Details

analyze418.0ms (12.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample2.2s (66.6%)

Results

1.1s	8256×	body	128	valid
978.0ms	8233×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify151.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

871×	`fma-neg_binary64`
804×	`unsub-neg_binary64`
461×	`distribute-neg-in_binary64`
434×	`sub-neg_binary64`
338×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	64	12
5	113	12
6	247	12
7	500	12
8	1560	12
9	2513	12
10	3218	12
11	3602	12
12	3803	12
13	3974	12
14	4075	12
15	4392	12
16	4836	12
17	4898	12
18	4901	12

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

30.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	28.0b	(sqrt.f64 (fma.f64 x x -1))

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
3.0ms	(sqrt.f64 (fma.f64 x x -1))
3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite50.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

671×	`log1p-expm1-u_binary64`
671×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
84×	`egg-rr`
69×	`add-sqr-sqrt_binary64`

Counts

3 → 84

Calls

3 calls:

48.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
48.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
48.0ms	(sqrt.f64 (fma.f64 x x -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	140	29
2	1688	29
3	5240	29
0	0	0
1	0	0

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary64`
301×	`sub-neg_binary64`
300×	`associate-/l/_binary64`
254×	`distribute-neg-frac_binary64`
233×	`fma-def_binary64`

Counts

120 → 147

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	681
1	306	648
2	873	646
3	2986	646
4	4808	646
5	4983	646

prune96.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	145	3	148

Error

Counts

148 → 3

Alt Table

Status	Error	Program
▶	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	30.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	30.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 2257 to 1665 computations (26.2% saved)

localize5.0ms (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

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	30.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	30.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 39 to 28 computations (28.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.0b	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))
✓	5.8b	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
	28.0b	(sqrt.f64 (fma.f64 x x -1))

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
3.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))
3.0ms	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))

rewrite51.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

748×	`expm1-log1p-u_binary64`
747×	`log1p-expm1-u_binary64`
710×	`prod-diff_binary64`
88×	`egg-rr`
77×	`add-sqr-sqrt_binary64`

Counts

3 → 88

Calls

3 calls:

49.0ms	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))
49.0ms	(+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1)))))
49.0ms	(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	159	29
2	1884	29
3	5866	29
0	0	0
1	0	0

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-neg_binary64`
301×	`sub-neg_binary64`
300×	`associate-/l/_binary64`
254×	`distribute-neg-frac_binary64`
233×	`fma-def_binary64`

Counts

124 → 151

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	681
1	306	648
2	873	646
3	2986	646
4	4808	646
5	4983	646

prune99.0ms (3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	197	0	197
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	197	3	200

Error

Counts

200 → 3

Alt Table

Status	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	30.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	30.0b	(log.f64 (+.f64 x (expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 3064 to 2293 computations (25.2% saved)

regimes36.0ms (1.1%)

Accuracy

Total 0.3b remaining (89.3%)

Threshold costs 0.3b (89.3%)

Counts

12 → 1

Compiler

Compiled 330 to 241 computations (27% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end49.0ms (1.5%)

Compiler: Compiled 44 to 32 computations (27.3% saved)

Details

analyze418.0ms (12.5%)

sample2.2s (66.6%)

simplify151.0ms (4.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series11.0ms (0.3%)

rewrite50.0ms (1.5%)

simplify58.0ms (1.7%)

prune96.0ms (2.8%)

localize5.0ms (0.1%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

series11.0ms (0.3%)

rewrite51.0ms (1.5%)

simplify64.0ms (1.9%)

prune99.0ms (3%)

regimes36.0ms (1.1%)

simplify2.0ms (0%)

end49.0ms (1.5%)

Profiling