Details

analyze372.0ms (7.8%)

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)

sample243.0ms (5.1%)

Algorithm

1×

intervals

Results

30.0ms	138×	body	2048	nan
16.0ms	256×	body	128	valid
10.0ms	64×	body	1024	nan
5.0ms	43×	body	512	nan
1.0ms	12×	body	256	nan
1.0ms	13×	body	128	nan
0.0ms	1×	body	4096	nan

Compiler

Compiled 22 to 16 computations (27.3% saved)

simplify157.0ms (3.3%)

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

35.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	35.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	0.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	33.0b	(sqrt.f64 (fma.f64 x x -1))

series14.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
5×	`pow1_binary64`

Counts

3 → 49

Calls

3 calls:

8.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
3.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
1.0ms	(sqrt.f64 (fma.f64 x x -1))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
330×	`sub-neg_binary64`
301×	`fma-def_binary64`
254×	`distribute-neg-frac_binary64`
210×	`associate-+l+_binary64`

Counts

85 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	1395
1	401	1305
2	1052	1265
3	3424	1265
4	4773	1265
5	4915	1265

prune65.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	116	3	119

Error

Counts

119 → 3

Alt Table

Status	Error	Program
▶	0.4b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
	0.6b	(+.f64 (log.f64 2) (log.f64 x))
✓	35.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 1902 to 1421 computations (25.3% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log-prod_binary64`
2×	`add-exp-log_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 14

Calls

1 calls:

1.0ms

(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

simplify95.0ms (2%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
535×	`times-frac_binary64`
409×	`cancel-sign-sub-inv_binary64`
345×	`sub-neg_binary64`
309×	`fma-neg_binary64`

Counts

26 → 38

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	79	493
1	184	449
2	525	449
3	1696	449
4	4117	449
5	4962	449
6	4996	449
7	4927	449

prune24.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.4b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
▶	0.6b	(+.f64 (log.f64 2) (log.f64 x))
✓	35.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 614 to 472 computations (23.1% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (log.f64 2) (log.f64 x))

series43.0ms (0.9%)

Counts

1 → 12

Calls

1 calls:

43.0ms

(+.f64 (log.f64 2) (log.f64 x))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
6×	`log-prod_binary64`
6×	`pow1_binary64`
5×	`log-pow_binary64`
4×	`distribute-lft-out_binary64`

Counts

1 → 27

Calls

1 calls:

4.0ms

(+.f64 (log.f64 2) (log.f64 x))

simplify79.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

539×	`sub-neg_binary64`
476×	`fma-def_binary64`
458×	`distribute-neg-in_binary64`
398×	`fma-neg_binary64`
397×	`unsub-neg_binary64`

Counts

39 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	54	363
1	120	344
2	274	342
3	660	342
4	2248	342
5	3872	342
6	4273	342
7	4971	342

prune20.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.4b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))
✓	0.6b	(+.f64 (log.f64 2) (log.f64 x))
✓	35.6b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 420 to 301 computations (28.3% saved)

regimes41.0ms (0.9%)

Accuracy

Total 0.3b remaining (99.6%)

Threshold costs 0.3b (99.6%)

Counts

10 → 1

Compiler

Compiled 306 to 229 computations (25.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

sample3.4s (72.8%)

Algorithm

1×

intervals

Results

1.3s	4127×	body	2048	nan
1.1s	2029×	body	1024	nan
428.0ms	8000×	body	128	valid
124.0ms	1016×	body	512	nan
39.0ms	484×	body	256	nan
20.0ms	484×	body	128	nan
2.0ms	9×	body	4096	nan

Compiler

Compiled 43 to 32 computations (25.6% saved)

Details

analyze372.0ms (7.8%)

sample243.0ms (5.1%)

simplify157.0ms (3.3%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series14.0ms (0.3%)

rewrite13.0ms (0.3%)

simplify85.0ms (1.8%)

prune65.0ms (1.4%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify95.0ms (2%)

prune24.0ms (0.5%)

localize5.0ms (0.1%)

series43.0ms (0.9%)

rewrite8.0ms (0.2%)

simplify79.0ms (1.7%)

prune20.0ms (0.4%)

regimes41.0ms (0.9%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.4s (72.8%)

Profiling