Details

analyze6.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample233.0ms (12.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify203.0ms (11.1%)

Algorithm

1×	egg-herbie

Rules

1115×	`distribute-rgt-neg-in_binary64`
788×	`distribute-rgt-out--_binary64`
692×	`unsub-neg_binary64`
492×	`fma-neg_binary64`
461×	`distribute-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	34	20
4	50	20
5	73	20
6	113	20
7	247	20
8	452	20
9	742	20
10	1560	20
11	2338	20
12	2392	20
13	2628	20
14	2776	20
15	2774	20
16	2851	20
17	3110	20
18	3673	20
19	4665	20
20	4910	20
21	4952	20
22	4963	20
23	4960	20
24	6208	20

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓	0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

series17.0ms (0.9%)

Counts

3 → 36

Calls

3 calls:

7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
5.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
5.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite31.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
28×	`sqrt-prod_binary64`

Counts

3 → 109

Calls

3 calls:

16.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
4.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify135.0ms (7.4%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
513×	`associate-/r*_binary64`
454×	`fma-neg_binary64`
403×	`associate-l_binary64`
384×	`associate-r_binary64`

Counts

145 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2614
1	524	2522
2	1462	2491
3	4611	2491
4	4998	2491
5	5000	2491
6	4917	2491

prune128.0ms (7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	2	187

Error

Counts

187 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.0b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))

Compiler

Compiled 4008 to 2780 computations (30.6% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
✓	0.0b	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
✓	0.0b	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

series8.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
3.0ms	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

rewrite20.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 67

Calls

2 calls:

10.0ms	(.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))
6.0ms	(+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)

simplify91.0ms (5%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
339×	`fma-def_binary64`
270×	`associate-l_binary64`
240×	`associate-r_binary64`
225×	`sub-neg_binary64`

Counts

91 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1603
1	390	1443
2	1110	1415
3	3349	1415
4	4842	1415
5	4995	1415

prune127.0ms (7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	190	2	192

Error

Counts

192 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
✓	0.0b	(log.f64 (.f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x)))

Compiler

Compiled 3856 to 2856 computations (25.9% saved)

regimes47.0ms (2.5%)

Accuracy

Total 0.0b remaining (2.8%)

Threshold costs 0.0b (2.8%)

Counts

16 → 1

Compiler

Compiled 598 to 460 computations (23.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	28	20
4	30	20
5	29	20

end0.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample761.0ms (41.6%)

Algorithm

1×

intervals

Results

537.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 58 to 43 computations (25.9% saved)

Details

analyze6.0ms (0.3%)

sample233.0ms (12.7%)

simplify203.0ms (11.1%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series17.0ms (0.9%)

rewrite31.0ms (1.7%)

simplify135.0ms (7.4%)

prune128.0ms (7%)

localize9.0ms (0.5%)

series8.0ms (0.5%)

rewrite20.0ms (1.1%)

simplify91.0ms (5%)

prune127.0ms (7%)

regimes47.0ms (2.5%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample761.0ms (41.6%)

Profiling