Details

analyze143.0ms (2.6%)

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
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
31.2%	68.7%	0.1%	6
50%	50%	0.1%	7
67.1%	32.8%	0.1%	8
74.9%	25%	0.1%	9
83.9%	16%	0.1%	10
87.4%	12.5%	0.1%	11
92%	7.9%	0.1%	12
93.7%	6.2%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample1.2s (21.6%)

Results

831.0ms	8254×	body	128	valid
8.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify222.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

2174×	`fma-neg_binary64`
1504×	`div-sub_binary64`
895×	`associate-/l/_binary64`
827×	`fma-def_binary64`
818×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	57	14
5	91	14
6	134	14
7	193	14
8	356	14
9	521	14
10	825	14
11	1475	14
12	2002	14
13	1877	14
14	1931	14
15	1961	14
16	1967	14
17	1967	14
18	2590	14
19	2366	14
20	2366	14
21	3254	14
22	4052	14
23	4024	14
24	4504	14
25	4470	14
26	4706	14
27	4913	14

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 47 to 31 computations (34% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	8.3b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series21.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
10.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 100

Calls

2 calls:

6.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
2.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

simplify159.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
422×	`fma-neg_binary64`
414×	`associate-/l*_binary64`
273×	`cancel-sign-sub-inv_binary64`
190×	`times-frac_binary64`

Counts

148 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4990
1	637	3475
2	1683	2934
3	4633	2926
4	4994	2926
5	4994	2926
6	4795	2926

prune126.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
	14.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
▶	7.9b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.3b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 4901 to 3111 computations (36.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
✓	0.0b	(log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	0.4b	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1))))
	8.3b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series50.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

29.0ms	(log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
10.0ms	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
10.0ms	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 53

Calls

3 calls:

6.0ms	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
0.0ms	(log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

simplify82.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

708×	`times-frac_binary64`
246×	`sub-neg_binary64`
245×	`fma-neg_binary64`
232×	`unswap-sqr_binary64`
229×	`fma-def_binary64`

Counts

125 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	3629
1	757	3311
2	2825	3191
3	4973	3191

prune155.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	182	4	186

Error

Counts

186 → 4

Alt Table

Status	Error	Program
▶	14.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	7.9b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.3b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 4972 to 3468 computations (30.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	0.1b	(/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))
✓	0.1b	(/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))
✓	3.6b	(sqrt.f64 (fma.f64 x (/.f64 y 2) 1))

series92.0ms (1.7%)

Counts

4 → 64

Calls

4 calls:

45.0ms	(/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))
24.0ms	(sqrt.f64 (fma.f64 x (/.f64 y 2) 1))
10.0ms	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
10.0ms	(/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))

rewrite255.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

1246×	`times-frac_binary64`
811×	`add-sqr-sqrt_binary64`
788×	`*-un-lft-identity_binary64`
786×	`add-cube-cbrt_binary64`
632×	`sqrt-prod_binary64`

Counts

4 → 801

Calls

4 calls:

40.0ms	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
7.0ms	(/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))
3.0ms	(/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))
1.0ms	(sqrt.f64 (fma.f64 x (/.f64 y 2) 1))

simplify1.2s (22.1%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
351×	`distribute-neg-frac_binary64`
328×	`associate-/l*_binary64`
265×	`associate-/l/_binary64`
253×	`fma-udef_binary64`

Counts

865 → 836

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	885	87844
1	2541	56677
2	4745	56677
3	5084	56677

prune1.4s (26.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	859	0	859
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	859	4	863

Error

Counts

863 → 4

Alt Table

Status	Error	Program
✓	14.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	7.9b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
▶	21.3b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 61290 to 43342 computations (29.3% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 2 x))

series2.0ms (0%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(-.f64 x (/.f64 2 x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`
37×	`times-frac_binary64`

Counts

1 → 71

Calls

1 calls:

6.0ms

(-.f64 x (/.f64 2 x))

simplify96.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

365×	`associate-*l/_binary64`
360×	`fma-neg_binary64`
342×	`exp-prod_binary64`
332×	`associate-*r/_binary64`
332×	`fma-def_binary64`

Counts

83 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	170	1025
1	409	890
2	989	651
3	3477	651
4	4031	651
5	4942	651
6	4527	651

prune57.0ms (1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	89	4	93

Error

Counts

93 → 4

Alt Table

Status	Error	Program
✓	14.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	7.9b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
✓	21.3b	(-.f64 x (/.f64 2 x))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 2184 to 1432 computations (34.4% saved)

regimes50.0ms (0.9%)

Accuracy

Total 0.0b remaining (81.2%)

Threshold costs 0.0b (81.2%)

Counts

16 → 1

Compiler

Compiled 518 to 380 computations (26.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	16	16
2	22	16
3	26	16
4	29	16
5	30	16
6	29	16

end60.0ms (1.1%)

Compiler: Compiled 80 to 56 computations (30% saved)

Details

analyze143.0ms (2.6%)

sample1.2s (21.6%)

simplify222.0ms (4.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series21.0ms (0.4%)

rewrite18.0ms (0.3%)

simplify159.0ms (2.9%)

prune126.0ms (2.3%)

localize9.0ms (0.2%)

series50.0ms (0.9%)

rewrite9.0ms (0.2%)

simplify82.0ms (1.5%)

prune155.0ms (2.9%)

localize9.0ms (0.2%)

series92.0ms (1.7%)

rewrite255.0ms (4.7%)

simplify1.2s (22.1%)

prune1.4s (26.2%)

localize3.0ms (0%)

series2.0ms (0%)

rewrite12.0ms (0.2%)

simplify96.0ms (1.8%)

prune57.0ms (1%)

regimes50.0ms (0.9%)

simplify3.0ms (0%)

end60.0ms (1.1%)

Profiling