Details

analyze641.0ms (15.2%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
14%	85.8%	0.1%	7
22.6%	77.2%	0.1%	8
23.8%	74.5%	1.7%	9
40%	56%	4%	10
47.3%	48.7%	4%	11
48.4%	45.8%	5.8%	12
58.6%	32.4%	9%	13
63.4%	27.5%	9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify168.0ms (4%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary64`
740×	`associate-/l/_binary64`
677×	`fma-def_binary64`
607×	`associate-/r/_binary64`
557×	`associate-*l/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	10
2	23	10
3	36	10
4	41	10
5	47	10
6	51	8
7	61	8
8	228	8
9	761	8
10	851	8
11	964	8
12	975	8
13	980	8
14	985	8
15	2231	8
16	2288	8
17	2637	8
18	2689	8
19	2901	8
20	3031	8
21	3278	8
22	3700	8
23	4109	8
24	4157	8
25	4872	8
26	4997	8
27	4889	8

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.6b	(fma.f64 x (/.f64 y z) x)
	14.0b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.3b	(fma.f64 x (/.f64 y z) x)

series12.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

12.0ms

(fma.f64 x (/.f64 y z) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (/.f64 y z) x)

simplify84.0ms (2%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
449×	`associate-/l/_binary64`
410×	`distribute-rgt-in_binary64`
404×	`distribute-rgt-out_binary64`
400×	`unswap-sqr_binary64`

Counts

46 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	451
1	32	374
2	63	374
3	171	374
4	650	374
5	2482	374
6	3613	374
7	3881	374
8	4329	374
9	5248	374

prune16.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	22	4	26

Error

0.1b

Counts

26 → 4

Alt Table

Status	Error	Program
▶	5.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	41.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (/.f64 y z) x) (fma.f64 x (/.f64 y z) x)) (fma.f64 x (/.f64 y z) x)))
✓	4.6b	(fma.f64 x (/.f64 y z) x)
	14.0b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 363 to 101 computations (72.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	0.6b	(cbrt.f64 (fma.f64 x (/.f64 y z) x))
	4.3b	(fma.f64 x (/.f64 y z) x)

series807.0ms (19.1%)

Counts

3 → 108

Calls

3 calls:

447.0ms

(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

347.0ms

(cbrt.f64 (fma.f64 x (/.f64 y z) x))

13.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))

1.0ms

(cbrt.f64 (fma.f64 x (/.f64 y z) x))

simplify135.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

884×	`times-frac_binary64`
509×	`fma-def_binary64`
305×	`fma-neg_binary64`
168×	`cancel-sign-sub-inv_binary64`
153×	`associate-r_binary64`

Counts

201 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	5248
1	697	4885
2	1919	4145
3	4758	4117
4	5006	4117

prune188.0ms (4.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	355	1	356
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	355	5	360

Error

0.0b

Counts

360 → 5

Alt Table

Status	Error	Program
	32.4b	(.f64 (cbrt.f64 (.f64 (fma.f64 x (/.f64 y z) x) (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
▶	14.0b	(/.f64 (*.f64 x (+.f64 y z)) z)
✓	5.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	41.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x (/.f64 y z) x) (fma.f64 x (/.f64 y z) x)) (fma.f64 x (/.f64 y z) x)))
✓	4.6b	(fma.f64 x (/.f64 y z) x)

Compiler

Compiled 12495 to 3384 computations (72.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 y z))
✓	13.4b	(/.f64 (*.f64 x (+.f64 y z)) z)

series18.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

12.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
6.0ms	(*.f64 x (+.f64 y z))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(*.f64 x (+.f64 y z))
5.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
653×	`times-frac_binary64`
561×	`associate-/l*_binary64`
379×	`associate-l_binary64`
280×	`distribute-rgt-in_binary64`

Counts

122 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	1193
1	243	1100
2	912	1064
3	3804	1064
4	4699	1064
5	4993	1064
6	5005	1064

prune34.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	79	6	85

Error

Counts

85 → 6

Alt Table

Status	Error	Program
	15.0b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (+.f64 y z))) z)
▶	4.6b	(/.f64 x (/.f64 z (+.f64 y z)))
	39.3b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 z (-.f64 y z)))
	5.2b	(fma.f64 (/.f64 x z) y x)
✓	4.6b	(fma.f64 x (/.f64 y z) x)
✓	14.0b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 1097 to 327 computations (70.2% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (+.f64 y z))
✓	4.3b	(/.f64 x (/.f64 z (+.f64 y z)))

series22.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
10.0ms	(/.f64 z (+.f64 y z))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
94×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
62×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

2 → 127

Calls

2 calls:

6.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
4.0ms	(/.f64 z (+.f64 y z))

simplify131.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
431×	`associate-/r/_binary64`
426×	`times-frac_binary64`
421×	`associate-/l*_binary64`
413×	`associate-*l/_binary64`

Counts

187 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	3275
1	468	3167
2	1547	3065
3	4392	3044
4	4977	3044
5	4975	3044

prune87.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Error

Counts

187 → 6

Alt Table

Status	Error	Program
	15.0b	(/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (*.f64 (cbrt.f64 x) (+.f64 y z))) z)
✓	4.6b	(/.f64 x (/.f64 z (+.f64 y z)))
	39.3b	(/.f64 (.f64 x (-.f64 (.f64 y y) (.f64 z z))) (.f64 z (-.f64 y z)))
	5.2b	(fma.f64 (/.f64 x z) y x)
✓	4.6b	(fma.f64 x (/.f64 y z) x)
✓	14.0b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 3019 to 728 computations (75.9% saved)

regimes546.0ms (12.9%)

Accuracy

Total 0.2b remaining (95.5%)

Threshold costs 0.2b (95.5%)

Counts

50 → 5

Compiler

Compiled 3648 to 1810 computations (50.4% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	106
1	28	106
2	28	106

end1.0ms (0%)

Compiler: Compiled 76 to 24 computations (68.4% saved)

sample1.1s (26.9%)

Algorithm

1×

intervals

Results

510.0ms	8000×	body	128	valid
36.0ms	687×	body	128	invalid

Compiler

Compiled 163 to 75 computations (54% saved)

Details

analyze641.0ms (15.2%)

sample19.0ms (0.4%)

simplify168.0ms (4%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify84.0ms (2%)

prune16.0ms (0.4%)

localize8.0ms (0.2%)

series807.0ms (19.1%)

rewrite20.0ms (0.5%)

simplify135.0ms (3.2%)

prune188.0ms (4.5%)

localize6.0ms (0.1%)

series18.0ms (0.4%)

rewrite13.0ms (0.3%)

simplify92.0ms (2.2%)

prune34.0ms (0.8%)

localize4.0ms (0.1%)

series22.0ms (0.5%)

rewrite21.0ms (0.5%)

simplify131.0ms (3.1%)

prune87.0ms (2.1%)

regimes546.0ms (12.9%)

bsearch2.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (26.9%)

Profiling