Details

analyze370.0ms (4.5%)

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
12.5%	87.4%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample42.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	204×	body	128	valid
5.0ms	22×	body	1024	valid
3.0ms	16×	body	512	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify248.0ms (3%)

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

13.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	13.7b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	22.3b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	13.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series38.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

21.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
17.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite15.0ms (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:

10.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
1.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify155.0ms (1.9%)

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

prune181.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
	24.2b	(fma.f64 y (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 y))) (/.f64 (+.f64 x -1) (sqrt.f64 (+.f64 1 y)))) 1)
▶	22.3b	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
	31.4b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	32.5b	(-.f64 (fma.f64 y y (fma.f64 y x 1)) (*.f64 (fma.f64 y x 1) y))

Compiler

Compiled 1962 to 1343 computations (31.5% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 1 y))
✓	3.4b	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
✓	8.0b	(/.f64 (*.f64 y x) (+.f64 1 y))

series47.0ms (0.6%)

Counts

3 → 39

Calls

3 calls:

22.0ms	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
21.0ms	(/.f64 (*.f64 y x) (+.f64 1 y))
5.0ms	(/.f64 y (+.f64 1 y))

rewrite97.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`*-un-lft-identity_binary64`
78×	`add-sqr-sqrt_binary64`
77×	`times-frac_binary64`
73×	`add-cube-cbrt_binary64`
72×	`prod-diff_binary64`

Counts

3 → 177

Calls

3 calls:

38.0ms	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
10.0ms	(/.f64 (*.f64 y x) (+.f64 1 y))
7.0ms	(/.f64 y (+.f64 1 y))

simplify317.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-neg_binary64`
407×	`distribute-rgt-in_binary64`
316×	`cancel-sign-sub-inv_binary64`
222×	`sub-neg_binary64`
188×	`distribute-rgt-neg-in_binary64`

Counts

216 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	326	8748
1	902	4963
2	2748	3902
3	4668	3902
4	4868	3902

prune406.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	249	2	251
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	251	4	255

Error

0.0b

Counts

255 → 4

Alt Table

Status	Error	Program
✓	22.3b	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
	31.4b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
▶	13.8b	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
	22.3b	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (+.f64 1 y) (*.f64 y x)))) (/.f64 y (+.f64 1 y)))

Compiler

Compiled 7902 to 5090 computations (35.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (+.f64 1 y))
✓	0.0b	(/.f64 (+.f64 1 y) x)
✓	3.4b	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
✓	6.9b	(/.f64 y (/.f64 (+.f64 1 y) x))

series39.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

18.0ms	(/.f64 y (/.f64 (+.f64 1 y) x))
15.0ms	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
6.0ms	(/.f64 (+.f64 1 y) x)

rewrite112.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

225×	`*-un-lft-identity_binary64`
169×	`times-frac_binary64`
125×	`add-sqr-sqrt_binary64`
120×	`add-cube-cbrt_binary64`
72×	`prod-diff_binary64`

Counts

3 → 234

Calls

3 calls:

38.0ms	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
9.0ms	(/.f64 (+.f64 1 y) x)
8.0ms	(/.f64 y (/.f64 (+.f64 1 y) x))

simplify338.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

479×	`fma-neg_binary64`
331×	`cancel-sign-sub-inv_binary64`
207×	`distribute-rgt-neg-in_binary64`
206×	`sub-neg_binary64`
184×	`associate-*l/_binary64`

Counts

294 → 329

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	411	8223
1	1044	5964
2	3249	5280
3	4519	5280
4	4832	5280

prune667.0ms (8.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	396	1	397
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	397	4	401

Error

0.0b

Counts

401 → 4

Alt Table

Status	Error	Program
✓	22.3b	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
	31.4b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	13.8b	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
▶	13.8b	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))) (/.f64 y (+.f64 1 y)))

Compiler

Compiled 11599 to 7604 computations (34.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (+.f64 1 y) x)
✓	0.5b	(/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))
✓	3.4b	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))) (/.f64 y (+.f64 1 y)))
✓	7.0b	(/.f64 (/.f64 (+.f64 1 y) x) y)

series68.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

24.0ms	(/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))
23.0ms	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))) (/.f64 y (+.f64 1 y)))
21.0ms	(/.f64 (/.f64 (+.f64 1 y) x) y)

rewrite241.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

661×	`times-frac_binary64`
532×	`*-un-lft-identity_binary64`
341×	`add-sqr-sqrt_binary64`
336×	`add-cube-cbrt_binary64`
106×	`distribute-lft-out_binary64`

Counts

3 → 457

Calls

3 calls:

82.0ms	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))) (/.f64 y (+.f64 1 y)))
22.0ms	(/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))
16.0ms	(/.f64 (/.f64 (+.f64 1 y) x) y)

simplify632.0ms (7.7%)

Algorithm

1×	egg-herbie

Rules

436×	`fma-neg_binary64`
341×	`cancel-sign-sub-inv_binary64`
339×	`associate-/r/_binary64`
228×	`associate-/l/_binary64`
227×	`associate-*r/_binary64`

Counts

529 → 532

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	503	16591
1	1241	11946
2	3780	10972
3	4851	10972
4	4851	10972

prune936.0ms (11.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	590	0	590
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	590	4	594

Error

0.0b

Counts

594 → 4

Alt Table

Status	Error	Program
✓	22.3b	(-.f64 (+.f64 1 (/.f64 (*.f64 y x) (+.f64 1 y))) (/.f64 y (+.f64 1 y)))
	31.4b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
✓	13.8b	(-.f64 (+.f64 1 (/.f64 y (/.f64 (+.f64 1 y) x))) (/.f64 y (+.f64 1 y)))
✓	13.8b	(-.f64 (+.f64 1 (/.f64 1 (/.f64 (/.f64 (+.f64 1 y) x) y))) (/.f64 y (+.f64 1 y)))

Compiler

Compiled 18743 to 12599 computations (32.8% saved)

regimes2.2s (27.5%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Counts

162 → 3

Compiler

Compiled 14886 to 10841 computations (27.2% saved)

bsearch33.0ms (0.4%)

Steps

Iters	Range		Point
8	1038.8614783312923	1388133.4245000205	12600.971116972236
9	-30135488075665064.0	-482858796.6169149	-489641527.8911863

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
13×	`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	36	93
1	53	93
2	70	93
3	91	93
4	112	93
5	125	93
6	130	93
7	131	93
8	128	93

end1.0ms (0%)

Compiler: Compiled 65 to 42 computations (35.4% saved)

sample862.0ms (10.6%)

Algorithm

1×

intervals

Results

280.0ms	6288×	body	128	valid
100.0ms	606×	body	1024	valid
86.0ms	682×	body	512	valid
33.0ms	418×	body	256	valid
1.0ms	6×	body	2048	valid

Compiler

Compiled 167 to 114 computations (31.7% saved)

Details

analyze370.0ms (4.5%)

sample42.0ms (0.5%)

simplify248.0ms (3%)

prune7.0ms (0.1%)

localize12.0ms (0.2%)

series38.0ms (0.5%)

rewrite15.0ms (0.2%)

simplify155.0ms (1.9%)

prune181.0ms (2.2%)

localize15.0ms (0.2%)

series47.0ms (0.6%)

rewrite97.0ms (1.2%)

simplify317.0ms (3.9%)

prune406.0ms (5%)

localize12.0ms (0.1%)

series39.0ms (0.5%)

rewrite112.0ms (1.4%)

simplify338.0ms (4.1%)

prune667.0ms (8.2%)

localize18.0ms (0.2%)

series68.0ms (0.8%)

rewrite241.0ms (3%)

simplify632.0ms (7.7%)

prune936.0ms (11.5%)

regimes2.2s (27.5%)

bsearch33.0ms (0.4%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample862.0ms (10.6%)

Profiling