Details

analyze50.0ms (0.6%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	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 14 to 11 computations (21.4% saved)

sample1.5s (18.1%)

Results

723.0ms	6402×	body	128	valid
254.0ms	692×	body	1024	valid
176.0ms	699×	body	512	valid
111.0ms	455×	body	256	valid
3.0ms	8×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify277.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

14.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	14.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	22.0b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	14.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series30.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
10.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

11.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
1.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune137.0ms (1.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	102	2	104

Error

0.0b

Counts

104 → 2

Alt Table

Status	Error	Program
✓	14.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
▶	32.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))

Compiler

Compiled 1844 to 1260 computations (31.7% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 y y))
✓	3.3b	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
✓	6.0b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	7.0b	(/.f64 x (*.f64 y y))

series153.0ms (1.9%)

Counts

4 → 84

Calls

4 calls:

67.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
47.0ms	(/.f64 x (*.f64 y y))
34.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
4.0ms	(/.f64 1 (*.f64 y y))

rewrite100.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
26×	`distribute-lft-out_binary64`
24×	`prod-diff_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

37.0ms	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))
23.0ms	(+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))
8.0ms	(/.f64 x (*.f64 y y))
8.0ms	(/.f64 1 (*.f64 y y))

simplify269.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
251×	`cancel-sign-sub-inv_binary64`
196×	`associate-/r/_binary64`
171×	`distribute-rgt-neg-in_binary64`
166×	`distribute-rgt-in_binary64`

Counts

230 → 189

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	5463
1	643	4334
2	2435	3523
3	4370	3521
4	4967	3521

prune220.0ms (2.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	188	3	191

Error

0.0b

Counts

191 → 3

Alt Table

Status	Error	Program
▶	37.1b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (.f64 (/.f64 (+.f64 x -1) (.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (-.f64 1 x) y))))
✓	14.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	32.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))

Compiler

Compiled 6091 to 2823 computations (53.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.0b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (.f64 (/.f64 (+.f64 x -1) (.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (-.f64 1 x) y))))
	7.0b	(/.f64 x (*.f64 y y))
✓	17.0b	(+.f64 (/.f64 1 (pow.f64 y 4)) (.f64 (/.f64 (+.f64 x -1) (.f64 y y)) (-.f64 1 x)))
✓	34.6b	(/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (.f64 (/.f64 (+.f64 x -1) (.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (-.f64 1 x) y)))

series1.5s (18.5%)

Counts

3 → 72

Calls

3 calls:

1.3s

(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (-.f64 1 x) y))))

160.0ms

(/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (-.f64 1 x) y)))

64.0ms

(+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x)))

rewrite297.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

251×	`*-un-lft-identity_binary64`
149×	`times-frac_binary64`
123×	`add-sqr-sqrt_binary64`
118×	`prod-diff_binary64`
118×	`add-cube-cbrt_binary64`

Counts

3 → 270

Calls

3 calls:

69.0ms

(-.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (-.f64 1 x) y))))

47.0ms

(/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (-.f64 1 x) y)))

26.0ms

(+.f64 (/.f64 1 (pow.f64 y 4)) (*.f64 (/.f64 (+.f64 x -1) (*.f64 y y)) (-.f64 1 x)))

simplify740.0ms (9.2%)

Algorithm

1×	egg-herbie

Rules

385×	`times-frac_binary64`
358×	`fma-def_binary64`
277×	`associate-/l*_binary64`
256×	`distribute-rgt-in_binary64`
236×	`distribute-lft-in_binary64`

Counts

342 → 389

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	645	36560
1	1994	24677
2	5208	24677

prune1.3s (15.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	417	0	417
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	417	3	420

Error

0.0b

Counts

420 → 3

Alt Table

Status	Error	Program
✓	37.1b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 (+.f64 (/.f64 1 (pow.f64 y 4)) (.f64 (/.f64 (+.f64 x -1) (.f64 y y)) (-.f64 1 x))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (-.f64 1 x) y))))
✓	14.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
✓	32.6b	(-.f64 (+.f64 x (/.f64 x (.f64 y y))) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))

Compiler

Compiled 33216 to 19400 computations (41.6% saved)

regimes1.2s (14.6%)

Accuracy

Total 0.1b remaining (69.2%)

Threshold costs 0.1b (69.2%)

Counts

67 → 3

Compiler

Compiled 6763 to 4569 computations (32.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
12×	`sub-neg_binary64`
11×	`*-commutative_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	95
1	43	95
2	58	95
3	74	95
4	86	95
5	95	95
6	101	95
7	105	95
8	108	95
9	109	95
10	107	95

end175.0ms (2.2%)

Compiler: Compiled 206 to 137 computations (33.5% saved)

Iter	Nodes	Cost
0	31	95
1	43	95
2	58	95
3	74	95
4	86	95
5	95	95
6	101	95
7	105	95
8	108	95
9	109	95
10	107	95

Iter	Nodes	Cost
0	31	95
1	43	95
2	58	95
3	74	95
4	86	95
5	95	95
6	101	95
7	105	95
8	108	95
9	109	95
10	107	95

Details

analyze50.0ms (0.6%)

sample1.5s (18.1%)

simplify277.0ms (3.4%)

prune7.0ms (0.1%)

localize8.0ms (0.1%)

series30.0ms (0.4%)

rewrite19.0ms (0.2%)

simplify126.0ms (1.6%)

prune137.0ms (1.7%)

localize22.0ms (0.3%)

series153.0ms (1.9%)

rewrite100.0ms (1.2%)

simplify269.0ms (3.3%)

prune220.0ms (2.7%)

localize20.0ms (0.2%)

series1.5s (18.5%)

rewrite297.0ms (3.7%)

simplify740.0ms (9.2%)

prune1.3s (15.8%)

regimes1.2s (14.6%)

bsearch2.0ms (0%)

simplify10.0ms (0.1%)

end175.0ms (2.2%)

Profiling

Iter	Nodes	Cost
0	31	95
1	43	95
2	58	95
3	74	95
4	86	95
5	95	95
6	101	95
7	105	95
8	108	95
9	109	95
10	107	95