Details

analyze610.0ms (7.3%)

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%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample2.5s (30.1%)

Results

872.0ms	5363×	body	128	valid
625.0ms	1172×	body	2048	valid
316.0ms	745×	body	1024	valid
271.0ms	437×	body	4096	valid
137.0ms	1084×	body	128	invalid
117.0ms	346×	body	512	valid
70.0ms	193×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify381.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

2009×	`fma-neg_binary64`
1508×	`div-sub_binary64`
1334×	`associate-/l*_binary64`
1156×	`fma-def_binary64`
685×	`associate-/l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	34	22
2	64	22
3	132	22
4	198	22
5	325	22
6	552	22
7	918	22
8	1352	22
9	1554	22
10	2359	22
11	3158	22
12	2565	22
13	2653	22
14	3219	22
15	3361	22
16	3461	22
17	3985	22
18	4171	22
19	4439	22
20	4659	22
21	4701	22
22	4757	22
23	4941	22
24	4941	22
25	3365	22
26	3059	22
27	2983	22
28	2985	22
29	2997	22
30	2997	22
31	2997	22
32	2997	22
33	2736	22

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

35.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	35.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
▶	35.4b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
✓	0.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
✓	1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
✓	25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series227.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

88.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
84.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
46.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

rewrite127.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

507×	`fma-neg_binary64`
277×	`expm1-udef_binary64`
277×	`log1p-udef_binary64`
178×	`egg-rr`
166×	`add-sqr-sqrt_binary64`

Counts

4 → 178

Calls

4 calls:

120.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (.f64 2 a))
120.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
120.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	74
1	338	62
2	4153	62
3	4979	62
4	5349	62
0	0	0
1	0	0

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
436×	`fma-def_binary64`
432×	`fma-neg_binary64`
426×	`associate-/r*_binary64`

Counts

274 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	398	2164
2	1327	2078
3	4954	2078
4	5218	2078

prune175.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	240	11	251
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	241	12	253

Error

4.3b

Counts

253 → 12

Alt Table

Status	Error	Program
	36.8b	(/.f64 (+.f64 (neg.f64 b) (.f64 (cbrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))) (cbrt.f64 (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))))) (.f64 2 a))
▶	35.5b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	49.4b	(.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4))))) (/.f64 1/2 a)))
	47.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	47.1b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
	42.4b	(/.f64 (+.f64 (neg.f64 b) (cbrt.f64 (pow.f64 (fma.f64 b b (.f64 (.f64 a c) -4)) 3/2))) (*.f64 2 a))
	45.1b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	37.8b	(neg.f64 (/.f64 c b))
	57.0b	(.f64 (/.f64 1 (sqrt.f64 (.f64 a 2))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (sqrt.f64 (*.f64 a 2))))
	49.5b	(.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (.f64 a c) -4)))) (/.f64 1/2 a))) (pow.f64 (cbrt.f64 (.f64 (+.f64 b (sqrt.f64 (fma.f64 b b (.f64 (*.f64 a c) -4)))) (/.f64 1/2 a))) 2))

Compiler

Compiled 6763 to 3884 computations (42.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
✓	0.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
✓	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
✓	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series187.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
51.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
39.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
9.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

rewrite87.0ms (1%)

Algorithm

2×	batch-egg-rewrite

Rules

781×	`prod-diff_binary64`
244×	`log1p-udef_binary64`
165×	`egg-rr`
138×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Counts

4 → 165

Calls

4 calls:

83.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
83.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
83.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
83.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
1	279	62
2	3385	62
3	5102	62
0	0	0
1	0	0

simplify134.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
467×	`associate-/l*_binary64`
436×	`fma-def_binary64`
432×	`fma-neg_binary64`
426×	`associate-/r*_binary64`

Counts

261 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2241
1	398	2164
2	1327	2078
3	4954	2078
4	5218	2078

prune169.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	235	3	238
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	241	9	250

Error

4.3b

Counts

250 → 9

Alt Table

Status	Error	Program
▶	35.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	47.1b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
	46.8b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	45.1b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
	37.8b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	47.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))

Compiler

Compiled 6470 to 3761 computations (41.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)
✓	0.3b	(cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))
	0.8b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
	25.1b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series857.0ms (10.3%)

Counts

2 → 40

Calls

2 calls:

517.0ms	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)
340.0ms	(cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

rewrite56.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

772×	`prod-diff_binary64`
222×	`expm1-udef_binary64`
222×	`log1p-udef_binary64`
129×	`add-sqr-sqrt_binary64`
125×	`log1p-expm1-u_binary64`

Counts

2 → 43

Calls

2 calls:

55.0ms	(pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)
55.0ms	(cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	39
1	269	37
2	2956	37
3	4893	37
0	0	0
1	0	0

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
436×	`unswap-sqr_binary64`
340×	`associate-r_binary64`
205×	`associate-l_binary64`
196×	`associate-/l*_binary64`

Counts

83 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	292	3058
1	921	2963
2	3128	2722
3	4948	2722

prune451.0ms (5.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	465	1	466
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	465	10	475

Error

4.3b

Counts

475 → 10

Alt Table

Status	Error	Program
✓	35.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	62.6b	(.f64 (.f64 (exp.f64 (.f64 1/3 (+.f64 (log.f64 c) (log.f64 (neg.f64 (.f64 2 (/.f64 a b))))))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	47.1b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
	46.8b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	45.1b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
▶	37.8b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	47.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))

Compiler

Compiled 23107 to 14400 computations (37.7% saved)

localize3.0ms (0%)

prune7.0ms (0.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	1	1
Total	10	10

Error

4.3b

Counts

10 → 10

Alt Table

Status	Error	Program
✓	35.9b	(.f64 (.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	62.6b	(.f64 (.f64 (exp.f64 (.f64 1/3 (+.f64 (log.f64 c) (log.f64 (neg.f64 (.f64 2 (/.f64 a b))))))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)) 2)) (/.f64 1/2 a))
	43.4b	(-.f64 (/.f64 c b) (/.f64 b a))
	43.3b	(/.f64 (neg.f64 b) a)
	47.1b	(/.f64 (.f64 -2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (*.f64 2 a))
	46.8b	(/.f64 (.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (/.f64 1/2 a)) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))
	45.1b	(/.f64 (.f64 -2 (/.f64 (.f64 c a) b)) (*.f64 2 a))
✓	37.8b	(neg.f64 (/.f64 c b))
	49.7b	(/.f64 (-.f64 (fma.f64 a (.f64 c -4) (.f64 b b)) (.f64 b b)) (.f64 (.f64 a 2) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))))
	47.0b	(/.f64 (-.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b) (*.f64 2 a))

Compiler

Compiled 209 to 134 computations (35.9% saved)

regimes1.8s (22.1%)

Accuracy

Total 4.7b remaining (45.6%)

Threshold costs 0b (0%)

Counts

91 → 5

Compiler

Compiled 8316 to 5678 computations (31.7% saved)

bsearch140.0ms (1.7%)

Steps

Iters	Range		Point
8	1.2344334649195314e-55	1.322700660035437e-51	4.4233955990605117e-54
5	6.863344029837293e-72	1.4734283974003753e-71	1.3948090615163448e-71
8	2.6189808425900012e-111	1.3010807537774533e-107	1.2846674157042731e-107
9	-1.2695432231346224e+46	-1.731480671832066e+41	-1.251564096671974e+46

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
13×	`*-commutative_binary64`
11×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	113
1	68	111
2	88	111
3	105	111
4	113	111
5	116	111
6	117	111
7	116	111

end161.0ms (1.9%)

Compiler: Compiled 365 to 218 computations (40.3% saved)

Details

analyze610.0ms (7.3%)

sample2.5s (30.1%)

simplify381.0ms (4.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series227.0ms (2.7%)

rewrite127.0ms (1.5%)

simplify82.0ms (1%)

prune175.0ms (2.1%)

localize9.0ms (0.1%)

series187.0ms (2.2%)

rewrite87.0ms (1%)

simplify134.0ms (1.6%)

prune169.0ms (2%)

localize14.0ms (0.2%)

series857.0ms (10.3%)

rewrite56.0ms (0.7%)

simplify73.0ms (0.9%)

prune451.0ms (5.4%)

localize3.0ms (0%)

prune7.0ms (0.1%)

regimes1.8s (22.1%)

bsearch140.0ms (1.7%)

simplify6.0ms (0.1%)

end161.0ms (1.9%)

Profiling