Details

analyze137.0ms (2.9%)

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 (24.6%)

Results

835.0ms	8254×	body	128	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify210.0ms (4.4%)

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)

localize7.0ms (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)))
✓	8.2b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series20.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

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

rewrite18.0ms (0.4%)

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)))
3.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

simplify154.0ms (3.2%)

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

prune164.0ms (3.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	147	3	150

Error

Counts

150 → 3

Alt Table

Status	Error	Program
	36.6b	(cbrt.f64 (.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	22.5b	(-.f64 x (/.f64 2 x))
▶	13.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 4931 to 3129 computations (36.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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)))
✓	4.7b	(sqrt.f64 (fma.f64 x (/.f64 y 2) 1))

series82.0ms (1.7%)

Counts

3 → 40

Calls

3 calls:

46.0ms	(/.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 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1)))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 233

Calls

3 calls:

8.0ms	(/.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))

simplify227.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

527×	`associate-l_binary64`
525×	`associate-/l/_binary64`
508×	`unswap-sqr_binary64`
464×	`times-frac_binary64`
397×	`associate-/r*_binary64`

Counts

273 → 288

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	278	10572
1	646	9594
2	1501	8940
3	4263	8733
4	5497	8733

prune284.0ms (5.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	311	3	314

Error

Counts

314 → 3

Alt Table

Status	Error	Program
	36.6b	(cbrt.f64 (.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
▶	22.5b	(-.f64 x (/.f64 2 x))
✓	13.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 10243 to 7142 computations (30.3% saved)

localize10.0ms (0.2%)

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))

rewrite11.0ms (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))

simplify95.0ms (2%)

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

prune55.0ms (1.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
▶	36.6b	(cbrt.f64 (.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
✓	22.5b	(-.f64 x (/.f64 2 x))
✓	13.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 2228 to 1460 computations (34.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))
✓	0.1b	(.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))
	8.2b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
✓	34.8b	(cbrt.f64 (.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))

series66.0ms (1.4%)

Counts

3 → 72

Calls

3 calls:

30.0ms

(*.f64 (*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

18.0ms

(*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

17.0ms

(cbrt.f64 (*.f64 (*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))

rewrite136.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`add-sqr-sqrt_binary64`
188×	`*-un-lft-identity_binary64`
172×	`add-cube-cbrt_binary64`
156×	`prod-diff_binary64`
149×	`times-frac_binary64`

Counts

3 → 356

Calls

3 calls:

21.0ms

(*.f64 (*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

15.0ms

(cbrt.f64 (*.f64 (*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))

15.0ms

(*.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

simplify621.0ms (13%)

Algorithm

1×	egg-herbie

Rules

457×	`fma-def_binary64`
358×	`distribute-rgt-in_binary64`
267×	`*-commutative_binary64`
265×	`distribute-lft-in_binary64`
201×	`fma-neg_binary64`

Counts

428 → 496

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	791	41637
1	1895	26381
2	4155	25483
3	4982	25483
4	5035	25483

prune820.0ms (17.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	634	0	634
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	634	3	637

Error

Counts

637 → 3

Alt Table

Status	Error	Program
✓	36.6b	(cbrt.f64 (.f64 (.f64 (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
✓	22.5b	(-.f64 x (/.f64 2 x))
✓	13.5b	(-.f64 x (/.f64 (/.f64 y (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))) (sqrt.f64 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 41113 to 26454 computations (35.7% saved)

regimes356.0ms (7.4%)

Accuracy

Total -0.1b remaining (-228.2%)

Threshold costs -0.1b (-228.2%)

Counts

109 → 1

Compiler

Compiled 6272 to 4397 computations (29.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	14
2	23	14
3	26	14
4	27	14
5	26	14

end68.0ms (1.4%)

Compiler: Compiled 87 to 59 computations (32.2% saved)

Details

analyze137.0ms (2.9%)

sample1.2s (24.6%)

simplify210.0ms (4.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series20.0ms (0.4%)

rewrite18.0ms (0.4%)

simplify154.0ms (3.2%)

prune164.0ms (3.4%)

localize8.0ms (0.2%)

series82.0ms (1.7%)

rewrite41.0ms (0.9%)

simplify227.0ms (4.7%)

prune284.0ms (5.9%)

localize10.0ms (0.2%)

series2.0ms (0%)

rewrite11.0ms (0.2%)

simplify95.0ms (2%)

prune55.0ms (1.1%)

localize10.0ms (0.2%)

series66.0ms (1.4%)

rewrite136.0ms (2.8%)

simplify621.0ms (13%)

prune820.0ms (17.1%)

regimes356.0ms (7.4%)

simplify3.0ms (0.1%)

end68.0ms (1.4%)

Profiling