Details

analyze193.0ms (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample30.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 21 to 13 computations (38.1% saved)

simplify86.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-neg_binary64`
439×	`fma-def_binary64`
382×	`times-frac_binary64`
357×	`div-sub_binary64`
168×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	9	10
2	14	10
3	21	10
4	28	10
5	51	10
6	74	10
7	104	10
8	154	10
9	319	10
10	479	10
11	806	10
12	1050	10
13	1216	10
14	1316	10
15	1330	10
16	1350	10
17	1350	10
18	1250	10

prune3.0ms (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	(/.f64 (+.f64 x y) (-.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))

series17.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

12.0ms

(/.f64 (+.f64 x y) (-.f64 x y))

simplify142.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

910×	`fma-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
387×	`distribute-rgt-in_binary64`
223×	`fma-def_binary64`
161×	`associate-/l*_binary64`

Counts

71 → 57

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	109	1282
1	280	1222
2	785	1160
3	2516	1148
4	4566	1139
5	5172	1139

prune61.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	30.1b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	33.4b	(fma.f64 (/.f64 x y) -2 -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
▶	29.9b	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 944 to 314 computations (66.7% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series47.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))
17.0ms	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

rewrite134.0ms (5%)

Algorithm

1×	rewrite-expression-head

Rules

248×	`*-un-lft-identity_binary64`
188×	`sqrt-prod_binary64`
161×	`add-sqr-sqrt_binary64`
157×	`times-frac_binary64`
64×	`add-cube-cbrt_binary64`

Counts

2 → 196

Calls

2 calls:

50.0ms	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))
10.0ms	(sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y)))

simplify227.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

864×	`times-frac_binary64`
633×	`associate-/l*_binary64`
318×	`fma-def_binary64`
170×	`associate-/l/_binary64`
160×	`associate-r_binary64`

Counts

244 → 213

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	5455
1	494	5203
2	1773	5018
3	5155	5018

prune340.0ms (12.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	379	0	379
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	379	4	383

Error

Counts

383 → 4

Alt Table

Status	Error	Program
▶	30.1b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
	33.4b	(fma.f64 (/.f64 x y) -2 -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	29.9b	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 9930 to 1972 computations (80.1% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

series26.0ms (1%)

Counts

1 → 24

Calls

1 calls:

26.0ms

(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 39

Calls

1 calls:

18.0ms

(*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x))

simplify179.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

332×	`associate-l_binary64`
268×	`associate-r_binary64`
245×	`associate-*l/_binary64`
242×	`associate-*r/_binary64`
228×	`distribute-rgt-in_binary64`

Counts

63 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	92	1078
1	227	929
2	773	850
3	2605	849
4	4059	838
5	4960	838

prune71.0ms (2.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	64	4	68

Error

Counts

68 → 4

Alt Table

Status	Error	Program
✓	30.1b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
▶	33.4b	(fma.f64 (/.f64 x y) -2 -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	29.9b	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 1290 to 636 computations (50.7% saved)

localize14.0ms (0.5%)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
✓	30.1b	(fma.f64 2 (*.f64 (+.f64 (/.f64 y x) 1) (/.f64 y x)) 1)
✓	33.4b	(fma.f64 (/.f64 x y) -2 -1)
✓	0.0b	(/.f64 (+.f64 x y) (-.f64 x y))
✓	29.9b	(*.f64 (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))) (sqrt.f64 (/.f64 (+.f64 x y) (-.f64 x y))))

Compiler

Compiled 50 to 27 computations (46% saved)

regimes102.0ms (3.8%)

Accuracy

Total 0.0b remaining (71.3%)

Threshold costs 0.0b (71.3%)

Counts

19 → 1

Compiler

Compiled 669 to 447 computations (33.2% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	11	14
2	16	14
3	18	14
4	19	14
5	19	14

end2.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

sample914.0ms (34.2%)

Algorithm

1×

intervals

Results

448.0ms

8000×

body

128

valid

Compiler

Compiled 73 to 42 computations (42.5% saved)

Details

analyze193.0ms (7.2%)

sample30.0ms (1.1%)

simplify86.0ms (3.2%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series17.0ms (0.6%)

rewrite19.0ms (0.7%)

simplify142.0ms (5.3%)

prune61.0ms (2.3%)

localize12.0ms (0.4%)

series47.0ms (1.8%)

rewrite134.0ms (5%)

simplify227.0ms (8.5%)

prune340.0ms (12.8%)

localize11.0ms (0.4%)

series26.0ms (1%)

rewrite23.0ms (0.8%)

simplify179.0ms (6.7%)

prune71.0ms (2.7%)

localize14.0ms (0.5%)

prune4.0ms (0.2%)

regimes102.0ms (3.8%)

simplify5.0ms (0.2%)

end2.0ms (0.1%)

sample914.0ms (34.2%)

Profiling