Details

analyze893.0ms (17.4%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
12.5%	85.8%	1.7%	9
16.4%	79.2%	4.4%	10
20.7%	72.4%	7%	11
32.6%	53.3%	14.1%	12
36%	45.5%	18.5%	13
38.3%	41.1%	20.6%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample1.4s (28.1%)

Results

1.0s	8256×	body	128	valid
344.0ms	2981×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

802×	`fma-def_binary64`
795×	`div-sub_binary64`
536×	`times-frac_binary64`
518×	`neg-mul-1_binary64`
376×	`distribute-frac-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	65	20
3	126	20
4	278	20
5	602	20
6	1317	19
7	2853	19
8	4446	19
9	4743	19
10	4991	19

prune4.0ms (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

10.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.7b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
	28.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	11.4b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series59.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
26.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
6.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite95.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

613×	`fma-def_binary64`
351×	`fma-neg_binary64`
344×	`egg-rr`
199×	`expm1-udef_binary64`
199×	`log1p-udef_binary64`

Counts

3 → 344

Calls

3 calls:

87.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
87.0ms	(-.f64 (.f64 z z) (.f64 x x))
87.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	39
1	216	39
2	3077	39
3	5085	39
0	0	0
1	0	0

simplify130.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

957×	`fma-neg_binary64`
377×	`associate-l_binary64`
347×	`neg-sub0_binary64`
345×	`neg-mul-1_binary64`
323×	`associate-r_binary64`

Counts

440 → 365

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	1234
1	54	1153
2	115	1153
3	283	1151
4	774	1151
5	2588	1151
6	4455	1151
7	4989	1151
8	4993	1151
9	4915	1151

prune275.0ms (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	360	5	365
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	361	6	367

Error

0.0b

Counts

367 → 6

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	11.0b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
	10.7b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))
	29.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	0.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	28.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 8473 to 2806 computations (66.9% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z x) y)
✓	0.1b	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

series29.0ms (0.6%)

Counts

2 → 64

Calls

2 calls:

20.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))
9.0ms	(/.f64 (-.f64 z x) y)

rewrite115.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

875×	`prod-diff_binary64`
349×	`egg-rr`
188×	`log1p-udef_binary64`
114×	`add-sqr-sqrt_binary64`
107×	`log1p-expm1-u_binary64`

Counts

2 → 349

Calls

2 calls:

104.0ms	(/.f64 (-.f64 z x) y)
104.0ms	(fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	227	21
2	2933	21
3	4977	21
0	0	0
1	0	0

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

768×	`div-sub_binary64`
717×	`fma-neg_binary64`
342×	`distribute-rgt-neg-in_binary64`
257×	`associate-l_binary64`
246×	`associate-r_binary64`

Counts

413 → 367

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	836
1	61	755
2	114	733
3	262	687
4	645	687
5	2192	687
6	4220	687
7	4971	687

prune240.0ms (4.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	366	1	367
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	366	7	373

Error

Counts

373 → 7

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	11.0b	(.f64 -1/2 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y)) 3) y))
	10.7b	(.f64 -1/2 (-.f64 (pow.f64 (/.f64 y (-.f64 (.f64 z z) (*.f64 x x))) -1) y))
	29.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
▶	0.5b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	28.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
	8.2b	(.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (+.f64 (fma.f64 z (/.f64 1 y) (neg.f64 (.f64 (/.f64 x (cbrt.f64 y)) (/.f64 1 (cbrt.f64 (.f64 y y)))))) (fma.f64 (neg.f64 (/.f64 x (cbrt.f64 y))) (/.f64 1 (cbrt.f64 (.f64 y y))) (.f64 (/.f64 x (cbrt.f64 y)) (/.f64 1 (cbrt.f64 (.f64 y y)))))) (neg.f64 y)))

Compiler

Compiled 13925 to 3558 computations (74.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2))
✓	0.3b	(*.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y)))
✓	0.5b	(pow.f64 (cbrt.f64 y) 2)
✓	0.5b	(cbrt.f64 y)

series347.0ms (6.7%)

Counts

4 → 96

Calls

4 calls:

221.0ms	(/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2))
51.0ms	(*.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y)))
39.0ms	(pow.f64 (cbrt.f64 y) 2)
36.0ms	(cbrt.f64 y)

rewrite78.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

758×	`prod-diff_binary64`
138×	`add-sqr-sqrt_binary64`
133×	`egg-rr`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`

Counts

4 → 133

Calls

4 calls:

75.0ms	(/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2))
75.0ms	(*.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y)))
75.0ms	(pow.f64 (cbrt.f64 y) 2)
75.0ms	(cbrt.f64 y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	274	34
2	3899	34
3	5413	34
0	0	0
1	0	0

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

739×	`unswap-sqr_binary64`
680×	`fma-def_binary64`
338×	`associate-l_binary64`
306×	`associate-r_binary64`
190×	`distribute-rgt-in_binary64`

Counts

229 → 155

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	1160
1	90	1160
2	191	1160
3	591	1160
4	2319	1160
5	4905	1160
6	4950	1160

prune149.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	184	4	188

Error

Counts

188 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	29.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	28.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 3987 to 1732 computations (56.6% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
✓	0.0b	(/.f64 y (-.f64 z x))
✓	0.2b	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

series58.0ms (1.1%)

Counts

3 → 96

Calls

3 calls:

24.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
19.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))
15.0ms	(/.f64 y (-.f64 z x))

rewrite86.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

475×	`fma-def_binary64`
263×	`fma-neg_binary64`
214×	`egg-rr`
210×	`expm1-udef_binary64`
210×	`log1p-udef_binary64`

Counts

3 → 214

Calls

3 calls:

81.0ms	(-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y)
81.0ms	(/.f64 y (-.f64 z x))
81.0ms	(/.f64 (+.f64 z x) (/.f64 y (-.f64 z x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	217	36
2	3344	36
3	5003	36
0	0	0
1	0	0

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-/r/_binary64`
406×	`cancel-sign-sub-inv_binary64`
382×	`associate-/l/_binary64`
242×	`fma-neg_binary64`
205×	`fma-def_binary64`

Counts

310 → 246

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	1630
1	165	1549
2	484	1441
3	1958	1402
4	4475	1402
5	4985	1402

prune142.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	246	0	246
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	246	4	250

Error

Counts

250 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (+.f64 z x) (/.f64 y (-.f64 z x))) y))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 z x) 1) (/.f64 (-.f64 z x) y) (neg.f64 y)))
	29.6b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))
	28.5b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 5233 to 1660 computations (68.3% saved)

regimes590.0ms (11.5%)

Accuracy

Total 0.1b remaining (85.1%)

Threshold costs 0.1b (85.1%)

Counts

80 → 1

Compiler

Compiled 9560 to 6190 computations (35.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	19	19
2	24	19
3	27	19
4	28	19
5	28	19

end66.0ms (1.3%)

Compiler: Compiled 104 to 65 computations (37.5% saved)

Details

analyze893.0ms (17.4%)

sample1.4s (28.1%)

simplify70.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.2%)

series59.0ms (1.1%)

rewrite95.0ms (1.8%)

simplify130.0ms (2.5%)

prune275.0ms (5.3%)

localize9.0ms (0.2%)

series29.0ms (0.6%)

rewrite115.0ms (2.2%)

simplify81.0ms (1.6%)

prune240.0ms (4.7%)

localize13.0ms (0.3%)

series347.0ms (6.7%)

rewrite78.0ms (1.5%)

simplify75.0ms (1.5%)

prune149.0ms (2.9%)

localize9.0ms (0.2%)

series58.0ms (1.1%)

rewrite86.0ms (1.7%)

simplify76.0ms (1.5%)

prune142.0ms (2.8%)

regimes590.0ms (11.5%)

simplify3.0ms (0.1%)

end66.0ms (1.3%)

Profiling