Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample29.0ms (1.6%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	10	8
2	9	8

prune2.0ms (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

13.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.6b	(/.f64 x (fma.f64 x x 1))

Compiler

Compiled 28 to 16 computations (42.9% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	13.6b	(/.f64 x (fma.f64 x x 1))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 x (fma.f64 x x 1))

rewrite7.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

6.0ms

(/.f64 x (fma.f64 x x 1))

simplify70.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

543×	`associate-/l*_binary64`
513×	`div-sub_binary64`
480×	`associate-/l/_binary64`
388×	`fma-neg_binary64`
289×	`distribute-rgt-in_binary64`

Counts

41 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	72	635
1	147	601
2	366	580
3	807	580
4	2019	580
5	4600	580
6	5498	580

prune33.0ms (1.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 x)
	13.6b	(/.f64 1 (/.f64 (fma.f64 x x 1) x))
▶	0.0b	(*.f64 (/.f64 1 (hypot.f64 1 x)) (/.f64 x (hypot.f64 1 x)))
	37.0b	(cbrt.f64 (pow.f64 (/.f64 x (fma.f64 x x 1)) 3))

Compiler

Compiled 677 to 418 computations (38.3% saved)

localize9.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (hypot.f64 1 x))
✓	0.0b	(hypot.f64 1 x)
✓	0.0b	(*.f64 (/.f64 1 (hypot.f64 1 x)) (/.f64 x (hypot.f64 1 x)))
✓	0.0b	(/.f64 x (hypot.f64 1 x))

series13.0ms (0.7%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(*.f64 (/.f64 1 (hypot.f64 1 x)) (/.f64 x (hypot.f64 1 x)))
3.0ms	(/.f64 x (hypot.f64 1 x))
3.0ms	(/.f64 1 (hypot.f64 1 x))
3.0ms	(hypot.f64 1 x)

rewrite28.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
34×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 130

Calls

4 calls:

12.0ms	(*.f64 (/.f64 1 (hypot.f64 1 x)) (/.f64 x (hypot.f64 1 x)))
2.0ms	(/.f64 1 (hypot.f64 1 x))
2.0ms	(/.f64 x (hypot.f64 1 x))
0.0ms	(hypot.f64 1 x)

simplify141.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-neg_binary64`
419×	`fma-def_binary64`
377×	`associate-/l*_binary64`
334×	`times-frac_binary64`
281×	`associate-*l/_binary64`

Counts

178 → 242

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	210	2692
1	564	2453
2	1668	2430
3	4268	2422
4	4904	2404
5	4938	2404

prune169.0ms (9.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	273	1	274
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	275	3	278

Error

Counts

278 → 3

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 x)
▶	0.0b	(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))
	13.6b	(/.f64 1 (/.f64 (fma.f64 x x 1) x))

Compiler

Compiled 5076 to 3817 computations (24.8% saved)

localize4.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))
	0.0b	(hypot.f64 1 x)
	0.0b	(/.f64 x (hypot.f64 1 x))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
13×	`associate-/l*_binary64`

Counts

1 → 72

Calls

1 calls:

4.0ms

(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))

simplify173.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
388×	`sub-neg_binary64`
340×	`associate-/l/_binary64`
330×	`fma-neg_binary64`
296×	`times-frac_binary64`

Counts

84 → 130

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	157	2206
1	348	2042
2	735	1889
3	1863	1818
4	2733	1770
5	4376	1645
6	4867	1597
7	4981	1597
8	5000	1597
9	4913	1597

prune135.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	247	3	250

Error

Counts

250 → 3

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 x)
✓	0.0b	(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))
▶	13.6b	(/.f64 1 (/.f64 (fma.f64 x x 1) x))

Compiler

Compiled 4302 to 3052 computations (29.1% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 x x 1) x))
✓	13.6b	(/.f64 (fma.f64 x x 1) x)

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1 (/.f64 (fma.f64 x x 1) x))
2.0ms	(/.f64 (fma.f64 x x 1) x)

rewrite14.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 x x 1) x))
2.0ms	(/.f64 (fma.f64 x x 1) x)

simplify112.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-neg_binary64`
480×	`distribute-rgt-in_binary64`
446×	`distribute-lft-in_binary64`
328×	`fma-def_binary64`
318×	`associate-/l*_binary64`

Counts

131 → 165

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	117	2207
1	225	1982
2	601	1871
3	1435	1871
4	2986	1838
5	4559	1838
6	4940	1838

prune82.0ms (4.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	165	0	165
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	165	3	168

Error

Counts

168 → 3

Alt Table

Status	Error	Program
	34.5b	(/.f64 1 x)
✓	0.0b	(/.f64 (/.f64 x (hypot.f64 1 x)) (hypot.f64 1 x))
✓	13.6b	(/.f64 1 (/.f64 (fma.f64 x x 1) x))

Compiler

Compiled 2722 to 1792 computations (34.2% saved)

regimes58.0ms (3.2%)

Accuracy

Total 0.0b remaining (65.2%)

Threshold costs 0.0b (65.2%)

Counts

34 → 1

Compiler

Compiled 650 to 434 computations (33.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	8	13
2	7	13

end0.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

sample668.0ms (37.3%)

Algorithm

1×

intervals

Results

462.0ms

8000×

body

128

valid

Compiler

Compiled 43 to 30 computations (30.2% saved)

Details

analyze1.0ms (0.1%)

sample29.0ms (1.6%)

simplify6.0ms (0.3%)

prune2.0ms (0.1%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite7.0ms (0.4%)

simplify70.0ms (3.9%)

prune33.0ms (1.8%)

localize9.0ms (0.5%)

series13.0ms (0.7%)

rewrite28.0ms (1.6%)

simplify141.0ms (7.9%)

prune169.0ms (9.5%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite11.0ms (0.6%)

simplify173.0ms (9.7%)

prune135.0ms (7.6%)

localize5.0ms (0.3%)

series6.0ms (0.3%)

rewrite14.0ms (0.8%)

simplify112.0ms (6.2%)

prune82.0ms (4.6%)

regimes58.0ms (3.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample668.0ms (37.3%)

Profiling