Details

analyze800.0ms (10.3%)

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%	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)

sample4.1s (52.3%)

Results

2.3s	4007×	body	8192	exit
814.0ms	6804×	body	128	valid
455.0ms	4057×	body	128	invalid
195.0ms	677×	body	512	valid
154.0ms	752×	body	256	valid
8.0ms	23×	body	1024	valid

Compiler

Compiled 56 to 26 computations (53.6% saved)

simplify79.0ms (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

12.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
	12.8b	(-.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)

localize8.0ms (0.1%)

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))
✓	4.7b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

series48.0ms (0.6%)

Counts

3 → 52

Calls

3 calls:

19.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
15.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
14.0ms	(/.f64 x (exp.f64 wj))

rewrite83.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Counts

3 → 162

Calls

3 calls:

77.0ms	(/.f64 x (exp.f64 wj))
77.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
77.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	39
1	232	39
2	3478	39
3	5008	39

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

685×	`fma-neg_binary64`
570×	`sub-neg_binary64`
284×	`associate--l+_binary64`
259×	`fma-def_binary64`
245×	`associate--r+_binary64`

Counts

214 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	1071
1	243	1062
2	736	1046
3	2794	1040
4	4672	1040
5	4972	1040

prune153.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	202	4	206
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	4	208

Error

0.0b

Counts

208 → 4

Alt Table

Status	Error	Program
	41.7b	(+.f64 wj (cbrt.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)))
	5.4b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
▶	1.5b	(-.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)))
	12.3b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)

Compiler

Compiled 4294 to 2079 computations (51.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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)))
✓	0.0b	(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))
✓	6.5b	(.f64 x (.f64 wj wj))

series54.0ms (0.7%)

Counts

4 → 72

Calls

4 calls:

25.0ms	(-.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)))
18.0ms	(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))
3.0ms	(*.f64 8/3 (pow.f64 wj 3))

rewrite85.0ms (1.1%)

Algorithm

1×	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 → 106

Calls

4 calls:

82.0ms	(-.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)))
82.0ms	(fma.f64 x (fma.f64 2 wj (*.f64 8/3 (pow.f64 wj 3))) (pow.f64 wj 3))
82.0ms	(*.f64 8/3 (pow.f64 wj 3))
82.0ms	(.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

simplify78.0ms (1%)

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

178 → 134

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

prune180.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	133	5	138

Error

0.0b

Counts

138 → 5

Alt Table

Status	Error	Program
	56.1b	(.f64 (.f64 wj wj) (+.f64 1 (-.f64 (.f64 x (+.f64 5/2 (.f64 wj -8/3))) wj)))
✓	1.5b	(-.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)))
	41.7b	(+.f64 wj (cbrt.f64 (pow.f64 (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)) 3)))
▶	5.4b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
	12.3b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)

Compiler

Compiled 4920 to 2782 computations (43.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 wj (+.f64 wj 1))
✓	0.0b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
✓	0.0b	(/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1))
✓	5.1b	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

series25.0ms (0.3%)

Counts

4 → 60

Calls

4 calls:

13.0ms	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
6.0ms	(/.f64 wj (+.f64 wj 1))
3.0ms	(/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1))
2.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

rewrite126.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

340×	`fma-def_binary64`
239×	`fma-neg_binary64`
231×	`egg-rr`
224×	`log-div_binary64`
197×	`log1p-udef_binary64`

Counts

4 → 231

Calls

4 calls:

121.0ms	(/.f64 wj (+.f64 wj 1))
121.0ms	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (/.f64 wj (+.f64 wj 1)) wj)))
121.0ms	(/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1))
121.0ms	(-.f64 (/.f64 wj (+.f64 wj 1)) wj)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	54
1	271	46
2	3070	46
3	4969	46
4	4933	46

simplify95.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
469×	`sub-neg_binary64`
290×	`times-frac_binary64`
271×	`fma-def_binary64`
197×	`neg-mul-1_binary64`

Counts

291 → 297

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1032
1	270	1017
2	749	966
3	2391	944
4	4621	944
5	4966	944
6	4976	944

prune309.0ms (4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	296	1	297
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	298	4	302

Error

Counts

302 → 4

Alt Table

Status	Error	Program
	56.1b	(.f64 (.f64 wj wj) (+.f64 1 (-.f64 (.f64 x (+.f64 5/2 (.f64 wj -8/3))) wj)))
✓	1.5b	(-.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)))
	12.3b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
▶	0.7b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))))

Compiler

Compiled 7434 to 4302 computations (42.1% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))
✓	0.0b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))))
✓	0.0b	(-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))
	0.0b	(/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1))

series36.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

29.0ms

(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))))

4.0ms

(-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))

3.0ms

(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

346×	`log1p-udef_binary64`
244×	`prod-diff_binary64`
224×	`log1p-expm1-u_binary64`
224×	`expm1-log1p-u_binary64`
219×	`add-sqr-sqrt_binary64`

Counts

3 → 89

Calls

3 calls:

71.0ms

(+.f64 (pow.f64 wj 4) (pow.f64 wj 2))

71.0ms

(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))))

71.0ms

(-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	70
1	487	59
2	4230	59
3	4928	59

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

768×	`sub-neg_binary64`
484×	`fma-neg_binary64`
473×	`associate-l_binary64`
377×	`associate-r_binary64`
264×	`associate-+l-_binary64`

Counts

125 → 120

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	681
1	143	651
2	443	622
3	1402	620
4	4350	620
5	5013	620

prune206.0ms (2.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	173	4	177

Error

Counts

177 → 4

Alt Table

Status	Error	Program
	56.1b	(.f64 (.f64 wj wj) (+.f64 1 (-.f64 (.f64 x (+.f64 5/2 (.f64 wj -8/3))) wj)))
✓	1.5b	(-.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)))
	12.3b	(fma.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (/.f64 1 (+.f64 wj 1)) wj)
✓	0.7b	(fma.f64 (/.f64 x 1) (/.f64 (exp.f64 (neg.f64 wj)) (+.f64 wj 1)) (neg.f64 (-.f64 (+.f64 (pow.f64 wj 5) (pow.f64 wj 3)) (+.f64 (pow.f64 wj 4) (pow.f64 wj 2)))))

Compiler

Compiled 5549 to 3567 computations (35.7% saved)

regimes970.0ms (12.5%)

Accuracy

Total 1.2b remaining (96.6%)

Threshold costs 0b (0%)

Counts

257 → 1

Compiler

Compiled 16824 to 11940 computations (29% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	34
1	26	34
2	34	34
3	42	34
4	47	34
5	49	34
6	48	34

end107.0ms (1.4%)

Compiler: Compiled 138 to 95 computations (31.2% saved)

Details

analyze800.0ms (10.3%)

sample4.1s (52.3%)

simplify79.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series48.0ms (0.6%)

rewrite83.0ms (1.1%)

simplify71.0ms (0.9%)

prune153.0ms (2%)

localize15.0ms (0.2%)

series54.0ms (0.7%)

rewrite85.0ms (1.1%)

simplify78.0ms (1%)

prune180.0ms (2.3%)

localize12.0ms (0.2%)

series25.0ms (0.3%)

rewrite126.0ms (1.6%)

simplify95.0ms (1.2%)

prune309.0ms (4%)

localize27.0ms (0.3%)

series36.0ms (0.5%)

rewrite77.0ms (1%)

simplify65.0ms (0.8%)

prune206.0ms (2.6%)

regimes970.0ms (12.5%)

simplify3.0ms (0%)

end107.0ms (1.4%)

Profiling