.f64 wj))
2.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`*-un-lft-identity_binary64`
82×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
75×	`add-cube-cbrt_binary64`
63×	`prod-diff_binary64`

Counts

4 → 184

Calls

4 calls:

13.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
9.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
4.0ms	(*.f64 wj (exp.f64 wj))
3.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))

simplify240.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

478×	`fma-neg_binary64`
328×	`cancel-sign-sub-inv_binary64`
258×	`sub-neg_binary64`
214×	`fma-def_binary64`
170×	`*-commutative_binary64`

Counts

256 → 310

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	401	10528
1	1088	7323
2	3163	5636
3	4676	5636
4	4965	5636
5	4867	5636

prune242.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	340	2	342

Error

Counts

342 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
	40.2b	(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)))))

Status

Error

Program

▶

0.0b

(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (*.f64 x wj) (fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))

40.2b

(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))))

Compiler

Compiled 12843 to 2425 computations (81.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))
✓	0.1b	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))
✓	4.5b	(*.f64 x (pow.f64 wj 3))
✓	7.1b	(.f64 x (.f64 wj wj))

series57.0ms (0.8%)

Counts

4 → 96

Calls

4 calls:

19.0ms	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))
18.0ms	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))
11.0ms	(*.f64 x (pow.f64 wj 3))
9.0ms	(.f64 x (.f64 wj wj))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 74

Calls

4 calls:

6.0ms	(*.f64 x (pow.f64 wj 3))
4.0ms	(.f64 x (.f64 wj wj))
0.0ms	(fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3)))
0.0ms	(fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))

simplify104.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

571×	`distribute-rgt-in_binary64`
570×	`distribute-lft-in_binary64`
542×	`fma-def_binary64`
264×	`associate-+r+_binary64`
263×	`associate-+l+_binary64`

Counts

170 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	2138
1	217	1829
2	706	1829
3	1530	1804
4	4804	1804
5	4981	1804
6	4966	1804

prune105.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	118	2	120

Error

Counts

120 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
▶	40.2b	(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)))))

Status

Error

Program

✓

0.0b

(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (*.f64 x wj) (fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))

▶

40.2b

(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))))

Compiler

Compiled 3843 to 1834 computations (52.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 wj (exp.f64 wj))
✓	0.1b	(/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x))))
✓	5.1b	(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)))))

series217.0ms (3%)

Counts

3 → 49

Calls

3 calls:

115.0ms

(/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))

56.0ms

(/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x))))

45.0ms

(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))))

rewrite384.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

1306×	`times-frac_binary64`
841×	`add-sqr-sqrt_binary64`
819×	`*-un-lft-identity_binary64`
817×	`add-cube-cbrt_binary64`
659×	`sqrt-prod_binary64`

Counts

3 → 856

Calls

3 calls:

60.0ms

(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))))

17.0ms

(/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x))))

6.0ms

(/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))

simplify2.0s (28.3%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary64`
300×	`distribute-neg-frac_binary64`
289×	`fma-udef_binary64`
263×	`sub-neg_binary64`
234×	`neg-mul-1_binary64`

Counts

905 → 939

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1103	131033
1	3199	121503
2	4760	121503
3	4968	121503

prune472.0ms (6.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	999	0	999
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	999	2	1001

Error

Counts

1001 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (.f64 x wj) (fma.f64 8/3 (.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))
✓	40.2b	(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (.f64 wj (exp.f64 wj)) x)))))

Status

Error

Program

✓

0.0b

(-.f64 (fma.f64 5/2 (*.f64 x (*.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 2 (*.f64 x wj) (fma.f64 8/3 (*.f64 x (pow.f64 wj 3)) (pow.f64 wj 3))))

✓

40.2b

(-.f64 wj (/.f64 (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)) (/.f64 (fma.f64 wj (exp.f64 wj) (exp.f64 wj)) (sqrt.f64 (-.f64 (*.f64 wj (exp.f64 wj)) x)))))

Compiler

Compiled 89637 to 8685 computations (90.3% saved)

regimes724.0ms (10%)

Accuracy

Total 0.5b remaining (28.3%)

Threshold costs 0.5b (28.3%)

Counts

205 → 1

Compiler

Compiled 14013 to 7161 computations (48.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	22	38
2	27	38
3	29	38
4	30	38
5	30	38

end1.0ms (0%)

Compiler: Compiled 29 to 18 computations (37.9% saved)

sample1.9s (26%)

Algorithm

1×

intervals

Results

902.0ms	3754×	body	8192	exit
306.0ms	6557×	body	128	valid
95.0ms	685×	body	512	valid
66.0ms	732×	body	256	valid
5.0ms	26×	body	1024	valid
4.0ms	88×	body	128	invalid
0.0ms	12×	body	128	overflowed

Compiler

Compiled 105 to 57 computations (45.7% saved)

Details

analyze395.0ms (5.5%)

sample138.0ms (1.9%)

simplify80.0ms (1.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series54.0ms (0.8%)

rewrite49.0ms (0.7%)

simplify240.0ms (3.3%)

prune242.0ms (3.3%)

localize14.0ms (0.2%)

series57.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify104.0ms (1.4%)

prune105.0ms (1.5%)

localize11.0ms (0.2%)

series217.0ms (3%)

rewrite384.0ms (5.3%)

simplify2.0s (28.3%)

prune472.0ms (6.5%)

regimes724.0ms (10%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.9s (26%)

Profiling