Details

analyze487.0ms (18.8%)

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
12.5%	87.4%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.1%	0.1%	7
35.9%	64%	0.1%	8
47.2%	52.7%	0.1%	9
52.1%	47.8%	0.1%	10
65.3%	34.5%	0.1%	11
71.4%	28.4%	0.1%	12
74.2%	25.6%	0.1%	13
81.7%	18.1%	0.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.2s (47.1%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

preprocess16.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

4×	`fma-neg_binary64`
4×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	72
1	35	72
2	39	72
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`fma-neg_binary64`
1×	`fma-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	13	18
2	14	18

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	2.5b	(+.f64 x (/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))))

Compiler

Compiled 57 to 35 computations (38.6% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))
✓	7.1b	(/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y))))

series41.0ms (1.6%)

Counts

2 → 72

Calls

18 calls:

6.0ms	(/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y))))	z	inf
6.0ms	(/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y))))	z	-inf
5.0ms	(/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y))))	y	-inf
3.0ms	(/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y))))	z	0
3.0ms	(fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))	z	0

rewrite38.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

725×	`log1p-expm1-u_binary64`
725×	`expm1-log1p-u_binary64`
176×	`expm1-udef_binary64`
176×	`log1p-udef_binary64`
98×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	182	27
2	1878	27

Stop Event

1×	node limit

Counts

2 → 33

simplify155.0ms (6%)

Algorithm

1×	egg-herbie

Rules

1177×	`sqr-pow_binary64`
832×	`pow-sqr_binary64`
133×	`cube-mult_binary64`
133×	`unpow3_binary64`
128×	`cube-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	1638
1	184	1638
2	215	1638
3	267	1638
4	348	1638
5	443	1638
6	574	1638
7	751	1638
8	1008	1638
9	1402	1638
10	2039	1638
11	3141	1638
12	3273	1638
13	3353	1638
14	3353	1638

Stop Event

1×	node limit

Counts

105 → 65

prune55.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	3	66

Error

0.0b

Counts

66 → 3

Alt Table

Status	Error	Program
	25.2b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	2.5b	(+.f64 x (/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))))
▶	18.1b	(+.f64 x (/.f64 -1 x))

Compiler

Compiled 1542 to 837 computations (45.7% saved)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	25.2b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	2.5b	(+.f64 x (/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))))
✓	18.1b	(+.f64 x (/.f64 -1 x))

Compiler

Compiled 45 to 32 computations (28.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (exp.f64 z))
✓	0.2b	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))

series32.0ms (1.2%)

Counts

2 → 8

Calls

12 calls:

11.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))	z	inf
3.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))	z	-inf
2.0ms	(/.f64 y (exp.f64 z))	z	inf
2.0ms	(/.f64 y (exp.f64 z))	z	-inf
2.0ms	(*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z)))	y	0

rewrite35.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

494×	`log1p-expm1-u_binary64`
494×	`expm1-log1p-u_binary64`
184×	`unpow-prod-down_binary64`
164×	`pow2_binary64`
156×	`log-prod_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	126	15
2	1287	15

Stop Event

1×	node limit

Counts

2 → 47

simplify252.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

1716×	`sqr-pow_binary64`
870×	`pow-sqr_binary64`
58×	`cube-prod_binary64`
58×	`cube-mult_binary64`
58×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	129
1	48	129
2	61	129
3	75	129
4	95	129
5	116	129
6	140	129
7	165	129
8	194	129
9	224	129
10	258	129
11	293	129
12	332	129
13	372	129
14	416	129
15	461	129
16	510	129
17	560	129
18	614	129
19	669	129
20	728	129
21	788	129
22	852	129
23	917	129
24	986	129
25	1056	129
26	1130	129
27	1205	129
28	1284	129
29	1364	129
30	1448	129
31	1533	129
32	1622	129
33	1712	129
34	1806	129
35	1901	129
36	2000	129
37	2100	129
38	2126	129
39	2128	129
40	2128	129
41	2227	129
42	2331	129
43	2438	129
44	2549	129
45	2661	129
46	2777	129
47	2894	129
48	3015	129
49	3137	129
50	3263	129
51	3390	129
52	3521	129
53	3653	129
54	3789	129
55	3926	129
56	3959	129
57	3961	129
58	3961	129
59	4097	129
60	4238	129
61	4382	129
62	4530	129
63	4679	129
64	4832	129
65	4986	129

Stop Event

1×	node limit

Counts

55 → 59

prune33.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	59	3	62

Error

0.0b

Counts

62 → 3

Alt Table

Status	Error	Program
✓	25.2b	(+.f64 x (*.f64 5000000000000000/5641895835477563 (/.f64 y (exp.f64 z))))
✓	2.5b	(+.f64 x (/.f64 y (fma.f64 5641895835477563/5000000000000000 (exp.f64 z) (neg.f64 (*.f64 x y)))))
✓	18.1b	(+.f64 x (/.f64 -1 x))

Compiler

Compiled 858 to 475 computations (44.6% saved)

regimes114.0ms (4.4%)

Accuracy

Total 1.1b remaining (99.3%)

Threshold costs 0b (0%)

Counts

14 → 2

Compiler

Compiled 1214 to 906 computations (25.4% saved)

bsearch30.0ms (1.2%)

Algorithm

1×	binary-search

Calls

1 calls:

30.0ms

(exp.f64 z)

Steps

Iters	Point		Range
6.79382622630013e-310	∈ [	0.0	,	1.7959519255265993e-7	]

Compiler

Compiled 5 to 4 computations (20% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	33

Stop Event

1×

saturated

end57.0ms (2.2%)

Stop Event

1×

done

Compiler

Compiled 84 to 56 computations (33.3% saved)

Details

analyze487.0ms (18.8%)

sample1.2s (47.1%)

preprocess16.0ms (0.6%)

simplify4.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series41.0ms (1.6%)

rewrite38.0ms (1.5%)

simplify155.0ms (6%)

prune55.0ms (2.1%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series32.0ms (1.2%)

rewrite35.0ms (1.4%)

simplify252.0ms (9.7%)

prune33.0ms (1.3%)

regimes114.0ms (4.4%)

bsearch30.0ms (1.2%)

simplify2.0ms (0.1%)

end57.0ms (2.2%)

Profiling