Details

analyze1.2s (16.2%)

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 (25.6%)

Results

975.0ms	8256×	body	128	valid
729.0ms	6170×	body	128	invalid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify8.0ms (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`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	20
2	45	20
3	55	20
4	55	20
5	55	20

prune66.0ms (0.9%)

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

29.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.8b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
	36.2b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	2.9b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
✓	11.2b	(/.f64 x (*.f64 y y))
✓	20.9b	(/.f64 (.f64 z z) (.f64 t t))

series250.0ms (3.3%)

Counts

3 → 96

Calls

3 calls:

126.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
98.0ms	(/.f64 x (*.f64 y y))
25.0ms	(/.f64 (.f64 z z) (.f64 t t))

rewrite66.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

338×	`prod-diff_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
196×	`log-pow_binary64`
177×	`log-div_binary64`

Counts

3 → 98

Calls

3 calls:

64.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
64.0ms	(/.f64 x (*.f64 y y))
64.0ms	(/.f64 (.f64 z z) (.f64 t t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	235	31
2	3026	31
3	4976	31
0	0	0
1	0	0

simplify200.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

652×	`unswap-sqr_binary64`
531×	`associate-/l*_binary64`
480×	`sqr-pow_binary64`
355×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`

Counts

194 → 105

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	1320
1	29	1320
2	51	1248
3	139	1248
4	545	1248
5	2705	1248
6	3974	1248
7	4023	1248
8	4311	1248
9	4697	1248
10	5074	1248

prune120.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	92	13	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	13	107

Error

2.4b

Counts

107 → 13

Alt Table

Status	Error	Program
	42.6b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
	34.1b	(pow.f64 (hypot.f64 (/.f64 z t) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) y))) 2)
	13.3b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 z t) 2)) 3))
	30.0b	(fma.f64 x (.f64 (cbrt.f64 (/.f64 x (.f64 y y))) (pow.f64 (cbrt.f64 (/.f64 x (.f64 y y))) 2)) (/.f64 (.f64 z z) (*.f64 t t)))
	17.1b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 1 (/.f64 t (/.f64 z t)))))
▶	13.0b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 3))
	43.3b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (/.f64 (.f64 z z) (.f64 t t)))
	22.0b	(fma.f64 x (.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) y)) (/.f64 (.f64 z z) (*.f64 t t)))
	21.6b	(fma.f64 x (.f64 (/.f64 x y) (/.f64 1 y)) (/.f64 (.f64 z z) (*.f64 t t)))
	29.7b	(fma.f64 x (.f64 x (pow.f64 y -2)) (/.f64 (.f64 z z) (*.f64 t t)))
	24.7b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (/.f64 z (*.f64 t t)) z))
	24.6b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (/.f64 (*.f64 z z) t) (/.f64 1 t)))

Compiler

Compiled 2307 to 898 computations (61.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(pow.f64 (/.f64 z t) 2)
✓	2.9b	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
	11.2b	(/.f64 x (*.f64 y y))

series71.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

60.0ms	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))
11.0ms	(pow.f64 (/.f64 z t) 2)

rewrite62.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`log-prod_binary64`
208×	`prod-diff_binary64`
204×	`expm1-udef_binary64`
204×	`log1p-udef_binary64`
188×	`log-pow_binary64`

Counts

2 → 70

Calls

2 calls:

60.0ms	(pow.f64 (/.f64 z t) 2)
60.0ms	(fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	233	24
2	2816	24
3	5294	24
0	0	0
1	0	0

simplify149.0ms (2%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
522×	`associate-/l*_binary64`
486×	`*-commutative_binary64`
484×	`sqr-pow_binary64`
336×	`associate-/r*_binary64`

Counts

142 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	1152
1	28	1152
2	49	1080
3	133	1080
4	523	1080
5	2593	1080
6	3237	1080
7	3524	1080
8	3828	1080
9	4206	1080
10	4677	1080
11	4965	1080
12	4944	1080

prune127.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	11	111
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	109	15	124

Error

1.3b

Counts

124 → 15

Alt Table

Status	Error	Program
	17.1b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (/.f64 1 (/.f64 t (/.f64 z t)))))
	16.7b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (*.f64 (/.f64 1 t) (/.f64 z t))))
	38.7b	(cbrt.f64 (pow.f64 (fma.f64 x (/.f64 x (*.f64 y y)) (pow.f64 (/.f64 z t) 2)) 3))
	49.3b	(/.f64 (+.f64 (pow.f64 (.f64 x (/.f64 x (.f64 y y))) 3) (pow.f64 (pow.f64 (/.f64 z t) 2) 3)) (fma.f64 (.f64 x (/.f64 x (.f64 y y))) (.f64 x (/.f64 x (.f64 y y))) (-.f64 (pow.f64 (/.f64 z t) 4) (.f64 (.f64 x (/.f64 x (*.f64 y y))) (pow.f64 (/.f64 z t) 2)))))
	42.6b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
	34.1b	(pow.f64 (hypot.f64 (/.f64 z t) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) y))) 2)
	13.2b	(fma.f64 x (.f64 (pow.f64 (cbrt.f64 (/.f64 x (.f64 y y))) 2) (cbrt.f64 (/.f64 x (*.f64 y y)))) (pow.f64 (/.f64 z t) 2))
	41.9b	(/.f64 (pow.f64 z 2) (pow.f64 t 2))
	24.5b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (cbrt.f64 (pow.f64 (/.f64 z t) 4))))
	13.1b	(fma.f64 x (*.f64 (pow.f64 y -2) x) (pow.f64 (/.f64 z t) 2))
▶	3.3b	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
	3.7b	(fma.f64 x (*.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) y) (/.f64 (cbrt.f64 x) y)) (pow.f64 (/.f64 z t) 2))
	35.5b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (pow.f64 (/.f64 z t) 2))
	16.4b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	16.4b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (*.f64 (/.f64 z t) z) (/.f64 1 t)))

Compiler

Compiled 2495 to 1054 computations (57.8% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 y) (/.f64 x y))
	0.3b	(pow.f64 (/.f64 z t) 2)
✓	2.9b	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))

series82.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

59.0ms	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))
22.0ms	(*.f64 (/.f64 1 y) (/.f64 x y))

rewrite61.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

280×	`prod-diff_binary64`
226×	`expm1-udef_binary64`
226×	`log1p-udef_binary64`
208×	`log-pow_binary64`
157×	`log-div_binary64`

Counts

2 → 71

Calls

2 calls:

60.0ms	(*.f64 (/.f64 1 y) (/.f64 x y))
60.0ms	(fma.f64 x (*.f64 (/.f64 1 y) (/.f64 x y)) (pow.f64 (/.f64 z t) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	24
1	273	23
2	3206	20
3	4977	20
0	0	0
1	0	0

simplify117.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

652×	`unswap-sqr_binary64`
531×	`associate-/l*_binary64`
480×	`sqr-pow_binary64`
355×	`associate-/r*_binary64`
289×	`associate-/l/_binary64`

Counts

143 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	1080
1	29	1080
2	51	1008
3	139	1008
4	545	1008
5	2705	1008
6	3974	1008
7	4023	1008
8	4311	1008
9	4697	1008
10	5074	1008

prune136.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	9	117
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	120	12	132

Error

0.0b

Counts

132 → 12

Alt Table

Status	Error	Program
	31.7b	(fma.f64 z (/.f64 z (.f64 t t)) (/.f64 (.f64 x x) (*.f64 y y)))
	24.5b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (cbrt.f64 (pow.f64 (/.f64 z t) 4))))
	7.3b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (.f64 (*.f64 (/.f64 z t) z) (/.f64 1 t)))
	16.7b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 z (*.f64 (/.f64 1 t) (/.f64 z t))))
	7.2b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 z (.f64 (/.f64 t z) t)))
	35.5b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (pow.f64 (/.f64 z t) 2))
	3.7b	(fma.f64 x (/.f64 (/.f64 (/.f64 x y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y)) (pow.f64 (/.f64 z t) 2))
▶	0.4b	(pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)
	3.3b	(fma.f64 x (/.f64 (/.f64 1 y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))
	3.3b	(fma.f64 x (/.f64 (/.f64 x y) y) (pow.f64 (/.f64 z t) 2))
	33.9b	(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2) 3))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)) 3)

Compiler

Compiled 2320 to 1098 computations (52.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (/.f64 x y) (/.f64 z t))
✓	0.4b	(pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)

series719.0ms (9.6%)

Counts

2 → 96

Calls

2 calls:

540.0ms	(pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)
179.0ms	(hypot.f64 (/.f64 x y) (/.f64 z t))

rewrite60.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

506×	`log-prod_binary64`
190×	`pow1/3_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
175×	`pow3_binary64`

Counts

2 → 73

Calls

2 calls:

58.0ms	(hypot.f64 (/.f64 x y) (/.f64 z t))
58.0ms	(pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	23
1	212	23
2	2524	23
3	5037	23
0	0	0
1	0	0

simplify86.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

912×	`associate-/l*_binary64`
768×	`associate-/r*_binary64`
242×	`fma-neg_binary64`
196×	`fma-def_binary64`
140×	`associate-/r/_binary64`

Counts

169 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	2816
1	271	2768
2	1141	2632
3	4986	2632
4	5108	2632

prune106.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Error

0.0b

Counts

121 → 12

Alt Table

Status	Error	Program
	31.7b	(fma.f64 z (/.f64 z (.f64 t t)) (/.f64 (.f64 x x) (*.f64 y y)))
	4.3b	(fma.f64 (*.f64 (/.f64 z t) z) (/.f64 1 t) (pow.f64 (/.f64 x y) 2))
	24.5b	(fma.f64 x (/.f64 x (.f64 y y)) (.f64 (pow.f64 (cbrt.f64 (/.f64 z t)) 2) (cbrt.f64 (pow.f64 (/.f64 z t) 4))))
	4.6b	(fma.f64 (*.f64 (/.f64 x y) x) (/.f64 1 y) (pow.f64 (/.f64 z t) 2))
	7.2b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 z (.f64 (/.f64 t z) t)))
	3.3b	(fma.f64 x (/.f64 (/.f64 x y) y) (pow.f64 (/.f64 z t) 2))
	21.5b	(fma.f64 (.f64 x x) (.f64 (/.f64 1 y) (/.f64 1 y)) (pow.f64 (/.f64 z t) 2))
	35.5b	(fma.f64 x (pow.f64 (/.f64 (sqrt.f64 x) y) 2) (pow.f64 (/.f64 z t) 2))
	3.7b	(fma.f64 x (/.f64 (/.f64 (/.f64 x y) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y)) (pow.f64 (/.f64 z t) 2))
	1.2b	(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 x y) (/.f64 z t)) 2)) 3)
	0.6b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 x y) (/.f64 z t))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 x y) (/.f64 z t))) (hypot.f64 (/.f64 x y) (/.f64 z t))))
	3.3b	(fma.f64 x (/.f64 (/.f64 1 y) (/.f64 y x)) (pow.f64 (/.f64 z t) 2))

Compiler

Compiled 2400 to 1147 computations (52.2% saved)

regimes1.5s (19.8%)

Accuracy

Total 0.4b remaining (89.4%)

Threshold costs 0.4b (89.4%)

Counts

110 → 1

Compiler

Compiled 24819 to 15740 computations (36.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end356.0ms (4.8%)

Compiler: Compiled 268 to 163 computations (39.2% saved)

Details

analyze1.2s (16.2%)

sample1.9s (25.6%)

simplify8.0ms (0.1%)

prune66.0ms (0.9%)

localize9.0ms (0.1%)

series250.0ms (3.3%)

rewrite66.0ms (0.9%)

simplify200.0ms (2.7%)

prune120.0ms (1.6%)

localize8.0ms (0.1%)

series71.0ms (0.9%)

rewrite62.0ms (0.8%)

simplify149.0ms (2%)

prune127.0ms (1.7%)

localize11.0ms (0.1%)

series82.0ms (1.1%)

rewrite61.0ms (0.8%)

simplify117.0ms (1.6%)

prune136.0ms (1.8%)

localize7.0ms (0.1%)

series719.0ms (9.6%)

rewrite60.0ms (0.8%)

simplify86.0ms (1.1%)

prune106.0ms (1.4%)

regimes1.5s (19.8%)

simplify2.0ms (0%)

end356.0ms (4.8%)

Profiling