Details

analyze132.0ms (3.4%)

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)

sample1.4s (36.3%)

Results

1.1s	8254×	body	128	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify211.0ms (5.4%)

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)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.6b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series16.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

16.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
594×	`cancel-sign-sub-inv_binary64`
507×	`fma-neg_binary64`
429×	`unswap-sqr_binary64`
267×	`distribute-rgt-neg-in_binary64`

Counts

53 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	1138
1	222	1084
2	633	1076
3	2141	1060
4	4943	1060
5	4935	1060

prune38.0ms (1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Error

Counts

47 → 4

Alt Table

Status	Error	Program
	0.2b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
	0.6b	(-.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (fma.f64 x (/.f64 y 2) 1))))
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
▶	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 1009 to 656 computations (35% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
✓	7.5b	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

series19.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

12.0ms	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
7.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

4.0ms	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
2.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

simplify119.0ms (3%)

Algorithm

1×	egg-herbie

Rules

620×	`cancel-sign-sub-inv_binary64`
500×	`fma-neg_binary64`
438×	`unswap-sqr_binary64`
320×	`associate-r_binary64`
314×	`associate-l_binary64`

Counts

155 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	3204
1	302	2905
2	877	2870
3	2896	2862
4	4835	2862
5	4951	2862

prune163.0ms (4.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	1	1	2
Picked	0	1	1
Done	1	0	1
Total	181	3	184

Error

Counts

184 → 3

Alt Table

Status	Error	Program
	0.2b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
▶	0.1b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 4075 to 2784 computations (31.7% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(/.f64 1 (fma.f64 1/2 x (/.f64 1 y)))
8.0ms	(fma.f64 1/2 x (/.f64 1 y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-exp-log_binary64`

Counts

2 → 43

Calls

2 calls:

2.0ms	(/.f64 1 (fma.f64 1/2 x (/.f64 1 y)))
0.0ms	(fma.f64 1/2 x (/.f64 1 y))

simplify74.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

773×	`times-frac_binary64`
685×	`fma-def_binary64`
669×	`fma-neg_binary64`
579×	`cancel-sign-sub-inv_binary64`
416×	`unswap-sqr_binary64`

Counts

91 → 65

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	85	1396
1	192	1325
2	532	1317
3	1810	1299
4	4739	1299
5	5917	1299

prune54.0ms (1.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	65	3	68

Error

Counts

68 → 3

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
✓	0.1b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 1195 to 880 computations (26.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))
✓	0.4b	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	1.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
✓	7.8b	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))

series90.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

32.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
27.0ms	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))
18.0ms	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))
13.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`add-exp-log_binary64`
59×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
31×	`cbrt-prod_binary64`

Counts

4 → 164

Calls

4 calls:

13.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
4.0ms	(/.f64 1 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
4.0ms	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))
1.0ms	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))

simplify284.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-/r*_binary64`
336×	`fma-neg_binary64`
227×	`*-commutative_binary64`
219×	`associate-*r/_binary64`
215×	`associate-r_binary64`

Counts

260 → 357

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	437	10184
1	1274	8330
2	4350	7603
3	4976	7603
4	4995	7603
5	4950	7603

prune554.0ms (14.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	465	0	465
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	465	3	468

Error

Counts

468 → 3

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (/.f64 y (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
✓	0.1b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 21067 to 15425 computations (26.8% saved)

regimes496.0ms (12.7%)

Accuracy

Total 0.0b remaining (84.1%)

Threshold costs 0.0b (84.1%)

Counts

116 → 1

Compiler

Compiled 7985 to 5843 computations (26.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	20	14
2	26	14
3	29	14
4	32	14
5	33	14
6	31	14

end65.0ms (1.7%)

Compiler: Compiled 81 to 58 computations (28.4% saved)

Details

analyze132.0ms (3.4%)

sample1.4s (36.3%)

simplify211.0ms (5.4%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series16.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify67.0ms (1.7%)

prune38.0ms (1%)

localize7.0ms (0.2%)

series19.0ms (0.5%)

rewrite14.0ms (0.3%)

simplify119.0ms (3%)

prune163.0ms (4.2%)

localize6.0ms (0.1%)

series18.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify74.0ms (1.9%)

prune54.0ms (1.4%)

localize12.0ms (0.3%)

series90.0ms (2.3%)

rewrite39.0ms (1%)

simplify284.0ms (7.3%)

prune554.0ms (14.2%)

regimes496.0ms (12.7%)

simplify2.0ms (0.1%)

end65.0ms (1.7%)

Profiling