Details

analyze389.0ms (14.2%)

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)

sample1.8s (66.8%)

Results

868.0ms	8256×	body	128	valid
776.0ms	8186×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify150.0ms (5.5%)

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

31.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.3b	(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 2 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	29.1b	(sqrt.f64 (fma.f64 x x -1))

series9.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms	(sqrt.f64 (fma.f64 x x -1))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify68.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

549×	`fma-neg_binary64`
294×	`associate-/l/_binary64`
291×	`sub-neg_binary64`
254×	`distribute-neg-frac_binary64`
221×	`fma-def_binary64`

Counts

56 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	988
1	330	928
2	885	889
3	3023	888
4	4940	888
5	4940	888

prune42.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Status	Error	Program
▶	0.5b	(log.f64 (+.f64 x x))
✓	31.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	31.3b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 1316 to 987 computations (25% 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
✓	0.5b	(log.f64 (+.f64 x x))
✓	31.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
▶	31.3b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 36 to 25 computations (30.6% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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))))
	29.1b	(sqrt.f64 (fma.f64 x x -1))

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

7.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
4.0ms	(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`log-prod_binary64`
8×	`*-un-lft-identity_binary64`
6×	`exp-sum_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 39

Calls

2 calls:

4.0ms	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))
2.0ms	(exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))

simplify70.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

561×	`fma-neg_binary64`
295×	`associate-/l/_binary64`
294×	`sub-neg_binary64`
254×	`distribute-neg-frac_binary64`
217×	`fma-def_binary64`

Counts

63 → 101

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	159	1126
1	354	1023
2	901	1020
3	3046	975
4	4991	975
5	5003	975

prune71.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	139	3	142

Error

Counts

142 → 3

Alt Table

Status	Error	Program
✓	0.5b	(log.f64 (+.f64 x x))
✓	31.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	31.3b	(log.f64 (+.f64 x (exp.f64 (log.f64 (sqrt.f64 (fma.f64 x x -1))))))

Compiler

Compiled 2363 to 1800 computations (23.8% saved)

regimes20.0ms (0.7%)

Accuracy

Total 0.5b remaining (91.5%)

Threshold costs 0.5b (91.5%)

Counts

5 → 1

Compiler

Compiled 165 to 115 computations (30.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end41.0ms (1.5%)

Compiler: Compiled 35 to 23 computations (34.3% saved)

Details

analyze389.0ms (14.2%)

sample1.8s (66.8%)

simplify150.0ms (5.5%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series9.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify68.0ms (2.5%)

prune42.0ms (1.5%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

series11.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify70.0ms (2.6%)

prune71.0ms (2.6%)

regimes20.0ms (0.7%)

simplify2.0ms (0.1%)

end41.0ms (1.5%)

Profiling