Details

analyze510.0ms (18.6%)

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%	3.7%	10
46.9%	48.7%	4.4%	11
48%	45.8%	6.2%	12
58.1%	32.2%	9.7%	13
62.1%	27.2%	10.6%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample107.0ms (3.9%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	41×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

823×	`div-sub_binary64`
529×	`fma-neg_binary64`
475×	`distribute-rgt-in_binary64`
409×	`fma-def_binary64`
380×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	50	11
3	156	11
4	331	11
5	666	11
6	1744	11
7	3988	11
8	4953	11

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

9.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.9b	(/.f64 (fma.f64 x (-.f64 y z) x) z)
	9.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)

Compiler

Compiled 66 to 38 computations (42.4% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 y z) x)
✓	9.3b	(/.f64 (fma.f64 x (-.f64 y z) x) z)

series27.0ms (1%)

Counts

2 → 72

Calls

2 calls:

19.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
7.0ms	(fma.f64 x (-.f64 y z) x)

rewrite4.0ms (0.2%)

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`
4×	`add-cbrt-cube_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
0.0ms	(fma.f64 x (-.f64 y z) x)

simplify74.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

672×	`associate-/l*_binary64`
629×	`fma-def_binary64`
448×	`associate-/l/_binary64`
308×	`associate-/r*_binary64`
291×	`associate-/r/_binary64`

Counts

111 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	1522
1	160	1371
2	374	1332
3	1227	1332
4	4358	1332
5	5042	1332

prune49.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	6	75

Error

0.0b

Counts

75 → 6

Alt Table

Status	Error	Program
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 z)))
▶	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	10.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	9.9b	(/.f64 (*.f64 x (+.f64 (-.f64 y z) 1)) z)
	40.2b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))

Compiler

Compiled 1169 to 297 computations (74.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
✓	2.5b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series36.0ms (1.3%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
18.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
2.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

simplify89.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

663×	`fma-neg_binary64`
438×	`associate-l_binary64`
352×	`associate-r_binary64`
336×	`fma-def_binary64`
307×	`distribute-rgt-out_binary64`

Counts

113 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1698
1	160	1621
2	607	1157
3	2730	1152
4	4468	1152
5	4961	1152

prune45.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Error

0.0b

Counts

80 → 6

Alt Table

Status	Error	Program
	11.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 (fma.f64 x (-.f64 y z) x))) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 (fma.f64 x (-.f64 y z) x)) (cbrt.f64 z)))
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	3.8b	(-.f64 (+.f64 (/.f64 (*.f64 y x) z) (/.f64 x z)) x)
	10.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
▶	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	40.2b	(*.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) (/.f64 (sqrt.f64 (fma.f64 x (-.f64 y z) x)) z))

Compiler

Compiled 1537 to 339 computations (77.9% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (/.f64 1 z))
✓	0.0b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
✓	2.3b	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)

series43.0ms (1.6%)

Counts

3 → 75

Calls

3 calls:

18.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
17.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
8.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

rewrite43.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
23×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

3 → 89

Calls

3 calls:

14.0ms	(*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x)
13.0ms	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
11.0ms	(+.f64 (/.f64 y z) (/.f64 1 z))

simplify99.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary64`
585×	`fma-def_binary64`
393×	`fma-neg_binary64`
381×	`distribute-rgt-in_binary64`
362×	`distribute-lft-in_binary64`

Counts

164 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	2112
1	301	2041
2	1225	1572
3	3819	1517
4	4989	1517

prune117.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	4	0	4
Picked	0	1	1
Done	0	1	1
Total	145	6	151

Error

Counts

151 → 6

Alt Table

Status	Error	Program
▶	3.9b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	34.3b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 z)) (fma.f64 x (/.f64 y (sqrt.f64 z)) (/.f64 x (sqrt.f64 z)))) x)
	25.3b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	32.8b	(-.f64 (.f64 (.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 x)) x)

Compiler

Compiled 2567 to 1205 computations (53.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	3.8b	(*.f64 (/.f64 1 z) (fma.f64 x y x))

series30.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

15.0ms	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
15.0ms	(*.f64 (/.f64 1 z) (fma.f64 x y x))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
13×	`associate-l_binary64`
13×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
11×	`times-frac_binary64`

Counts

2 → 61

Calls

2 calls:

6.0ms	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
5.0ms	(*.f64 (/.f64 1 z) (fma.f64 x y x))

simplify102.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-def_binary64`
440×	`fma-neg_binary64`
329×	`distribute-rgt-in_binary64`
324×	`distribute-lft-in_binary64`
227×	`associate-/l*_binary64`

Counts

133 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	129	1600
1	261	1388
2	993	1371
3	3418	1371
4	4697	1371
5	4967	1371
6	4874	1371

prune72.0ms (2.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	110	6	116

Error

Counts

116 → 6

Alt Table

Status	Error	Program
✓	3.9b	(-.f64 (*.f64 (/.f64 1 z) (fma.f64 x y x)) x)
✓	1.7b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	34.3b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 z)) (fma.f64 x (/.f64 y (sqrt.f64 z)) (/.f64 x (sqrt.f64 z)))) x)
	25.3b	(-.f64 (/.f64 (.f64 x (fma.f64 z y z)) (.f64 z z)) x)
✓	2.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	32.8b	(-.f64 (.f64 (.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) (sqrt.f64 x)) (sqrt.f64 x)) x)

Compiler

Compiled 1863 to 770 computations (58.7% saved)

regimes425.0ms (15.6%)

Accuracy

Total 0.5b remaining (96.8%)

Threshold costs 0.5b (96.8%)

Counts

76 → 3

Compiler

Compiled 4464 to 2526 computations (43.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	86
1	44	86
2	53	86
3	57	86
4	59	86
5	58	86

end1.0ms (0%)

Compiler: Compiled 61 to 32 computations (47.5% saved)

sample729.0ms (26.7%)

Algorithm

1×

intervals

Results

307.0ms	8000×	body	128	valid
39.0ms	1099×	body	128	invalid

Compiler

Compiled 170 to 97 computations (42.9% saved)

Details

analyze510.0ms (18.6%)

sample107.0ms (3.9%)

simplify58.0ms (2.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series27.0ms (1%)

rewrite4.0ms (0.2%)

simplify74.0ms (2.7%)

prune49.0ms (1.8%)

localize6.0ms (0.2%)

series36.0ms (1.3%)

rewrite7.0ms (0.3%)

simplify89.0ms (3.2%)

prune45.0ms (1.7%)

localize8.0ms (0.3%)

series43.0ms (1.6%)

rewrite43.0ms (1.6%)

simplify99.0ms (3.6%)

prune117.0ms (4.3%)

localize6.0ms (0.2%)

series30.0ms (1.1%)

rewrite16.0ms (0.6%)

simplify102.0ms (3.7%)

prune72.0ms (2.6%)

regimes425.0ms (15.6%)

bsearch3.0ms (0.1%)

simplify17.0ms (0.6%)

end1.0ms (0%)

sample729.0ms (26.7%)

Profiling