Details

analyze835.0ms (17.3%)

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)

sample1.3s (27.1%)

Results

904.0ms	8256×	body	128	valid
350.0ms	3169×	body	128	invalid

Compiler

Compiled 56 to 35 computations (37.5% saved)

simplify29.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

801×	`div-sub_binary64`
796×	`fma-def_binary64`
540×	`times-frac_binary64`
202×	`distribute-rgt-in_binary64`
197×	`fma-neg_binary64`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	27	20
2	67	20
3	136	20
4	320	20
5	748	20
6	1891	19
7	4408	19

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
	28.2b	(/.f64 (-.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (.f64 y 2))

Compiler

Compiled 99 to 60 computations (39.4% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series29.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))
8.0ms	(/.f64 (+.f64 x z) y)

rewrite72.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

917×	`prod-diff_binary64`
201×	`egg-rr`
180×	`log1p-udef_binary64`
109×	`add-sqr-sqrt_binary64`
103×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	206	21
2	3135	21

Stop Event

1×	node limit

Counts

2 → 201

Calls

2 calls:

67.0ms	(/.f64 (+.f64 x z) y)
67.0ms	(fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y))

simplify42.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
450×	`fma-neg_binary64`
447×	`cancel-sign-sub-inv_binary64`
299×	`distribute-rgt-in_binary64`
270×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	874
1	51	793
2	93	793
3	203	791
4	564	791
5	2006	791

Stop Event

1×	node limit

Counts

273 → 219

prune146.0ms (3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	215	4	219
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	216	5	221

Error

0.0b

Counts

221 → 5

Alt Table

Status	Error	Program
	6.3b	(.f64 -1/2 (fma.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (cbrt.f64 (pow.f64 (/.f64 (+.f64 x z) y) 2))) (-.f64 z x) (neg.f64 y)))
▶	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 x z) y) (-.f64 z x) (neg.f64 y)))
	11.7b	(*.f64 -1/2 (-.f64 (/.f64 (pow.f64 z 2) y) (+.f64 y (/.f64 (pow.f64 x 2) y))))
	44.8b	(.f64 -1/2 (+.f64 (fma.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x z) y) 2)) (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (-.f64 z x)) y) (fma.f64 -1 y y)))

Compiler

Compiled 6128 to 1918 computations (68.7% 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)))

series67.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

33.0ms	(-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y)
20.0ms	(/.f64 (-.f64 z x) (/.f64 y (+.f64 z x)))
14.0ms	(/.f64 y (+.f64 z x))

rewrite85.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

515×	`fma-def_binary64`
379×	`fma-neg_binary64`
261×	`egg-rr`
214×	`expm1-udef_binary64`
214×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	220	36
2	3714	36

Stop Event

1×	node limit

Counts

3 → 261

Calls

3 calls:

78.0ms	(-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y)
78.0ms	(/.f64 y (+.f64 z x))
78.0ms	(/.f64 (-.f64 z x) (/.f64 y (+.f64 z x)))

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

753×	`cancel-sign-sub-inv_binary64`
651×	`fma-def_binary64`
391×	`fma-neg_binary64`
189×	`distribute-rgt-neg-in_binary64`
188×	`distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1606
1	151	1525
2	435	1453
3	1982	1397

Stop Event

1×	node limit

Counts

357 → 292

prune256.0ms (5.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	290	2	292
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	292	5	297

Error

0.0b

Counts

297 → 5

Alt Table

Status	Error	Program
	44.8b	(.f64 -1/2 (+.f64 (fma.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x z) y) 2)) (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (-.f64 z x)) y) (fma.f64 -1 y y)))
	34.4b	(*.f64 -1/2 (fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y)))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
▶	6.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (.f64 (/.f64 x y) (+.f64 z x)))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y))

Compiler

Compiled 6680 to 2066 computations (69.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 z x))
✓	0.2b	(/.f64 z (/.f64 1 (+.f64 z x)))
✓	4.3b	(*.f64 (/.f64 x y) (+.f64 z x))
✓	6.8b	(fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (*.f64 (/.f64 x y) (+.f64 z x))))

series59.0ms (1.2%)

Counts

4 → 120

Calls

4 calls:

32.0ms	(fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (*.f64 (/.f64 x y) (+.f64 z x))))
15.0ms	(*.f64 (/.f64 x y) (+.f64 z x))
7.0ms	(/.f64 1 (+.f64 z x))
4.0ms	(/.f64 z (/.f64 1 (+.f64 z x)))

rewrite79.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

244×	`expm1-udef_binary64`
244×	`log1p-udef_binary64`
156×	`egg-rr`
149×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	296	46
2	4473	46

Stop Event

1×	node limit

Counts

4 → 156

Calls

4 calls:

70.0ms	(/.f64 1 (+.f64 z x))
70.0ms	(/.f64 z (/.f64 1 (+.f64 z x)))
70.0ms	(*.f64 (/.f64 x y) (+.f64 z x))
70.0ms	(fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (*.f64 (/.f64 x y) (+.f64 z x))))

simplify48.0ms (1%)

Algorithm

1×	egg-herbie

Rules

485×	`associate-/l*_binary64`
415×	`associate-/r*_binary64`
264×	`cancel-sign-sub-inv_binary64`
256×	`associate-*l/_binary64`
250×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	1638
1	123	1584
2	316	1488
3	1119	1344

Stop Event

1×	node limit

Counts

276 → 191

prune166.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	191	5	196

Error

0.0b

Counts

196 → 5

Alt Table

Status	Error	Program
	44.8b	(.f64 -1/2 (+.f64 (fma.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x z) y) 2)) (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (-.f64 z x)) y) (fma.f64 -1 y y)))
▶	34.4b	(*.f64 -1/2 (fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y)))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
✓	6.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (.f64 (/.f64 x y) (+.f64 z x)))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y))

Compiler

Compiled 5362 to 2266 computations (57.7% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 z x))
✓	0.1b	(/.f64 (sqrt.f64 (-.f64 z x)) y)
✓	0.2b	(/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x)))
✓	4.3b	(fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y))

series154.0ms (3.2%)

Counts

3 → 48

Calls

3 calls:

108.0ms	(fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y))
24.0ms	(/.f64 (sqrt.f64 (-.f64 z x)) y)
21.0ms	(/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x)))

rewrite104.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

762×	`prod-diff_binary64`
254×	`egg-rr`
142×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	53
1	286	40
2	4047	40

Stop Event

1×	node limit

Counts

3 → 254

Calls

3 calls:

86.0ms	(/.f64 (sqrt.f64 (-.f64 z x)) y)
86.0ms	(/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x)))
86.0ms	(fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y))

simplify40.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

399×	`times-frac_binary64`
382×	`fma-def_binary64`
325×	`associate-/l*_binary64`
268×	`associate-r_binary64`
248×	`associate-/r*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	119	1152
1	365	1025
2	1227	962

Stop Event

1×	node limit

Counts

302 → 301

prune204.0ms (4.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	340	0	340
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	340	5	345

Error

0.0b

Counts

345 → 5

Alt Table

Status	Error	Program
	44.8b	(.f64 -1/2 (+.f64 (fma.f64 (cbrt.f64 (pow.f64 (/.f64 (+.f64 x z) y) 2)) (.f64 (cbrt.f64 (/.f64 (+.f64 x z) y)) (-.f64 z x)) y) (fma.f64 -1 y y)))
✓	34.4b	(*.f64 -1/2 (fma.f64 (/.f64 (sqrt.f64 (-.f64 z x)) y) (/.f64 (sqrt.f64 (-.f64 z x)) (/.f64 1 (+.f64 z x))) (neg.f64 y)))
✓	0.1b	(*.f64 -1/2 (fma.f64 (/.f64 (+.f64 x z) y) (-.f64 z x) (neg.f64 y)))
✓	6.8b	(.f64 -1/2 (-.f64 (fma.f64 (/.f64 1 y) (/.f64 z (/.f64 1 (+.f64 z x))) (neg.f64 (.f64 (/.f64 x y) (+.f64 z x)))) y))
✓	0.1b	(*.f64 -1/2 (-.f64 (/.f64 (-.f64 z x) (/.f64 y (+.f64 z x))) y))

Compiler

Compiled 11019 to 3864 computations (64.9% saved)

regimes918.0ms (19%)

Accuracy

Total 0.1b remaining (71.1%)

Threshold costs 0.1b (71.1%)

Counts

154 → 1

Compiler

Compiled 20526 to 12795 computations (37.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	25	28
2	39	28
3	63	28
4	80	28
5	91	28
6	97	28
7	99	28

Stop Event

1×

saturated

end85.0ms (1.8%)

Compiler: Compiled 156 to 91 computations (41.7% saved)

Details

analyze835.0ms (17.3%)

sample1.3s (27.1%)

simplify29.0ms (0.6%)

prune6.0ms (0.1%)

localize8.0ms (0.2%)

series29.0ms (0.6%)

rewrite72.0ms (1.5%)

simplify42.0ms (0.9%)

prune146.0ms (3%)

localize9.0ms (0.2%)

series67.0ms (1.4%)

rewrite85.0ms (1.8%)

simplify50.0ms (1%)

prune256.0ms (5.3%)

localize12.0ms (0.3%)

series59.0ms (1.2%)

rewrite79.0ms (1.6%)

simplify48.0ms (1%)

prune166.0ms (3.4%)

localize12.0ms (0.3%)

series154.0ms (3.2%)

rewrite104.0ms (2.2%)

simplify40.0ms (0.8%)

prune204.0ms (4.2%)

regimes918.0ms (19%)

simplify4.0ms (0.1%)

end85.0ms (1.8%)

Profiling