Details

analyze29.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 28 to 17 computations (39.3% saved)

sample2.4s (44.6%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 73 to 43 computations (41.1% saved)

simplify93.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

917×	`times-frac_binary64`
816×	`unsub-neg_binary64`
772×	`fma-def_binary64`
484×	`fma-neg_binary64`
376×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	24	20
2	55	20
3	112	20
4	271	20
5	657	20
6	1234	20
7	2620	20
8	3288	20
9	4652	20
10	5075	20

prune5.0ms (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

22.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	22.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Compiler

Compiled 63 to 27 computations (57.1% saved)

localize16.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (*.f64 y y))
✓	22.2b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

series43.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
13.0ms	(fma.f64 x x (*.f64 y y))

rewrite82.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

932×	`prod-diff_binary64`
189×	`log1p-udef_binary64`
108×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`
103×	`expm1-log1p-u_binary64`

Counts

2 → 67

Calls

2 calls:

79.0ms	(fma.f64 x x (*.f64 y y))
79.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	208	26
2	2987	26
3	5151	26
0	0	0
1	0	0

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
528×	`associate-*l/_binary64`
454×	`associate-*r/_binary64`
387×	`fma-def_binary64`
330×	`cancel-sign-sub-inv_binary64`

Counts

115 → 87

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	37	738
1	111	678
2	312	642
3	1210	609
4	4403	594
5	5036	594

prune103.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Error

0.0b

Counts

88 → 4

Alt Table

Status	Error	Program
	22.8b	(-.f64 (/.f64 x (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))) (/.f64 y (/.f64 (pow.f64 (hypot.f64 x y) 2) (+.f64 x y))))
	47.4b	1
✓	22.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
▶	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 1659 to 648 computations (60.9% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series84.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

47.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
19.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
18.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

rewrite204.0ms (3.8%)

Algorithm

2×	batch-egg-rewrite

Rules

805×	`prod-diff_binary64`
260×	`egg-rr`
200×	`log1p-udef_binary64`
111×	`add-sqr-sqrt_binary64`
106×	`log1p-expm1-u_binary64`

Counts

3 → 260

Calls

3 calls:

184.0ms	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))
184.0ms	(/.f64 (-.f64 x y) (hypot.f64 x y))
184.0ms	(/.f64 (+.f64 x y) (hypot.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	42
1	214	39
2	3271	39
3	5276	39
0	0	0
1	0	0

simplify164.0ms (3%)

Algorithm

1×	egg-herbie

Rules

425×	`distribute-neg-frac_binary64`
389×	`times-frac_binary64`
325×	`sub-neg_binary64`
252×	`fma-def_binary64`
246×	`unswap-sqr_binary64`

Counts

332 → 320

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	78	1324
1	270	1252
2	882	1152
3	3668	1098
4	4982	1098
5	4975	1098
6	4995	1098
7	4966	1098

prune422.0ms (7.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	318	2	320
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	320	4	324

Error

Counts

324 → 4

Alt Table

Status	Error	Program
✓	22.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
	0.0b	(/.f64 (-.f64 x y) (/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))))
▶	0.0b	(/.f64 (+.f64 x y) (*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y))))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 12748 to 2873 computations (77.5% saved)

localize15.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series80.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

45.0ms	(/.f64 (+.f64 x y) (*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y))))
18.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))
17.0ms	(*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y)))

rewrite115.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

650×	`prod-diff_binary64`
200×	`expm1-udef_binary64`
200×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`

Counts

3 → 103

Calls

3 calls:

107.0ms	(/.f64 (+.f64 x y) (*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y))))
107.0ms	(*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y)))
107.0ms	(/.f64 (hypot.f64 x y) (-.f64 x y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	210	42
2	3137	42
3	5080	42
0	0	0
1	0	0

simplify110.0ms (2%)

Algorithm

1×	egg-herbie

Rules

966×	`fma-neg_binary64`
434×	`times-frac_binary64`
258×	`fma-def_binary64`
224×	`sub-neg_binary64`
223×	`associate-/l*_binary64`

Counts

175 → 155

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	87	1233
1	274	1185
2	889	1102
3	3798	1053
4	4935	1053
5	4969	1053

prune192.0ms (3.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	155	4	159

Error

Counts

159 → 4

Alt Table

Status	Error	Program
✓	22.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
▶	0.0b	(/.f64 (-.f64 x y) (/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y))))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 3033 to 1120 computations (63.1% saved)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series76.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

58.0ms	(/.f64 (-.f64 x y) (/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))))
17.0ms	(/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y)))

rewrite146.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

282×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
181×	`log-pow_binary64`
177×	`fma-neg_binary64`

Counts

2 → 110

Calls

2 calls:

140.0ms	(/.f64 (-.f64 x y) (/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))))
140.0ms	(/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	38
1	218	32
2	3450	32
3	4993	32
4	5000	32
0	0	0
1	0	0

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
384×	`associate-/l/_binary64`
335×	`times-frac_binary64`
333×	`distribute-rgt-neg-in_binary64`
330×	`distribute-lft-neg-in_binary64`

Counts

158 → 136

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	828
1	173	786
2	511	750
3	2204	699
4	4887	684
5	5057	684

prune239.0ms (4.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	195	4	199

Error

Counts

199 → 4

Alt Table

Status	Error	Program
✓	22.5b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (fma.f64 x x (.f64 y y)))
✓	0.0b	(/.f64 (-.f64 x y) (/.f64 (hypot.f64 x y) (/.f64 (+.f64 x y) (hypot.f64 x y))))
✓	0.0b	(/.f64 (+.f64 x y) (*.f64 (hypot.f64 x y) (/.f64 (hypot.f64 x y) (-.f64 x y))))
✓	0.0b	(*.f64 (/.f64 (-.f64 x y) (hypot.f64 x y)) (/.f64 (+.f64 x y) (hypot.f64 x y)))

Compiler

Compiled 4165 to 1529 computations (63.3% saved)

regimes419.0ms (7.7%)

Accuracy

Total 0.0b remaining (60.5%)

Threshold costs 0.0b (60.5%)

Counts

90 → 1

Compiler

Compiled 4546 to 2555 computations (43.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	13	22
2	18	22
3	20	22
4	21	22
5	21	22

end163.0ms (3%)

Compiler: Compiled 101 to 48 computations (52.5% saved)

Details

analyze29.0ms (0.5%)

sample2.4s (44.6%)

simplify93.0ms (1.7%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series43.0ms (0.8%)

rewrite82.0ms (1.5%)

simplify78.0ms (1.4%)

prune103.0ms (1.9%)

localize15.0ms (0.3%)

series84.0ms (1.5%)

rewrite204.0ms (3.8%)

simplify164.0ms (3%)

prune422.0ms (7.8%)

localize15.0ms (0.3%)

series80.0ms (1.5%)

rewrite115.0ms (2.1%)

simplify110.0ms (2%)

prune192.0ms (3.5%)

localize14.0ms (0.3%)

series76.0ms (1.4%)

rewrite146.0ms (2.7%)

simplify88.0ms (1.6%)

prune239.0ms (4.4%)

regimes419.0ms (7.7%)

simplify4.0ms (0.1%)

end163.0ms (3%)

Profiling