Details

analyze1.3s (19.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
9.4%	90.4%	0.2%	10
14%	83.4%	2.5%	11
18.7%	78.2%	3.1%	12
28.1%	65.5%	6.4%	13
30.7%	59.4%	9.9%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample1.9s (28.8%)

Results

1.0s	8256×	body	128	valid
801.0ms	6318×	body	128	invalid

Compiler

Compiled 40 to 24 computations (40% saved)

preprocess23.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

36×	`fma-def_binary64`
32×	`associate-/l*_binary64`
22×	`associate-*r/_binary64`
22×	`associate-/r/_binary64`
20×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	154
1	83	140
2	169	140
3	225	140
4	237	140
0	4	4

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`associate-/l*_binary64`
6×	`associate-*r/_binary64`
6×	`associate-/r/_binary64`
6×	`fma-def_binary64`
4×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	20
2	45	20
3	59	20
4	61	20

Stop Event

1×

saturated

Counts

1 → 2

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

10.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	10.2b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
	33.0b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))
✓	3.8b	(.f64 x (/.f64 x (.f64 y y)))
✓	9.4b	(/.f64 x (*.f64 y y))

series111.0ms (1.7%)

Counts

3 → 96

Calls

24 calls:

7.0ms	(.f64 x (/.f64 x (.f64 y y)))	x	-inf
7.0ms	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))	z	inf
7.0ms	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (/.f64 x (.f64 y y))))	x	inf
7.0ms	(/.f64 x (*.f64 y y))	x	0
7.0ms	(/.f64 x (*.f64 y y))	x	-inf

rewrite53.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

565×	`log-prod_binary64`
257×	`prod-diff_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
180×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	211	27
2	2881	27

Stop Event

1×	node limit

Counts

3 → 95

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

652×	`unswap-sqr_binary64`
529×	`associate-/l*_binary64`
347×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`
229×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	1320
1	29	1320
2	55	1248
3	143	1248
4	622	1248
5	3635	1248
6	4970	1248

Stop Event

1×	node limit

Counts

191 → 103

prune150.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	12	105

Error

0.1b

Counts

105 → 12

Alt Table

Status	Error	Program
	4.9b	(fma.f64 (/.f64 z t) (/.f64 z t) (/.f64 (*.f64 (/.f64 x y) x) y))
	40.2b	(/.f64 z (/.f64 (*.f64 t t) z))
	32.1b	(/.f64 (-.f64 (*.f64 (pow.f64 (/.f64 z t) 2) (pow.f64 (/.f64 z t) 2)) (pow.f64 (pow.f64 (/.f64 x y) 2) 2)) (-.f64 (pow.f64 (/.f64 z t) 2) (pow.f64 (/.f64 x y) 2)))
	2.6b	(fma.f64 (/.f64 z t) (/.f64 z t) (/.f64 x (/.f64 y (/.f64 x y))))
	33.0b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))
▶	0.4b	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))
	3.3b	(fma.f64 (/.f64 z t) (/.f64 z t) (.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) y))))
	34.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2) 3))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	43.4b	(/.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 z t) 2) 3) (pow.f64 (pow.f64 (/.f64 x y) 2) 3)) (fma.f64 (pow.f64 (/.f64 z t) 2) (pow.f64 (/.f64 z t) 2) (-.f64 (pow.f64 (pow.f64 (/.f64 x y) 2) 2) (*.f64 (pow.f64 (/.f64 z t) 2) (pow.f64 (/.f64 x y) 2)))))
	24.3b	(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2) 2)))
	53.8b	(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))) (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2))))) (log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)))))

Compiler

Compiled 2310 to 1056 computations (54.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))
✓	0.3b	(pow.f64 (/.f64 x y) 2)
✓	0.3b	(pow.f64 (/.f64 z t) 2)

series144.0ms (2.2%)

Counts

3 → 96

Calls

24 calls:

28.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))	x	-inf
28.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))	z	0
9.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))	z	-inf
8.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))	z	inf
8.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (/.f64 z t) 2))	x	inf

rewrite61.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

579×	`log-prod_binary64`
247×	`fma-def_binary64`
213×	`expm1-udef_binary64`
213×	`log1p-udef_binary64`
194×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	243	27
2	3278	27

Stop Event

1×	node limit

Counts

3 → 139

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
520×	`associate-/l*_binary64`
422×	`*-commutative_binary64`
328×	`associate-/r*_binary64`
258×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	1392
1	28	1392
2	53	1320
3	137	1320
4	595	1320
5	3414	1320
6	4838	1320

Stop Event

1×	node limit

Counts

235 → 145

prune156.0ms (2.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	135	10	145
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	146	11	157

Error

0.0b

Counts

157 → 11

Alt Table

Status	Error	Program
▶	0.4b	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))
	0.5b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 1 (*.f64 (/.f64 t z) (/.f64 t z))))
	4.9b	(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (pow.f64 (/.f64 z t) 2))
	5.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (*.f64 z (/.f64 z t)) t))
	3.3b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (*.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	10.2b	(+.f64 (.f64 x (/.f64 x (.f64 y y))) (pow.f64 (/.f64 z t) 2))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
	0.4b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))
	3.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 z (*.f64 (/.f64 t z) t)))
	0.7b	(fma.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (*.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 2783 to 1319 computations (52.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))
✓	0.2b	(/.f64 (/.f64 x y) (/.f64 y x))
	0.3b	(pow.f64 (/.f64 z t) 2)

series110.0ms (1.7%)

Counts

2 → 72

Calls

18 calls:

9.0ms	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))	z	inf
9.0ms	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))	x	0
9.0ms	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))	x	-inf
8.0ms	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))	z	-inf
8.0ms	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))	x	inf

rewrite66.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

349×	`fma-def_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
193×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	273	20
2	3987	20

Stop Event

1×	node limit

Counts

2 → 127

simplify60.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
520×	`associate-/l*_binary64`
422×	`*-commutative_binary64`
328×	`associate-/r*_binary64`
258×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	1152
1	28	1152
2	53	1080
3	137	1080
4	595	1080
5	3414	1080
6	4838	1080

Stop Event

1×	node limit

Counts

199 → 132

prune164.0ms (2.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	172	12	184

Error

0.0b

Counts

184 → 12

Alt Table

Status	Error	Program
✓	0.4b	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))
	0.5b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 1 (*.f64 (/.f64 t z) (/.f64 t z))))
	10.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
	4.9b	(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (pow.f64 (/.f64 z t) 2))
	5.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (*.f64 z (/.f64 z t)) t))
	3.3b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (*.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
▶	0.4b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))
	3.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 z (*.f64 (/.f64 t z) t)))
	0.9b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y))) (pow.f64 (/.f64 z t) 2))
	0.7b	(fma.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (*.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 3499 to 1439 computations (58.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))
✓	0.2b	(/.f64 (/.f64 z t) (/.f64 t z))
	0.3b	(pow.f64 (/.f64 x y) 2)

series164.0ms (2.5%)

Counts

2 → 72

Calls

18 calls:

52.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))	t	-inf
14.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))	z	inf
9.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))	x	inf
9.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))	y	inf
8.0ms	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))	z	-inf

rewrite64.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

297×	`fma-def_binary64`
239×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
186×	`fma-neg_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	29
1	273	20
2	3994	20

Stop Event

1×	node limit

Counts

2 → 127

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
520×	`associate-/l*_binary64`
422×	`*-commutative_binary64`
328×	`associate-/r*_binary64`
258×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	1152
1	28	1152
2	53	1080
3	137	1080
4	595	1080
5	3414	1080
6	4838	1080

Stop Event

1×	node limit

Counts

199 → 132

prune164.0ms (2.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	173	12	185

Error

0.0b

Counts

185 → 12

Alt Table

Status	Error	Program
	10.2b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
	4.9b	(+.f64 (/.f64 (*.f64 x (/.f64 x y)) y) (pow.f64 (/.f64 z t) 2))
	5.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (*.f64 z (/.f64 z t)) t))
	3.3b	(fma.f64 z (*.f64 (/.f64 1 t) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	0.8b	(fma.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (*.f64 (cbrt.f64 (/.f64 z t)) (/.f64 z t)) (pow.f64 (/.f64 x y) 2))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 2)) 3)
✓	0.4b	(+.f64 (/.f64 (/.f64 x y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))
✓	0.4b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 (/.f64 z t) (/.f64 t z)))
	3.3b	(+.f64 (pow.f64 (/.f64 x y) 2) (/.f64 z (*.f64 (/.f64 t z) t)))
	0.5b	(+.f64 (pow.f64 (/.f64 x y) 2) (pow.f64 (pow.f64 (/.f64 t z) 2) -1))
	0.9b	(+.f64 (.f64 (pow.f64 (cbrt.f64 (/.f64 x y)) 2) (.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y))) (pow.f64 (/.f64 z t) 2))
	0.7b	(fma.f64 (cbrt.f64 (pow.f64 (/.f64 x y) 2)) (*.f64 (cbrt.f64 (/.f64 x y)) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 3279 to 1305 computations (60.2% saved)

regimes1.5s (22.4%)

Accuracy

Total 0.3b remaining (89.2%)

Threshold costs 0.3b (89.2%)

Counts

141 → 1

Compiler

Compiled 30800 to 20078 computations (34.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	13	19

Stop Event

1×

saturated

end146.0ms (2.2%)

Stop Event

1×

fuel

Compiler

Compiled 259 to 165 computations (36.3% saved)

Details

analyze1.3s (19.5%)

sample1.9s (28.8%)

preprocess23.0ms (0.3%)

simplify9.0ms (0.1%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series111.0ms (1.7%)

rewrite53.0ms (0.8%)

simplify65.0ms (1%)

prune150.0ms (2.3%)

localize8.0ms (0.1%)

series144.0ms (2.2%)

rewrite61.0ms (0.9%)

simplify82.0ms (1.3%)

prune156.0ms (2.4%)

localize8.0ms (0.1%)

series110.0ms (1.7%)

rewrite66.0ms (1%)

simplify60.0ms (0.9%)

prune164.0ms (2.5%)

localize8.0ms (0.1%)

series164.0ms (2.5%)

rewrite64.0ms (1%)

simplify79.0ms (1.2%)

prune164.0ms (2.5%)

regimes1.5s (22.4%)

simplify2.0ms (0%)

end146.0ms (2.2%)

Profiling