Details

analyze391.0ms (10.4%)

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)

sample2.1s (56.1%)

Results

1.1s	8256×	body	128	valid
842.0ms	7975×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify151.0ms (4%)

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

34.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.5b	(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	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	0.2b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	32.0b	(sqrt.f64 (fma.f64 x x -1))

series14.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
4.0ms	(sqrt.f64 (fma.f64 x x -1))
3.0ms	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))

rewrite8.0ms (0.2%)

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:

3.0ms	(+.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))

simplify82.0ms (2.2%)

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

prune70.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Error

0.0b

Counts

119 → 2

Alt Table

Status	Error	Program
	0.3b	(+.f64 (log.f64 2) (log.f64 x))
▶	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1893 to 1415 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)))

rewrite1.0ms (0%)

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)))

simplify90.0ms (2.4%)

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

prune26.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	2	40

Error

0.0b

Counts

40 → 2

Alt Table

Status	Error	Program
▶	0.3b	(+.f64 (log.f64 2) (log.f64 x))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 605 to 466 computations (23% 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 (1.2%)

Counts

1 → 12

Calls

1 calls:

43.0ms

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

rewrite5.0ms (0.1%)

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))

simplify80.0ms (2.1%)

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

prune21.0ms (0.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	38	2	40

Error

Counts

40 → 2

Alt Table

Status	Error	Program
▶	1.1b	(exp.f64 (log.f64 (+.f64 (log.f64 2) (log.f64 x))))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 421 to 304 computations (27.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(log.f64 (+.f64 (log.f64 2) (log.f64 x)))
	0.2b	(+.f64 (log.f64 2) (log.f64 x))
✓	1.0b	(exp.f64 (log.f64 (+.f64 (log.f64 2) (log.f64 x))))

series370.0ms (9.8%)

Counts

2 → 20

Calls

2 calls:

328.0ms	(log.f64 (+.f64 (log.f64 2) (log.f64 x)))
41.0ms	(exp.f64 (log.f64 (+.f64 (log.f64 2) (log.f64 x))))

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-prod_binary64`
13×	`*-un-lft-identity_binary64`
12×	`pow1_binary64`
10×	`log-pow_binary64`
8×	`distribute-lft-out_binary64`

Counts

2 → 43

Calls

2 calls:

4.0ms	(exp.f64 (log.f64 (+.f64 (log.f64 2) (log.f64 x))))
3.0ms	(log.f64 (+.f64 (log.f64 2) (log.f64 x)))

simplify121.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

666×	`sub-neg_binary64`
640×	`unsub-neg_binary64`
398×	`associate--r+_binary64`
330×	`unswap-sqr_binary64`
293×	`associate--l+_binary64`

Counts

63 → 63

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	864
1	117	777
2	208	771
3	444	763
4	1619	763
5	3321	763
6	3982	763
7	4789	763
8	4958	763
9	4802	763

prune46.0ms (1.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	101	2	103

Error

Counts

103 → 2

Alt Table

Status	Error	Program
✓	1.1b	(exp.f64 (log.f64 (+.f64 (log.f64 2) (log.f64 x))))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1351 to 1015 computations (24.9% saved)

regimes53.0ms (1.4%)

Accuracy

Total 0.1b remaining (18.6%)

Threshold costs 0.1b (18.6%)

Counts

14 → 1

Compiler

Compiled 390 to 301 computations (22.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	7	10

end45.0ms (1.2%)

Compiler: Compiled 32 to 25 computations (21.9% saved)

Details

analyze391.0ms (10.4%)

sample2.1s (56.1%)

simplify151.0ms (4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series14.0ms (0.4%)

rewrite8.0ms (0.2%)

simplify82.0ms (2.2%)

prune70.0ms (1.8%)

localize5.0ms (0.1%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify90.0ms (2.4%)

prune26.0ms (0.7%)

localize5.0ms (0.1%)

series43.0ms (1.2%)

rewrite5.0ms (0.1%)

simplify80.0ms (2.1%)

prune21.0ms (0.6%)

localize8.0ms (0.2%)

series370.0ms (9.8%)

rewrite8.0ms (0.2%)

simplify121.0ms (3.2%)

prune46.0ms (1.2%)

regimes53.0ms (1.4%)

simplify2.0ms (0%)

end45.0ms (1.2%)

Profiling