Details

analyze1.5s (11.1%)

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%	81.2%	0.1%	6
28.1%	71.8%	0.1%	7
32.8%	67.1%	0.1%	8
38.2%	61.7%	0.1%	9
41%	58.9%	0.1%	10
43.9%	56%	0.1%	11
45.4%	54.5%	0.1%	12
46.9%	53%	0.1%	13
47.7%	52.2%	0.1%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample7.2s (53.6%)

Results

4.2s	3960×	body	8192	exit
1.4s	6774×	body	128	valid
812.0ms	3991×	body	128	invalid
391.0ms	695×	body	512	valid
280.0ms	770×	body	256	valid
12.0ms	17×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify108.0ms (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%)

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

14.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.1b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	14.3b	(-.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 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (exp.f64 wj)) wj)
✓	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
✓	6.6b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series123.0ms (0.9%)

Counts

4 → 61

Calls

4 calls:

41.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
32.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
30.0ms	(/.f64 x (exp.f64 wj))
19.0ms	(-.f64 (/.f64 x (exp.f64 wj)) wj)

rewrite173.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

528×	`fma-def_binary64`
354×	`fma-neg_binary64`
259×	`egg-rr`
218×	`log1p-udef_binary64`
217×	`expm1-udef_binary64`

Counts

4 → 259

Calls

4 calls:

161.0ms	(-.f64 (/.f64 x (exp.f64 wj)) wj)
161.0ms	(/.f64 x (exp.f64 wj))
161.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
161.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	48
1	232	48
2	3478	48
3	5008	48
0	0	0
1	0	0

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

883×	`fma-neg_binary64`
645×	`sub-neg_binary64`
314×	`associate--l+_binary64`
307×	`fma-def_binary64`
273×	`associate--r+_binary64`

Counts

320 → 312

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1147
1	268	1138
2	822	1118
3	3079	1111
4	4825	1111
5	5038	1111

prune446.0ms (3.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	310	2	312
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	312	2	314

Error

0.0b

Counts

314 → 2

Alt Table

Status	Error	Program
▶	0.6b	(-.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)))
	8.2b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (/.f64 x (exp.f64 wj)) (sqrt.f64 (+.f64 wj 1))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))

Status

Error

Program

▶

0.6b

(-.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)))

8.2b

(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (/.f64 x (exp.f64 wj)) (sqrt.f64 (+.f64 wj 1))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))

Compiler

Compiled 6502 to 2882 computations (55.7% saved)

localize28.0ms (0.2%)

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))
✓	0.1b	(*.f64 8/3 (pow.f64 wj 3))
✓	0.2b	(-.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)))
✓	8.0b	(.f64 x (.f64 wj wj))

series104.0ms (0.8%)

Counts

4 → 72

Calls

4 calls:

50.0ms	(-.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)))
34.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
15.0ms	(.f64 x (.f64 wj wj))
5.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite135.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

977×	`prod-diff_binary64`
162×	`add-sqr-sqrt_binary64`
157×	`log1p-expm1-u_binary64`
157×	`expm1-log1p-u_binary64`
153×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

128.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
128.0ms	(*.f64 8/3 (pow.f64 wj 3))
128.0ms	(-.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)))
128.0ms	(.f64 x (.f64 wj wj))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	67
1	340	67
2	3800	67
3	5605	67
0	0	0
1	0	0

simplify118.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-neg_binary64`
853×	`sub-neg_binary64`
355×	`fma-def_binary64`
310×	`cancel-sign-sub-inv_binary64`
300×	`associate-+l-_binary64`

Counts

174 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	1354
1	142	1214
2	536	1168
3	1811	1130
4	4590	1130
5	5452	1130

prune270.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	129	3	132

Error

Counts

132 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.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)))
	53.1b	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
▶	8.2b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (/.f64 x (exp.f64 wj)) (sqrt.f64 (+.f64 wj 1))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))

Compiler

Compiled 4776 to 2702 computations (43.4% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 x (exp.f64 wj))
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(/.f64 1 (sqrt.f64 (+.f64 wj 1)))
✓	5.3b	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

series24.0ms (0.2%)

Counts

3 → 28

Calls

3 calls:

16.0ms	(/.f64 1 (sqrt.f64 (+.f64 wj 1)))
4.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)
4.0ms	(/.f64 wj (+.f64 wj 1))

rewrite251.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

983×	`prod-diff_binary64`
323×	`fma-def_binary64`
212×	`egg-rr`
191×	`fma-neg_binary64`
156×	`log1p-udef_binary64`

Counts

3 → 212

Calls

3 calls:

152.0ms	(/.f64 wj (+.f64 wj 1))
152.0ms	(/.f64 1 (sqrt.f64 (+.f64 wj 1)))
152.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	183	24
2	2376	24
3	4918	24
4	5494	24
0	0	0
1	0	0

simplify172.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary64`
453×	`sub-neg_binary64`
376×	`cancel-sign-sub-inv_binary64`
317×	`distribute-rgt-neg-in_binary64`
315×	`fma-neg_binary64`

Counts

240 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	311
1	131	301
2	353	292
3	949	282
4	3153	282
5	4437	282
6	4971	282

prune545.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	284	3	287

Error

Counts

287 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.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)))
▶	53.1b	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
✓	8.2b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (/.f64 x (exp.f64 wj)) (sqrt.f64 (+.f64 wj 1))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))

Compiler

Compiled 9774 to 5962 computations (39% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
✓	0.2b	(fma.f64 x 8/3 1)
✓	0.2b	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
✓	8.0b	(.f64 (.f64 wj wj) (fma.f64 x 8/3 1))

series89.0ms (0.7%)

Counts

4 → 84

Calls

4 calls:

48.0ms	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
20.0ms	(.f64 (.f64 wj wj) (fma.f64 x 8/3 1))
18.0ms	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
3.0ms	(fma.f64 x 8/3 1)

rewrite136.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

414×	`fma-def_binary64`
271×	`expm1-udef_binary64`
271×	`log1p-udef_binary64`
196×	`fma-neg_binary64`
155×	`add-sqr-sqrt_binary64`

Counts

4 → 83

Calls

4 calls:

132.0ms	(.f64 (.f64 wj x) (fma.f64 wj 5/2 -2))
132.0ms	(fma.f64 x 8/3 1)
132.0ms	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
132.0ms	(.f64 (.f64 wj wj) (fma.f64 x 8/3 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	55
1	316	54
2	3690	54
3	4961	54
0	0	0
1	0	0

simplify180.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

911×	`fma-neg_binary64`
530×	`distribute-rgt-neg-in_binary64`
473×	`sub-neg_binary64`
401×	`distribute-lft-neg-in_binary64`
354×	`fma-def_binary64`

Counts

167 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	48	1526
1	156	1288
2	487	1133
3	1535	1109
4	3535	1107
5	4600	1107
6	4964	1107

prune148.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	115	3	118

Error

Counts

118 → 3

Alt Table

Status	Error	Program
✓	0.6b	(-.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)))
✓	53.1b	(fma.f64 wj (-.f64 wj (.f64 (.f64 wj wj) (fma.f64 x 8/3 1))) (.f64 (.f64 wj x) (fma.f64 wj 5/2 -2)))
✓	8.2b	(fma.f64 (/.f64 1 (sqrt.f64 (+.f64 wj 1))) (/.f64 (/.f64 x (exp.f64 wj)) (sqrt.f64 (+.f64 wj 1))) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))

Compiler

Compiled 2684 to 1555 computations (42.1% saved)

regimes1.3s (9.8%)

Accuracy

Total 1.1b remaining (78.3%)

Threshold costs 0b (0%)

Counts

223 → 1

Compiler

Compiled 12720 to 8436 computations (33.7% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`distribute-rgt-neg-in_binary64`
9×	`cancel-sign-sub-inv_binary64`
7×	`distribute-neg-in_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	16	37
1	27	37
2	37	37
3	54	35
4	69	35
5	76	35
6	72	35

end171.0ms (1.3%)

Compiler: Compiled 125 to 86 computations (31.2% saved)

Details

analyze1.5s (11.1%)

sample7.2s (53.6%)

simplify108.0ms (0.8%)

prune6.0ms (0%)

localize15.0ms (0.1%)

series123.0ms (0.9%)

rewrite173.0ms (1.3%)

simplify118.0ms (0.9%)

prune446.0ms (3.3%)

localize28.0ms (0.2%)

series104.0ms (0.8%)

rewrite135.0ms (1%)

simplify118.0ms (0.9%)

prune270.0ms (2%)

localize27.0ms (0.2%)

series24.0ms (0.2%)

rewrite251.0ms (1.9%)

simplify172.0ms (1.3%)

prune545.0ms (4.1%)

localize23.0ms (0.2%)

series89.0ms (0.7%)

rewrite136.0ms (1%)

simplify180.0ms (1.3%)

prune148.0ms (1.1%)

regimes1.3s (9.8%)

simplify7.0ms (0.1%)

end171.0ms (1.3%)

Profiling