Details

analyze395.0ms (13.5%)

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)

sample1.9s (63.8%)

Results

865.0ms	8256×	body	128	valid
808.0ms	8257×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify152.0ms (5.2%)

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

30.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.5b	(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)))
✓	28.4b	(sqrt.f64 (fma.f64 x x -1))

series11.0ms (0.4%)

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)))

rewrite49.0ms (1.7%)

Algorithm

1×	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:

47.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
47.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
47.0ms	(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

simplify65.0ms (2.2%)

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

prune75.0ms (2.6%)

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
	30.5b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
▶	0.8b	(log.f64 (+.f64 x x))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 2251 to 1659 computations (26.3% 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

Counts

3 → 3

Alt Table

Status	Error	Program
▶	30.5b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.8b	(log.f64 (+.f64 x x))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
✓	0.0b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	5.6b	(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
	28.4b	(sqrt.f64 (fma.f64 x x -1))

series13.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
3.0ms	(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))
3.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))

rewrite52.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`log1p-expm1-u_binary64`
733×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
84×	`egg-rr`
77×	`add-sqr-sqrt_binary64`

Counts

3 → 84

Calls

3 calls:

50.0ms	(+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1)))))
50.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
50.0ms	(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	156	29
2	1859	29
3	5626	29

simplify62.0ms (2.1%)

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 (3.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	193	3	196

Error

Counts

196 → 3

Alt Table

Status	Error	Program
✓	30.5b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
✓	0.8b	(log.f64 (+.f64 x x))
✓	30.5b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 2982 to 2228 computations (25.3% saved)

regimes23.0ms (0.8%)

Accuracy

Total 0.2b remaining (83.2%)

Threshold costs 0.2b (83.2%)

Counts

6 → 1

Compiler

Compiled 189 to 133 computations (29.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end41.0ms (1.4%)

Compiler: Compiled 41 to 29 computations (29.3% saved)

Details

analyze395.0ms (13.5%)

sample1.9s (63.8%)

simplify152.0ms (5.2%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series11.0ms (0.4%)

rewrite49.0ms (1.7%)

simplify65.0ms (2.2%)

prune75.0ms (2.6%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series13.0ms (0.5%)

rewrite52.0ms (1.8%)

simplify62.0ms (2.1%)

prune96.0ms (3.3%)

regimes23.0ms (0.8%)

simplify2.0ms (0.1%)

end41.0ms (1.4%)

Profiling