Details

analyze526.0ms (16.5%)

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)

sample1.0s (32.2%)

Results

811.0ms	8256×	body	128	valid
109.0ms	1069×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify59.0ms (1.9%)

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

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

9.9b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 42 to 22 computations (47.6% 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)

series22.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 x (-.f64 y z) x) z)
8.0ms	(fma.f64 x (-.f64 y z) x)

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`
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)

simplify69.0ms (2.2%)

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

prune41.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	5	74

Error

0.0b

Counts

74 → 5

Alt Table

Status	Error	Program
	3.8b	(*.f64 1 (-.f64 (/.f64 (fma.f64 y x x) z) x))
▶	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	10.0b	(/.f64 1 (/.f64 z (fma.f64 x (-.f64 y z) x)))
	37.5b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))

Compiler

Compiled 1089 to 273 computations (74.9% saved)

localize5.0ms (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)
✓	2.8b	(fma.f64 (/.f64 x z) y (/.f64 x z))

series34.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

18.0ms	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
16.0ms	(fma.f64 (/.f64 x z) y (/.f64 x z))

rewrite5.0ms (0.2%)

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

simplify90.0ms (2.8%)

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

prune37.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	74	5	79

Error

0.0b

Counts

79 → 5

Alt Table

Status	Error	Program
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
▶	3.8b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
	4.4b	(-.f64 (*.f64 (+.f64 (/.f64 y z) (/.f64 1 z)) x) x)
	37.5b	(/.f64 (/.f64 (fma.f64 x (-.f64 y z) x) (sqrt.f64 z)) (sqrt.f64 z))

Compiler

Compiled 1453 to 313 computations (78.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
✓	0.0b	(+.f64 (*.f64 y x) x)
✓	3.6b	(/.f64 (+.f64 (*.f64 y x) x) z)

series32.0ms (1%)

Counts

3 → 75

Calls

3 calls:

15.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
13.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)
3.0ms	(+.f64 (*.f64 y x) x)

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
74×	`add-sqr-sqrt_binary64`
69×	`add-cube-cbrt_binary64`
57×	`prod-diff_binary64`

Counts

3 → 150

Calls

3 calls:

9.0ms	(-.f64 (/.f64 (+.f64 (*.f64 y x) x) z) x)
4.0ms	(/.f64 (+.f64 (*.f64 y x) x) z)
4.0ms	(+.f64 (*.f64 y x) x)

simplify114.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-def_binary64`
530×	`times-frac_binary64`
439×	`fma-neg_binary64`
245×	`distribute-rgt-in_binary64`
228×	`distribute-lft-in_binary64`

Counts

225 → 223

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	4142
1	369	3265
2	1388	2876
3	4348	2874
4	4936	2874

prune111.0ms (3.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	221	2	223
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	224	4	228

Error

0.0b

Counts

228 → 4

Alt Table

Status	Error	Program
▶	4.1b	(-.f64 (/.f64 x (/.f64 z (+.f64 y 1))) x)
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	4.3b	(-.f64 (fma.f64 (/.f64 y z) x (/.f64 x z)) x)

Compiler

Compiled 4681 to 1024 computations (78.1% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (/.f64 z (+.f64 y 1))) x)
✓	3.9b	(/.f64 x (/.f64 z (+.f64 y 1)))

series30.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

16.0ms	(-.f64 (/.f64 x (/.f64 z (+.f64 y 1))) x)
14.0ms	(/.f64 x (/.f64 z (+.f64 y 1)))

rewrite95.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

465×	`times-frac_binary64`
383×	`*-un-lft-identity_binary64`
294×	`add-sqr-sqrt_binary64`
285×	`add-cube-cbrt_binary64`
177×	`prod-diff_binary64`

Counts

2 → 348

Calls

2 calls:

32.0ms	(-.f64 (/.f64 x (/.f64 z (+.f64 y 1))) x)
6.0ms	(/.f64 x (/.f64 z (+.f64 y 1)))

simplify204.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

579×	`distribute-rgt-in_binary64`
562×	`distribute-lft-in_binary64`
194×	`associate-/l*_binary64`
160×	`fma-neg_binary64`
159×	`associate-*l/_binary64`

Counts

420 → 430

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	375	10874
1	643	8949
2	2660	8002
3	5088	8002

prune245.0ms (7.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	429	1	430
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	430	4	434

Error

Counts

434 → 4

Alt Table

Status	Error	Program
✓	4.1b	(-.f64 (/.f64 x (/.f64 z (+.f64 y 1))) x)
✓	1.3b	(-.f64 (fma.f64 (/.f64 x z) y (/.f64 x z)) x)
	10.0b	(*.f64 (fma.f64 x (-.f64 y z) x) (/.f64 1 z))
	4.2b	(-.f64 (/.f64 1 (/.f64 (/.f64 z (+.f64 y 1)) x)) x)

Compiler

Compiled 11524 to 5121 computations (55.6% saved)

regimes288.0ms (9%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Counts

53 → 3

Compiler

Compiled 3344 to 1966 computations (41.2% saved)

bsearch27.0ms (0.8%)

Steps

Iters	Range		Point
10	2147.666766333595	2264299378117239000.0	220123720629973600.0
1	-7.717413464269338e+88	-2.574413274709626e+86	-4.471222327351869e+87

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	31	51
2	37	51
3	39	51
4	40	51
5	39	51

end69.0ms (2.2%)

Compiler: Compiled 128 to 80 computations (37.5% saved)

Details

analyze526.0ms (16.5%)

sample1.0s (32.2%)

simplify59.0ms (1.9%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series22.0ms (0.7%)

rewrite4.0ms (0.1%)

simplify69.0ms (2.2%)

prune41.0ms (1.3%)

localize5.0ms (0.2%)

series34.0ms (1.1%)

rewrite5.0ms (0.2%)

simplify90.0ms (2.8%)

prune37.0ms (1.2%)

localize6.0ms (0.2%)

series32.0ms (1%)

rewrite29.0ms (0.9%)

simplify114.0ms (3.6%)

prune111.0ms (3.5%)

localize6.0ms (0.2%)

series30.0ms (0.9%)

rewrite95.0ms (3%)

simplify204.0ms (6.4%)

prune245.0ms (7.7%)

regimes288.0ms (9%)

bsearch27.0ms (0.8%)

simplify3.0ms (0.1%)

end69.0ms (2.2%)

Profiling