Details

analyze1.6s (20.2%)

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)

sample2.4s (30.8%)

Results

1.7s	8256×	body	128	valid
614.0ms	2910×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify76.0ms (1%)

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%)

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

13.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	30.3b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))
▶	13.8b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))

Compiler

Compiled 99 to 58 computations (41.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
✓	0.2b	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
✓	1.4b	(-.f64 (.f64 z z) (.f64 x x))
✓	13.6b	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

series99.0ms (1.3%)

Counts

4 → 132

Calls

4 calls:

39.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
26.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
25.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)
8.0ms	(-.f64 (.f64 z z) (.f64 x x))

rewrite100.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

624×	`fma-def_binary64`
357×	`fma-neg_binary64`
339×	`egg-rr`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`

Counts

4 → 339

Calls

4 calls:

91.0ms	(-.f64 (/.f64 (-.f64 (.f64 z z) (.f64 x x)) y) y)
91.0ms	(.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))
91.0ms	(-.f64 (.f64 z z) (.f64 x x))
91.0ms	(/.f64 (-.f64 (.f64 z z) (.f64 x x)) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
1	257	58
2	3506	58
3	5128	58
0	0	0
1	0	0

simplify103.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
738×	`fma-def_binary64`
445×	`associate-/l*_binary64`
409×	`div-sub_binary64`
360×	`cancel-sign-sub-inv_binary64`

Counts

471 → 375

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	1999
1	88	1783
2	200	1756
3	493	1752
4	1475	1698
5	4170	1698
6	5235	1698

prune336.0ms (4.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	367	8	375
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	369	8	377

Error

0.2b

Counts

377 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	40.9b	(pow.f64 (sqrt.f64 (.f64 -1/2 (-.f64 (/.f64 (-.f64 (.f64 z z) (*.f64 x x)) y) y))) 2)
	0.9b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (pow.f64 (cbrt.f64 y) 2)) (/.f64 (-.f64 z x) (cbrt.f64 y))) y))
	14.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) y)) y))
▶	0.3b	(*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))
	7.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 z 1) (/.f64 z y) (neg.f64 (/.f64 (.f64 x x) y))) y))
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
	33.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))

Compiler

Compiled 8645 to 2850 computations (67% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x z) y)
✓	0.1b	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y)
✓	0.2b	(*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))

series60.0ms (0.8%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))
18.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y)
10.0ms	(/.f64 (+.f64 x z) y)

rewrite123.0ms (1.6%)

Algorithm

2×	batch-egg-rewrite

Rules

621×	`prod-diff_binary64`
461×	`fma-udef_binary64`
272×	`fma-def_binary64`
220×	`fma-neg_binary64`
207×	`expm1-udef_binary64`

Counts

3 → 73

Calls

3 calls:

121.0ms	(/.f64 (+.f64 x z) y)
121.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y)
121.0ms	(*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	221	38
2	2964	38
3	4969	38
4	4953	38
5	4958	38
0	0	0
1	0	0

simplify131.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-neg_binary64`
519×	`cancel-sign-sub-inv_binary64`
431×	`associate-l_binary64`
392×	`fma-def_binary64`
381×	`associate-r_binary64`

Counts

181 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	1552
1	76	1390
2	147	1390
3	315	1386
4	863	1278
5	2977	1278
6	4729	1278
7	4978	1278
8	4994	1278
9	4931	1278

prune88.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	104	7	111

Error

0.2b

Counts

111 → 7

Alt Table

Status	Error	Program
	0.4b	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	33.2b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))) 2)
▶	0.4b	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
	14.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) y)) y))
	7.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 z 1) (/.f64 z y) (neg.f64 (/.f64 (.f64 x x) y))) y))
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
	33.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))

Compiler

Compiled 1809 to 723 computations (60% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (+.f64 x z))
✓	0.1b	(fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y)
✓	0.2b	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
✓	0.8b	(pow.f64 (/.f64 y (+.f64 x z)) -1)

series315.0ms (4%)

Counts

4 → 144

Calls

4 calls:

112.0ms	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
96.0ms	(fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y)
88.0ms	(pow.f64 (/.f64 y (+.f64 x z)) -1)
19.0ms	(/.f64 y (+.f64 x z))

rewrite70.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

616×	`prod-diff_binary64`
234×	`log1p-udef_binary64`
133×	`add-sqr-sqrt_binary64`
126×	`log1p-expm1-u_binary64`
126×	`expm1-log1p-u_binary64`

Counts

4 → 118

Calls

4 calls:

68.0ms	(/.f64 y (+.f64 x z))
68.0ms	(fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y)
68.0ms	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
68.0ms	(pow.f64 (/.f64 y (+.f64 x z)) -1)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	263	45
2	3329	45
3	4897	45
0	0	0
1	0	0

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-neg_binary64`
738×	`cancel-sign-sub-inv_binary64`
609×	`fma-def_binary64`
374×	`associate-/l/_binary64`
221×	`neg-mul-1_binary64`

Counts

262 → 164

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	2218
1	162	2056
2	433	1984
3	1747	1926
4	4146	1926
5	5052	1926

prune124.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	164	7	171

Error

0.2b

Counts

171 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	33.2b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))) 2)
✓	0.4b	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
	14.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) y)) y))
	7.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 z 1) (/.f64 z y) (neg.f64 (/.f64 (.f64 x x) y))) y))
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
	33.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))

Compiler

Compiled 3059 to 1253 computations (59% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (+.f64 z x) (*.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y))
✓	0.2b	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
✓	0.2b	(*.f64 (-.f64 z x) (/.f64 1 y))

series69.0ms (0.9%)

Counts

3 → 108

Calls

3 calls:

32.0ms	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
20.0ms	(fma.f64 (+.f64 z x) (*.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y))
17.0ms	(*.f64 (-.f64 z x) (/.f64 1 y))

rewrite89.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

715×	`prod-diff_binary64`
237×	`egg-rr`
225×	`log1p-udef_binary64`
137×	`add-sqr-sqrt_binary64`
128×	`log1p-expm1-u_binary64`

Counts

3 → 237

Calls

3 calls:

82.0ms	(fma.f64 (+.f64 z x) (*.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y))
82.0ms	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
82.0ms	(*.f64 (-.f64 z x) (/.f64 1 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	277	38
2	3207	38
3	4902	38
0	0	0
1	0	0

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
656×	`fma-neg_binary64`
427×	`div-sub_binary64`
426×	`associate-/l*_binary64`
308×	`distribute-rgt-in_binary64`

Counts

345 → 269

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	1591
1	99	1429
2	201	1429
3	482	1371
4	1368	1344
5	4071	1344
6	4989	1344

prune148.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	269	0	269
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	269	7	276

Error

0.2b

Counts

276 → 7

Alt Table

Status	Error	Program
✓	0.4b	(.f64 -1/2 (fma.f64 (+.f64 z x) (.f64 (-.f64 z x) (/.f64 1 y)) (neg.f64 y)))
	33.2b	(pow.f64 (sqrt.f64 (*.f64 1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 x z) y))) 2)
✓	0.4b	(*.f64 1/2 (fma.f64 (pow.f64 (/.f64 y (+.f64 x z)) -1) (-.f64 x z) y))
	14.1b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) 2) 1) (/.f64 (cbrt.f64 (-.f64 (.f64 z z) (.f64 x x))) y)) y))
	7.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 z 1) (/.f64 z y) (neg.f64 (/.f64 (.f64 x x) y))) y))
	23.0b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) y))
	33.7b	(.f64 -1/2 (-.f64 (.f64 (/.f64 (+.f64 z x) (sqrt.f64 y)) (/.f64 (-.f64 z x) (sqrt.f64 y))) y))

Compiler

Compiled 6949 to 1803 computations (74.1% saved)

regimes1.6s (20.2%)

Accuracy

Total 0.1b remaining (52.6%)

Threshold costs 0.1b (52.6%)

Counts

191 → 1

Compiler

Compiled 23032 to 14862 computations (35.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
6×	`*-commutative_binary64`
6×	`distribute-neg-in_binary64`
6×	`sub-neg_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	22	21
2	30	21
3	40	19
4	57	19
5	66	19
6	67	19
7	63	19

end126.0ms (1.6%)

Compiler: Compiled 167 to 105 computations (37.1% saved)

Details

analyze1.6s (20.2%)

sample2.4s (30.8%)

simplify76.0ms (1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series99.0ms (1.3%)

rewrite100.0ms (1.3%)

simplify103.0ms (1.3%)

prune336.0ms (4.3%)

localize7.0ms (0.1%)

series60.0ms (0.8%)

rewrite123.0ms (1.6%)

simplify131.0ms (1.7%)

prune88.0ms (1.1%)

localize8.0ms (0.1%)

series315.0ms (4%)

rewrite70.0ms (0.9%)

simplify90.0ms (1.1%)

prune124.0ms (1.6%)

localize9.0ms (0.1%)

series69.0ms (0.9%)

rewrite89.0ms (1.1%)

simplify86.0ms (1.1%)

prune148.0ms (1.9%)

regimes1.6s (20.2%)

simplify4.0ms (0%)

end126.0ms (1.6%)

Profiling