Details

analyze475.0ms (12.4%)

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
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)

sample1.1s (27.5%)

Results

765.0ms	8256×	body	128	valid
74.0ms	768×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify168.0ms (4.4%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.8b	(fma.f64 x (/.f64 y z) x)
	11.1b	(/.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
✓	2.6b	(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:

1.0ms

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

simplify80.0ms (2.1%)

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

prune15.0ms (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

0.0b

Counts

26 → 4

Alt Table

Status	Error	Program
	35.7b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
▶	4.0b	(.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)))
✓	2.8b	(fma.f64 x (/.f64 y z) x)
	11.1b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 351 to 99 computations (71.8% saved)

localize7.0ms (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)))
✓	0.5b	(cbrt.f64 (fma.f64 x (/.f64 y z) x))
	2.6b	(fma.f64 x (/.f64 y z) x)

series797.0ms (20.7%)

Counts

3 → 108

Calls

3 calls:

438.0ms

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

346.0ms

(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)))

rewrite19.0ms (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 (3.5%)

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

prune156.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	354	2	356
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	354	6	360

Error

0.0b

Counts

360 → 6

Alt Table

Status	Error	Program
	28.0b	(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) 6)) (cbrt.f64 (fma.f64 x (/.f64 y z) x)))
	36.1b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)) (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (*.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x))) (sqrt.f64 (cbrt.f64 (fma.f64 x (/.f64 y z) x)))))
	35.7b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	4.0b	(.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)))
✓	2.8b	(fma.f64 x (/.f64 y z) x)
▶	11.1b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 12547 to 3404 computations (72.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 y z))
✓	10.5b	(/.f64 (*.f64 x (+.f64 y z)) z)

series18.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

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

rewrite12.0ms (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:

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

simplify90.0ms (2.3%)

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

prune36.0ms (0.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	3	0	3
Picked	1	0	1
Done	1	1	2
Total	81	5	86

Error

Counts

86 → 5

Alt Table

Status	Error	Program
	11.1b	(/.f64 (/.f64 (*.f64 x (+.f64 y z)) 1) z)
	39.1b	(/.f64 (/.f64 (*.f64 x (+.f64 y z)) (sqrt.f64 z)) (sqrt.f64 z))
▶	2.4b	(/.f64 x (/.f64 z (+.f64 y z)))
	39.4b	(.f64 (sqrt.f64 (/.f64 (.f64 x (+.f64 y z)) z)) (sqrt.f64 (/.f64 (*.f64 x (+.f64 y z)) z)))
✓	2.8b	(fma.f64 x (/.f64 y z) x)

Compiler

Compiled 1091 to 321 computations (70.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 z (+.f64 y z))
✓	2.3b	(/.f64 x (/.f64 z (+.f64 y z)))

series21.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

12.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
9.0ms	(/.f64 z (+.f64 y z))

rewrite20.0ms (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:

7.0ms	(/.f64 x (/.f64 z (+.f64 y z)))
3.0ms	(/.f64 z (+.f64 y z))

simplify127.0ms (3.3%)

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

prune72.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	181	5	186

Error

Counts

186 → 5

Alt Table

Status	Error	Program
✓	2.8b	(fma.f64 x (/.f64 y z) x)
	11.1b	(*.f64 (/.f64 1 z) (/.f64 x (/.f64 1 (+.f64 y z))))
	39.1b	(/.f64 (/.f64 (*.f64 x (+.f64 y z)) (sqrt.f64 z)) (sqrt.f64 z))
✓	2.4b	(/.f64 x (/.f64 z (+.f64 y z)))
	11.1b	(/.f64 (*.f64 (+.f64 y z) x) z)

Compiler

Compiled 3003 to 722 computations (76% saved)

regimes441.0ms (11.5%)

Accuracy

Total 0.2b remaining (93.6%)

Threshold costs 0.2b (93.6%)

Counts

55 → 5

Compiler

Compiled 4150 to 1936 computations (53.3% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	28	110
2	27	110

end60.0ms (1.6%)

Compiler: Compiled 213 to 75 computations (64.8% saved)

Details

analyze475.0ms (12.4%)

sample1.1s (27.5%)

simplify168.0ms (4.4%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

series12.0ms (0.3%)

rewrite1.0ms (0%)

simplify80.0ms (2.1%)

prune15.0ms (0.4%)

localize7.0ms (0.2%)

series797.0ms (20.7%)

rewrite19.0ms (0.5%)

simplify135.0ms (3.5%)

prune156.0ms (4.1%)

localize5.0ms (0.1%)

series18.0ms (0.5%)

rewrite12.0ms (0.3%)

simplify90.0ms (2.3%)

prune36.0ms (0.9%)

localize5.0ms (0.1%)

series21.0ms (0.5%)

rewrite20.0ms (0.5%)

simplify127.0ms (3.3%)

prune72.0ms (1.9%)

regimes441.0ms (11.5%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end60.0ms (1.6%)

Profiling