Details

analyze645.0ms (8.4%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.3s (30.4%)

Results

724.0ms	5353×	body	128	valid
612.0ms	1147×	body	2048	valid
332.0ms	775×	body	1024	valid
264.0ms	414×	body	4096	valid
139.0ms	1057×	body	128	invalid
139.0ms	389×	body	512	valid
43.0ms	178×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify316.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	22

Stop Event

1×

saturated

Counts

1 → 2

prune4.0ms (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

32.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	2.2b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	19.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series127.0ms (1.7%)

Counts

4 → 96

Calls

4 calls:

54.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
36.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

rewrite100.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`fma-def_binary64`
366×	`fma-neg_binary64`
297×	`egg-rr`
248×	`expm1-udef_binary64`
248×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	74
1	297	62
2	3769	62
3	5480	62

Stop Event

1×	node limit

Counts

4 → 297

Calls

4 calls:

91.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
91.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
91.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
91.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify65.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
487×	`associate-/l*_binary64`
417×	`associate-/r*_binary64`
406×	`fma-def_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2325
1	425	2249
2	1382	2208
3	4979	2208

Stop Event

1×	node limit

Counts

393 → 370

prune296.0ms (3.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	360	10	370
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	361	11	372

Error

7.2b

Counts

372 → 11

Alt Table

Status	Error	Program
▶	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	44.7b	(.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) 1/3) (/.f64 1 a))
	45.7b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	46.7b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	43.1b	(/.f64 (/.f64 (-.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))) (.f64 3 a))
	41.4b	(*.f64 -1/2 (/.f64 c b))
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	34.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) 3)) (*.f64 3 a))
	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))

Compiler

Compiled 11056 to 6057 computations (45.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 c (.f64 a -3) (.f64 b b))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
✓	2.2b	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
✓	19.9b	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))

series122.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

52.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
33.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
24.0ms	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))
12.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))

rewrite71.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

354×	`fma-def_binary64`
224×	`expm1-udef_binary64`
224×	`log1p-udef_binary64`
205×	`fma-neg_binary64`
197×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	66
1	299	62
2	3248	59
3	4918	59

Stop Event

1×	node limit

Counts

4 → 167

Calls

4 calls:

68.0ms	(fma.f64 c (.f64 a -3) (.f64 b b))
68.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
68.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b))))
68.0ms	(sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))

simplify62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

780×	`times-frac_binary64`
487×	`associate-/l*_binary64`
417×	`associate-/r*_binary64`
406×	`fma-def_binary64`
142×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2325
1	425	2249
2	1382	2208
3	4979	2208

Stop Event

1×	node limit

Counts

263 → 240

prune160.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	235	5	240
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	238	13	251

Error

3.0b

Counts

251 → 13

Alt Table

Status	Error	Program
	46.4b	(*.f64 (/.f64 b a) -2/3)
	41.4b	(*.f64 -1/2 (/.f64 c b))
	45.2b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -3) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))) (.f64 3 a))
▶	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	44.8b	(.f64 (.f64 (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))) 1/3) (/.f64 1 a))
	38.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3))))))) (*.f64 3 a))
	45.7b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	32.7b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))))) (*.f64 3 a))
	57.0b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 3 a))
	34.2b	(/.f64 (+.f64 (neg.f64 b) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) 3)) (*.f64 3 a))

Compiler

Compiled 5890 to 3725 computations (36.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
✓	0.3b	(/.f64 1/3 a)
✓	2.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
✓	19.9b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series112.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

52.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
34.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
24.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
1.0ms	(/.f64 1/3 a)

rewrite70.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

781×	`prod-diff_binary64`
245×	`log1p-udef_binary64`
159×	`egg-rr`
139×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	280	55
2	3406	55
3	5118	55

Stop Event

1×	node limit

Counts

4 → 159

Calls

4 calls:

66.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
66.0ms	(/.f64 1/3 a)
66.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
66.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

simplify71.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

766×	`times-frac_binary64`
487×	`associate-/l*_binary64`
405×	`associate-/r*_binary64`
391×	`fma-def_binary64`
368×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1923
1	420	1901
2	1372	1860
3	4965	1854
4	5172	1854

Stop Event

1×	node limit

Counts

219 → 226

prune174.0ms (2.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	226	13	239

Error

3.0b

Counts

239 → 13

Alt Table

Status	Error	Program
	46.4b	(*.f64 (/.f64 b a) -2/3)
	41.4b	(*.f64 -1/2 (/.f64 c b))
	45.2b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -3) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))) (.f64 3 a))
✓	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	35.8b	(.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))) b) (/.f64 1/3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
	46.4b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
▶	32.6b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/3 a))
	32.8b	(.f64 (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)) 2) (/.f64 1/3 a))
	45.7b	(/.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (*.f64 3 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))))) (*.f64 3 a))

Compiler

Compiled 6253 to 3682 computations (41.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
✓	0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)
	2.2b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	19.9b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series96.0ms (1.2%)

Counts

2 → 40

Calls

2 calls:

55.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
41.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)

rewrite56.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`prod-diff_binary64`
246×	`log1p-udef_binary64`
139×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	279	41
2	3475	41
3	5231	41

Stop Event

1×	node limit

Counts

2 → 63

Calls

2 calls:

52.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
52.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)

simplify61.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary64`
467×	`associate-/l*_binary64`
371×	`associate-/r*_binary64`
336×	`fma-def_binary64`
310×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1382
1	362	1368
2	1200	1336
3	4925	1330
4	5084	1330

Stop Event

1×	node limit

Counts

103 → 108

prune177.0ms (2.3%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	246	14	260

Error

3.0b

Counts

260 → 14

Alt Table

Status	Error	Program
	46.4b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
	46.4b	(/.f64 (*.f64 -2/3 b) a)
	46.4b	(*.f64 (/.f64 b a) -2/3)
	41.4b	(*.f64 -1/2 (/.f64 c b))
	57.0b	(*.f64 (-.f64 b b) (/.f64 1/3 a))
	45.6b	(/.f64 (.f64 -1/2 (/.f64 (.f64 c a) b)) a)
	45.2b	(/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 c (.f64 a -3) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 c (.f64 a -3)))))) (.f64 3 a))
✓	32.7b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	35.8b	(.f64 (-.f64 (exp.f64 (log.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))) b) (/.f64 1/3 a))
✓	32.6b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 c (.f64 a -3) (.f64 b b)))) (*.f64 3 a))
	46.4b	(/.f64 (.f64 -2 b) (.f64 3 a))
✓	32.6b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
	32.8b	(.f64 (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b)) 2) (/.f64 1/3 a))
	46.6b	(/.f64 (+.f64 (neg.f64 b) (hypot.f64 b (.f64 (sqrt.f64 c) (sqrt.f64 (.f64 a -3))))) (*.f64 3 a))

Compiler

Compiled 6609 to 3919 computations (40.7% saved)

regimes2.3s (29.6%)

Accuracy

Total 7.2b remaining (70.2%)

Threshold costs 0b (0%)

Counts

173 → 3

Compiler

Compiled 17642 to 12194 computations (30.9% saved)

bsearch94.0ms (1.2%)

Steps

Iters	Range		Point
10	3.73241376909039e-65	6.985216029906585e-55	1.2e-60
9	-1.1839448174746177e+114	-1.8526072091911443e+105	-8e+113

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	50
1	36	48
2	39	48
3	40	48
4	40	48

Stop Event

1×

saturated

end168.0ms (2.2%)

Compiler: Compiled 283 to 195 computations (31.1% saved)

Details

analyze645.0ms (8.4%)

sample2.3s (30.4%)

simplify316.0ms (4.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series127.0ms (1.7%)

rewrite100.0ms (1.3%)

simplify65.0ms (0.8%)

prune296.0ms (3.8%)

localize12.0ms (0.2%)

series122.0ms (1.6%)

rewrite71.0ms (0.9%)

simplify62.0ms (0.8%)

prune160.0ms (2.1%)

localize12.0ms (0.2%)

series112.0ms (1.4%)

rewrite70.0ms (0.9%)

simplify71.0ms (0.9%)

prune174.0ms (2.3%)

localize9.0ms (0.1%)

series96.0ms (1.2%)

rewrite56.0ms (0.7%)

simplify61.0ms (0.8%)

prune177.0ms (2.3%)

regimes2.3s (29.6%)

bsearch94.0ms (1.2%)

simplify3.0ms (0%)

end168.0ms (2.2%)

Profiling