Details

analyze971.0ms (9%)

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)

sample125.0ms (1.2%)

Algorithm

1×

intervals

Results

66.0ms	121×	body	8192	exit
21.0ms	211×	body	128	valid
5.0ms	28×	body	256	valid
4.0ms	16×	body	512	valid
0.0ms	1×	body	1024	valid
0.0ms	2×	body	128	overflowed

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify88.0ms (0.8%)

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

12.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	13.8b	(-.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)

localize15.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.2b	(/.f64 x (exp.f64 wj))
✓	6.9b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series104.0ms (1%)

Counts

3 → 52

Calls

3 calls:

41.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
32.0ms	(/.f64 x (exp.f64 wj))
31.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

rewrite74.0ms (0.7%)

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:

29.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
25.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
6.0ms	(/.f64 x (exp.f64 wj))

simplify220.0ms (2%)

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 → 152

Iterations

Useful iterations: 3 (0.0ms)

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

prune221.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Error

0.1b

Counts

154 → 5

Alt Table

Status	Error	Program
	13.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
	33.8b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
▶	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	42.4b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))

Compiler

Compiled 3295 to 1440 computations (56.3% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
✓	0.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	8.4b	(.f64 x (.f64 wj wj))

series117.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

57.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
38.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
16.0ms	(.f64 x (.f64 wj wj))
5.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`

Counts

4 → 96

Calls

4 calls:

9.0ms	(*.f64 8/3 (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
8.0ms	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
1.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))

simplify200.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

806×	`fma-def_binary64`
521×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
479×	`fma-neg_binary64`
401×	`cancel-sign-sub-inv_binary64`

Counts

168 → 173

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	191	3853
1	409	3376
2	1438	3085
3	4985	3004
4	5189	3004

prune386.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	172	6	178

Error

0.1b

Counts

178 → 6

Alt Table

Status	Error	Program
▶	13.8b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
	33.8b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	55.4b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
✓	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	42.4b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))

Compiler

Compiled 6368 to 3477 computations (45.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 wj (exp.f64 wj))
✓	0.0b	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
✓	1.0b	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
✓	6.9b	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))

series119.0ms (1.1%)

Counts

4 → 72

Calls

4 calls:

63.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
45.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
6.0ms	(*.f64 wj (exp.f64 wj))
5.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))

rewrite104.0ms (1%)

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:

29.0ms	(-.f64 wj (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj)))))
15.0ms	(/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))
7.0ms	(+.f64 (exp.f64 wj) (*.f64 wj (exp.f64 wj)))
7.0ms	(*.f64 wj (exp.f64 wj))

simplify443.0ms (4.1%)

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

prune443.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	338	6	344

Error

0.1b

Counts

344 → 6

Alt Table

Status	Error	Program
✓	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	40.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (neg.f64 (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))))
▶	33.8b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	55.4b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
	42.4b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))

Compiler

Compiled 12932 to 2499 computations (80.7% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	0.2b	(/.f64 x (exp.f64 wj))
✓	3.9b	(-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))
✓	22.8b	(/.f64 (-.f64 (.f64 wj wj) (.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

series1.0s (9.3%)

Counts

3 → 72

Calls

3 calls:

812.0ms

(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

126.0ms

(-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

68.0ms

(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite222.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

257×	`*-un-lft-identity_binary64`
204×	`add-sqr-sqrt_binary64`
197×	`times-frac_binary64`
67×	`add-cube-cbrt_binary64`
58×	`difference-of-squares_binary64`

Counts

3 → 214

Calls

3 calls:

72.0ms

(*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

43.0ms

(/.f64 (-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

9.0ms

(-.f64 (*.f64 wj wj) (*.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))

simplify665.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
193×	`+-commutative_binary64`
188×	`distribute-rgt-in_binary64`
186×	`distribute-lft-in_binary64`
184×	`*-commutative_binary64`

Counts

286 → 345

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	767	21269
1	2742	19845
2	4911	19803
3	4968	19803

prune750.0ms (6.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	461	1	462
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	462	6	468

Error

0.1b

Counts

468 → 6

Alt Table

Status	Error	Program
✓	12.8b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	40.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (neg.f64 (/.f64 (-.f64 (.f64 wj (exp.f64 wj)) x) (+.f64 (exp.f64 wj) (.f64 wj (exp.f64 wj))))))
	47.8b	(exp.f64 (log.f64 (/.f64 (-.f64 (.f64 wj wj) (/.f64 (.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (-.f64 (/.f64 x (exp.f64 wj)) wj)) (pow.f64 (+.f64 wj 1) 2))) (-.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))))))
	55.4b	(fma.f64 wj wj (.f64 (.f64 wj wj) (-.f64 (.f64 5/2 x) (.f64 (fma.f64 x 8/3 1) wj))))
✓	2.0b	(-.f64 (fma.f64 5/2 (.f64 x (.f64 wj wj)) (fma.f64 wj wj x)) (fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3)))
	42.4b	(cbrt.f64 (pow.f64 (+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))) 3))

Compiler

Compiled 29500 to 12786 computations (56.7% saved)

regimes551.0ms (5.1%)

Accuracy

Total 0.3b remaining (74.8%)

Threshold costs 0.3b (74.8%)

Counts

84 → 2

Compiler

Compiled 4977 to 2991 computations (39.9% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 18 to 8 computations (55.6% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative_binary64`
18×	`distribute-rgt-neg-in_binary64`
18×	`sub-neg_binary64`
17×	`cancel-sign-sub-inv_binary64`
16×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	48	87
2	65	87
3	81	87
4	106	87
5	122	87
6	135	87
7	153	87
8	166	87
9	175	87
10	177	87
11	173	87

end2.0ms (0%)

Compiler: Compiled 60 to 31 computations (48.3% saved)

sample3.9s (35.6%)

Algorithm

1×

intervals

Results

1.9s	3864×	body	8192	exit
575.0ms	6550×	body	128	valid
195.0ms	694×	body	512	valid
131.0ms	729×	body	256	valid
11.0ms	27×	body	1024	valid
8.0ms	78×	body	128	invalid
1.0ms	16×	body	128	overflowed

Compiler

Compiled 220 to 122 computations (44.5% saved)

Iter	Nodes	Cost
0	31	87
1	48	87
2	65	87
3	81	87
4	106	87
5	122	87
6	135	87
7	153	87
8	166	87
9	175	87
10	177	87
11	173	87

Iter	Nodes	Cost
0	31	87
1	48	87
2	65	87
3	81	87
4	106	87
5	122	87
6	135	87
7	153	87
8	166	87
9	175	87
10	177	87
11	173	87

Details

analyze971.0ms (9%)

sample125.0ms (1.2%)

simplify88.0ms (0.8%)

prune6.0ms (0.1%)

localize15.0ms (0.1%)

series104.0ms (1%)

rewrite74.0ms (0.7%)

simplify220.0ms (2%)

prune221.0ms (2%)

localize29.0ms (0.3%)

series117.0ms (1.1%)

rewrite38.0ms (0.4%)

simplify200.0ms (1.9%)

prune386.0ms (3.6%)

localize16.0ms (0.1%)

series119.0ms (1.1%)

rewrite104.0ms (1%)

simplify443.0ms (4.1%)

prune443.0ms (4.1%)

localize23.0ms (0.2%)

series1.0s (9.3%)

rewrite222.0ms (2.1%)

simplify665.0ms (6.1%)

prune750.0ms (6.9%)

regimes551.0ms (5.1%)

bsearch5.0ms (0.1%)

simplify15.0ms (0.1%)

end2.0ms (0%)

sample3.9s (35.6%)

Profiling

Iter	Nodes	Cost
0	31	87
1	48	87
2	65	87
3	81	87
4	106	87
5	122	87
6	135	87
7	153	87
8	166	87
9	175	87
10	177	87
11	173	87