Details

analyze1.1s (4.8%)

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)

sample4.7s (20%)

Results

1.7s	5374×	body	128	valid
1.1s	1189×	body	2048	valid
578.0ms	435×	body	4096	valid
558.0ms	718×	body	1024	valid
278.0ms	1079×	body	128	invalid
201.0ms	358×	body	512	valid
74.0ms	182×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify362.0ms (1.6%)

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`

Counts

1 → 2

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

prune8.0ms (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

35.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	35.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
	35.4b	(/.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)

localize21.0ms (0.1%)

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))
✓	0.4b	(/.f64 1/3 a)
✓	0.9b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
✓	23.5b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series328.0ms (1.4%)

Counts

4 → 60

Calls

4 calls:

155.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
93.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
77.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))
3.0ms	(/.f64 1/3 a)

rewrite116.0ms (0.5%)

Algorithm

2×	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`

Counts

4 → 159

Calls

4 calls:

108.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
108.0ms	(/.f64 1/3 a)
108.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
108.0ms	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify122.0ms (0.5%)

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`

Counts

219 → 226

Iterations

Useful iterations: 3 (0.0ms)

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

prune476.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	216	10	226
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	217	11	228

Error

4.8b

Counts

228 → 11

Alt Table

Status	Error	Program
	45.1b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
	45.1b	(*.f64 -2/3 (/.f64 b a))
	35.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b) (.f64 1/3 (/.f64 1 a)))
	46.5b	(.f64 (/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))) (/.f64 1/3 a))
▶	35.2b	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
	37.1b	(.f64 (exp.f64 (log.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b))) (/.f64 1/3 a))
	37.3b	(*.f64 -1/2 (/.f64 c b))
	45.2b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	49.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	36.9b	(.f64 (fma.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (/.f64 1/3 a))

Compiler

Compiled 6296 to 3691 computations (41.4% saved)

localize20.0ms (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)
✓	0.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)
	0.9b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) b)
	23.5b	(sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b)))

series284.0ms (1.2%)

Counts

2 → 40

Calls

2 calls:

158.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
126.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)

rewrite86.0ms (0.4%)

Algorithm

2×	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`

Counts

2 → 63

Calls

2 calls:

83.0ms	(/.f64 (.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3) a)
83.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) 1/3)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify94.0ms (0.4%)

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`

Counts

103 → 108

Iterations

Useful iterations: 3 (0.0ms)

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

prune442.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	243	4	247
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	248	10	258

Error

4.8b

Counts

258 → 10

Alt Table

Status	Error	Program
	45.1b	(.f64 (.f64 -2 b) (/.f64 1/3 a))
	43.6b	(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))))) a)
▶	35.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	37.0b	(/.f64 (.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (fma.f64 -1 b b)) 1/3) a)
	37.3b	(*.f64 -1/2 (/.f64 c b))
	45.2b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	45.1b	(/.f64 (*.f64 -2/3 b) a)
	35.8b	(-.f64 (/.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (.f64 a 3)) (/.f64 b (.f64 a 3)))
	49.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	36.9b	(.f64 (fma.f64 (cbrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (cbrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b)))) (neg.f64 b)) (/.f64 1/3 a))

Compiler

Compiled 6842 to 4058 computations (40.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.9b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
✓	1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	23.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series419.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

221.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
96.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
83.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
18.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

rewrite177.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

4 → 297

Calls

4 calls:

160.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
160.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
160.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
160.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify123.0ms (0.5%)

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`

Counts

393 → 370

Iterations

Useful iterations: 2 (0.0ms)

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

prune599.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	367	3	370
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	371	9	380

Error

4.8b

Counts

380 → 9

Alt Table

Status	Error	Program
▶	35.5b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	37.3b	(*.f64 -1/2 (/.f64 c b))
	45.2b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	43.6b	(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))))) a)
	45.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
✓	35.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	35.8b	(-.f64 (/.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (.f64 a 3)) (/.f64 b (.f64 a 3)))
	49.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	36.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (.f64 (cbrt.f64 b) b) (.f64 -3 (.f64 a c))))) (.f64 3 a))

Compiler

Compiled 11050 to 6043 computations (45.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (*.f64 a -3))
✓	0.9b	(-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))
✓	1.9b	(fma.f64 -3 (.f64 a c) (.f64 b b))
✓	23.5b	(sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))

series218.0ms (0.9%)

Counts

4 → 88

Calls

4 calls:

113.0ms	(-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))
82.0ms	(sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))
20.0ms	(fma.f64 -3 (.f64 a c) (.f64 b b))
3.0ms	(/.f64 1 (*.f64 a -3))

rewrite168.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

729×	`prod-diff_binary64`
231×	`log1p-udef_binary64`
230×	`expm1-udef_binary64`
148×	`egg-rr`
133×	`add-sqr-sqrt_binary64`

Counts

4 → 148

Calls

4 calls:

160.0ms	(/.f64 1 (*.f64 a -3))
160.0ms	(-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b))))
160.0ms	(fma.f64 -3 (.f64 a c) (.f64 b b))
160.0ms	(sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	47
1	271	44
2	3156	44
3	4996	44
4	5171	44
0	0	0
1	0	0

simplify144.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

455×	`times-frac_binary64`
447×	`unswap-sqr_binary64`
407×	`fma-neg_binary64`
274×	`associate-/l*_binary64`
273×	`associate-r_binary64`

Counts

236 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1684
1	254	1618
2	775	1604
3	3863	1602
4	5014	1602

prune357.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	199	10	209

Error

4.8b

Counts

209 → 10

Alt Table

Status	Error	Program
✓	35.5b	(.f64 (-.f64 b (sqrt.f64 (fma.f64 -3 (.f64 a c) (.f64 b b)))) (/.f64 1 (.f64 a -3)))
	37.3b	(*.f64 -1/2 (/.f64 c b))
	45.3b	(.f64 (.f64 2 b) (/.f64 1 (*.f64 a -3)))
	45.2b	(fma.f64 1/2 (/.f64 c b) (*.f64 (/.f64 b a) -2/3))
	43.6b	(/.f64 (/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) 3/2) (pow.f64 b 3)) 1/3) (+.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))))))) a)
	45.3b	(/.f64 (.f64 -2 b) (.f64 3 a))
✓	35.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	35.8b	(-.f64 (/.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (.f64 b b))) (.f64 a 3)) (/.f64 b (.f64 a 3)))
	49.5b	(/.f64 (-.f64 (fma.f64 a (.f64 c -3) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 3) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))))))
	36.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 (pow.f64 (cbrt.f64 b) 2) (.f64 (cbrt.f64 b) b) (.f64 -3 (.f64 a c))))) (.f64 3 a))

Compiler

Compiled 6582 to 3744 computations (43.1% saved)

regimes12.3s (52.6%)

Accuracy

Total 5.0b remaining (46.8%)

Threshold costs 0b (0%)

Counts

325 → 5

Compiler

Compiled 38527 to 26271 computations (31.8% saved)

bsearch314.0ms (1.3%)

Steps

Iters	Range		Point
8	7.560900787665848e-46	3.1287933573560865e-43	1.1474036072114028e-45
10	4.083050964430481e-102	1.197830895422842e-91	4.629430298105775e-102
7	9.04385804579909e-134	2.35081976312017e-132	2.3252761482698304e-132
9	-8.644997366783787e+79	-1.5160909950614094e+71	-7.129467328473503e+79

Compiler

Compiled 4 to 3 computations (25% saved)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	106
1	61	104
2	74	104
3	82	104
4	86	104
5	87	104
6	86	104

end321.0ms (1.4%)

Compiler: Compiled 353 to 228 computations (35.4% saved)

Details

analyze1.1s (4.8%)

sample4.7s (20%)

simplify362.0ms (1.6%)

prune8.0ms (0%)

localize21.0ms (0.1%)

series328.0ms (1.4%)

rewrite116.0ms (0.5%)

simplify122.0ms (0.5%)

prune476.0ms (2%)

localize20.0ms (0.1%)

series284.0ms (1.2%)

rewrite86.0ms (0.4%)

simplify94.0ms (0.4%)

prune442.0ms (1.9%)

localize20.0ms (0.1%)

series419.0ms (1.8%)

rewrite177.0ms (0.8%)

simplify123.0ms (0.5%)

prune599.0ms (2.6%)

localize22.0ms (0.1%)

series218.0ms (0.9%)

rewrite168.0ms (0.7%)

simplify144.0ms (0.6%)

prune357.0ms (1.5%)

regimes12.3s (52.6%)

bsearch314.0ms (1.3%)

simplify10.0ms (0%)

end321.0ms (1.4%)

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