Details

analyze548.0ms (19.7%)

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)

sample1.2s (43%)

Results

921.0ms	8256×	body	128	valid
76.0ms	781×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify171.0ms (6.1%)

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
▶	2.3b	(fma.f64 x (/.f64 y z) x)
	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 x (/.f64 y z) x)

series14.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(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)

simplify74.0ms (2.6%)

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

prune12.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

0.0b

Counts

26 → 3

Alt Table

Status	Error	Program
	29.8b	(*.f64 (sqrt.f64 (fma.f64 x (/.f64 y z) x)) (sqrt.f64 (fma.f64 x (/.f64 y z) x)))
✓	2.3b	(fma.f64 x (/.f64 y z) x)
▶	12.8b	(/.f64 (*.f64 x (+.f64 y z)) z)

Compiler

Compiled 299 to 83 computations (72.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 y z))
✓	12.1b	(/.f64 (*.f64 x (+.f64 y z)) z)

series30.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

22.0ms	(/.f64 (*.f64 x (+.f64 y z)) z)
7.0ms	(*.f64 x (+.f64 y z))

rewrite13.0ms (0.5%)

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

simplify91.0ms (3.3%)

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 (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	78	5	83

Error

Counts

83 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 x (/.f64 y z) x)
▶	4.3b	(fma.f64 (/.f64 x z) y x)
	37.2b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 y z))) z)
	12.9b	(.f64 (.f64 x (+.f64 y z)) (/.f64 1 z))
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (+.f64 y z) (sqrt.f64 z)))

Compiler

Compiled 1077 to 319 computations (70.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 (/.f64 x z) y x)

series13.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

13.0ms

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

simplify84.0ms (3%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-def_binary64`
536×	`associate-/l*_binary64`
448×	`associate-/l/_binary64`
432×	`unswap-sqr_binary64`
415×	`fabs-mul_binary64`

Counts

46 → 24

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	451
1	33	434
2	66	374
3	149	374
4	563	374
5	2135	374
6	3271	374
7	3518	374
8	3915	374
9	4905	374
10	5492	374

prune15.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	24	0	24
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	24	5	29

Error

Counts

29 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 x (/.f64 y z) x)
✓	4.3b	(fma.f64 (/.f64 x z) y x)
	37.2b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 y z))) z)
▶	12.9b	(.f64 (.f64 x (+.f64 y z)) (/.f64 1 z))
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (+.f64 y z) (sqrt.f64 z)))

Compiler

Compiled 332 to 111 computations (66.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 x (+.f64 y z))
✓	12.2b	(.f64 (.f64 x (+.f64 y z)) (/.f64 1 z))

series13.0ms (0.5%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(*.f64 (*.f64 x (+.f64 y z)) (/.f64 1 z))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
12×	`prod-exp_binary64`
9×	`times-frac_binary64`

Counts

1 → 44

Calls

1 calls:

10.0ms

(*.f64 (*.f64 x (+.f64 y z)) (/.f64 1 z))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary64`
546×	`associate-/r*_binary64`
441×	`distribute-rgt-in_binary64`
432×	`distribute-lft-in_binary64`
411×	`associate-/l/_binary64`

Counts

80 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	976
1	254	868
2	879	868
3	2987	757
4	5169	757

prune99.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Error

Counts

112 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 x (/.f64 y z) x)
✓	4.3b	(fma.f64 (/.f64 x z) y x)
	37.2b	(/.f64 (.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (+.f64 y z))) z)
✓	12.9b	(.f64 (.f64 x (+.f64 y z)) (/.f64 1 z))
	37.1b	(*.f64 (/.f64 x (sqrt.f64 z)) (/.f64 (+.f64 y z) (sqrt.f64 z)))

Compiler

Compiled 1625 to 639 computations (60.7% saved)

regimes177.0ms (6.4%)

Accuracy

Total 1.9b remaining (99.2%)

Threshold costs 0b (0%)

Counts

22 → 3

Compiler

Compiled 1108 to 606 computations (45.3% saved)

bsearch30.0ms (1.1%)

Steps

Iters	Range		Point
10	2.9550354382012066e-147	2.713617851841958e-133	2.074166328143206e-140
3	-14898154350.665077	-4779113269.58353	-5649729669.802156

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	22	40
2	22	40

end71.0ms (2.5%)

Compiler: Compiled 120 to 66 computations (45% saved)

Details

analyze548.0ms (19.7%)

sample1.2s (43%)

simplify171.0ms (6.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite1.0ms (0%)

simplify74.0ms (2.6%)

prune12.0ms (0.4%)

localize5.0ms (0.2%)

series30.0ms (1.1%)

rewrite13.0ms (0.5%)

simplify91.0ms (3.3%)

prune36.0ms (1.3%)

localize4.0ms (0.1%)

series13.0ms (0.5%)

rewrite1.0ms (0%)

simplify84.0ms (3%)

prune15.0ms (0.6%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite13.0ms (0.5%)

simplify56.0ms (2%)

prune99.0ms (3.6%)

regimes177.0ms (6.4%)

bsearch30.0ms (1.1%)

simplify2.0ms (0.1%)

end71.0ms (2.5%)

Profiling