Details

analyze421.0ms (8.3%)

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)

sample152.0ms (3%)

Algorithm

1×

intervals

Results

36.0ms	134×	body	8192	exit
13.0ms	205×	body	128	valid
4.0ms	26×	body	512	valid
3.0ms	25×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 39 to 19 computations (51.3% saved)

simplify80.0ms (1.6%)

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 (0.1%)

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

13.3b

Counts

3 → 2

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)))))
▶	13.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Compiler

Compiled 94 to 48 computations (48.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	5.0b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series49.0ms (1%)

Counts

3 → 52

Calls

3 calls:

18.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
16.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
15.0ms	(/.f64 x (exp.f64 wj))

rewrite32.0ms (0.6%)

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:

12.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
10.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))

simplify112.0ms (2.2%)

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

prune118.0ms (2.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	148	4	152
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	4	154

Error

0.0b

Counts

154 → 4

Alt Table

Status	Error	Program
	7.8b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
	36.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	13.6b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
▶	2.1b	(-.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)))

Compiler

Compiled 3245 to 1423 computations (56.1% saved)

localize15.0ms (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	(fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3)))
✓	0.2b	(*.f64 8/3 (pow.f64 wj 3))
✓	7.4b	(.f64 x (.f64 wj wj))

series101.0ms (2%)

Counts

4 → 60

Calls

4 calls:

86.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
8.0ms	(.f64 x (.f64 wj wj))
4.0ms	(fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3)))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite12.0ms (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:

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

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

453×	`sqr-pow_binary64`
405×	`*-commutative_binary64`
367×	`fma-def_binary64`
351×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`

Counts

134 → 119

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1718
1	228	1524
2	639	1524
3	1296	1500
4	2708	1494
5	4000	1494
6	4888	1494

prune151.0ms (3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	119	4	123

Error

0.0b

Counts

123 → 4

Alt Table

Status	Error	Program
▶	7.8b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
	36.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	13.6b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.1b	(-.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)))

Compiler

Compiled 3693 to 1940 computations (47.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(*.f64 (exp.f64 wj) (+.f64 wj 1))
✓	0.0b	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
✓	5.0b	(-.f64 wj (/.f64 wj (+.f64 wj 1)))

series30.0ms (0.6%)

Counts

4 → 60

Calls

4 calls:

22.0ms	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
3.0ms	(-.f64 wj (/.f64 wj (+.f64 wj 1)))
2.0ms	(*.f64 (exp.f64 wj) (+.f64 wj 1))
2.0ms	(/.f64 wj (+.f64 wj 1))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
64×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

4 → 176

Calls

4 calls:

10.0ms	(-.f64 wj (/.f64 wj (+.f64 wj 1)))
7.0ms	(*.f64 (exp.f64 wj) (+.f64 wj 1))
5.0ms	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
3.0ms	(/.f64 wj (+.f64 wj 1))

simplify141.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

813×	`fma-neg_binary64`
476×	`distribute-rgt-in_binary64`
264×	`cancel-sign-sub-inv_binary64`
182×	`distribute-rgt-neg-in_binary64`
159×	`sub-neg_binary64`

Counts

236 → 249

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	341	5313
1	852	3689
2	2535	3170
3	4541	3167
4	4886	3167

prune276.0ms (5.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	248	5	253

Error

Counts

253 → 5

Alt Table

Status	Error	Program
▶	1.7b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)) (pow.f64 wj 3))))
	36.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	7.8b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
	13.6b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.1b	(-.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)))

Compiler

Compiled 8019 to 4972 computations (38% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (*.f64 (exp.f64 wj) (+.f64 wj 1)))
	0.0b	(*.f64 (exp.f64 wj) (+.f64 wj 1))
✓	0.0b	(-.f64 (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)) (pow.f64 wj 3))
✓	0.0b	(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))

series7.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

4.0ms	(-.f64 (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)) (pow.f64 wj 3))
3.0ms	(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`*-un-lft-identity_binary64`
48×	`prod-diff_binary64`
39×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
19×	`unpow-prod-down_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(-.f64 (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)) (pow.f64 wj 3))
6.0ms	(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))

simplify137.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

514×	`exp-prod_binary64`
326×	`unswap-sqr_binary64`
311×	`cancel-sign-sub-inv_binary64`
287×	`fma-neg_binary64`
242×	`distribute-rgt-out_binary64`

Counts

115 → 106

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	144	3764
1	254	1767
2	983	1467
3	3401	1449
4	4367	1449
5	4868	1449
6	4763	1449

prune267.0ms (5.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	198	5	203

Error

Counts

203 → 5

Alt Table

Status	Error	Program
✓	1.7b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)) (pow.f64 wj 3))))
	36.2b	(fma.f64 (sqrt.f64 wj) (sqrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	7.8b	(.f64 1 (+.f64 (/.f64 x (.f64 (exp.f64 wj) (+.f64 wj 1))) (-.f64 wj (/.f64 wj (+.f64 wj 1)))))
	13.6b	(fma.f64 (*.f64 (cbrt.f64 wj) (cbrt.f64 wj)) (cbrt.f64 wj) (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
✓	2.1b	(-.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)))

Compiler

Compiled 6478 to 4343 computations (33% saved)

regimes560.0ms (11.1%)

Accuracy

Total 0.2b remaining (75%)

Threshold costs 0.2b (75%)

Counts

120 → 2

Compiler

Compiled 6588 to 4473 computations (32.1% saved)

bsearch4.0ms (0.1%)

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

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
21×	`distribute-rgt-neg-in_binary64`
20×	`cancel-sign-sub-inv_binary64`
20×	`sub-neg_binary64`
18×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	86
1	56	86
2	73	86
3	88	86
4	111	86
5	126	86
6	139	86
7	159	86
8	176	86
9	189	86
10	196	86
11	198	86
12	194	86

end1.0ms (0%)

Compiler: Compiled 58 to 35 computations (39.7% saved)

sample2.2s (43.1%)

Algorithm

1×

intervals

Results

1.1s	3976×	body	8192	exit
320.0ms	6490×	body	128	valid
114.0ms	722×	body	512	valid
74.0ms	761×	body	256	valid
6.0ms	27×	body	1024	valid
5.0ms	85×	body	128	invalid
1.0ms	14×	body	128	overflowed

Compiler

Compiled 187 to 116 computations (38% saved)

Iter	Nodes	Cost
0	35	86
1	56	86
2	73	86
3	88	86
4	111	86
5	126	86
6	139	86
7	159	86
8	176	86
9	189	86
10	196	86
11	198	86
12	194	86

Iter	Nodes	Cost
0	35	86
1	56	86
2	73	86
3	88	86
4	111	86
5	126	86
6	139	86
7	159	86
8	176	86
9	189	86
10	196	86
11	198	86
12	194	86

Details

analyze421.0ms (8.3%)

sample152.0ms (3%)

simplify80.0ms (1.6%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series49.0ms (1%)

rewrite32.0ms (0.6%)

simplify112.0ms (2.2%)

prune118.0ms (2.3%)

localize15.0ms (0.3%)

series101.0ms (2%)

rewrite12.0ms (0.2%)

simplify94.0ms (1.9%)

prune151.0ms (3%)

localize9.0ms (0.2%)

series30.0ms (0.6%)

rewrite40.0ms (0.8%)

simplify141.0ms (2.8%)

prune276.0ms (5.5%)

localize15.0ms (0.3%)

series7.0ms (0.1%)

rewrite27.0ms (0.5%)

simplify137.0ms (2.7%)

prune267.0ms (5.3%)

regimes560.0ms (11.1%)

bsearch4.0ms (0.1%)

simplify10.0ms (0.2%)

end1.0ms (0%)

sample2.2s (43.1%)

Profiling

Iter	Nodes	Cost
0	35	86
1	56	86
2	73	86
3	88	86
4	111	86
5	126	86
6	139	86
7	159	86
8	176	86
9	189	86
10	196	86
11	198	86
12	194	86