Details

analyze188.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.8s (49.2%)

Results

1.5s	8256×	body	128	valid
15.0ms	100×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify34.0ms (1%)

Algorithm

1×	egg-herbie

Rules

474×	`fma-neg_binary64`
309×	`fma-def_binary64`
228×	`cancel-sign-sub-inv_binary64`
83×	`associate-/l*_binary64`
72×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
▶	0.2b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))

Compiler

Compiled 85 to 66 computations (22.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
✓	0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
✓	0.3b	(*.f64 3 (sqrt.f64 x))
✓	0.4b	(/.f64 1 (*.f64 x 9))

series59.0ms (1.6%)

Counts

4 → 38

Calls

4 calls:

24.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
23.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
10.0ms	(*.f64 3 (sqrt.f64 x))
1.0ms	(/.f64 1 (*.f64 x 9))

rewrite89.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

435×	`fma-def_binary64`
240×	`expm1-udef_binary64`
239×	`log1p-udef_binary64`
185×	`fma-neg_binary64`
184×	`egg-rr`

Counts

4 → 184

Calls

4 calls:

84.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
84.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
84.0ms	(*.f64 3 (sqrt.f64 x))
84.0ms	(/.f64 1 (*.f64 x 9))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	289	37
2	3726	35
3	4952	35
0	0	0
1	0	0

simplify45.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
277×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64`

Counts

222 → 194

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	417
1	40	399
2	84	399
3	145	399
4	297	399
5	419	399
6	576	399
7	676	399
8	735	399
9	742	399
10	675	399

prune240.0ms (6.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	184	10	194
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	185	11	196

Error

0.0b

Counts

196 → 11

Alt Table

Status	Error	Program
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
▶	0.2b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
	0.3b	(-.f64 1 (fma.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))) (/.f64 1/9 x)))
	34.4b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 (sqrt.f64 y) 3) (/.f64 (sqrt.f64 y) (sqrt.f64 x))))
	25.7b	(.f64 (-.f64 (pow.f64 (-.f64 1 (/.f64 1/9 x)) 2) (/.f64 (.f64 y y) (*.f64 x 9))) (/.f64 1 (fma.f64 y (/.f64 1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))))
	15.4b	(-.f64 (-.f64 1 (sqrt.f64 (pow.f64 (.f64 x 9) -2))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	0.3b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (pow.f64 (sqrt.f64 (.f64 3 (sqrt.f64 x))) 2)))
	0.6b	(-.f64 (-.f64 1 (.f64 (cbrt.f64 (/.f64 1/9 x)) (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 2))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	14.9b	(-.f64 (-.f64 1 (.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 x x) 81)) -1) (pow.f64 (cbrt.f64 (.f64 x 9)) -1))) (/.f64 y (*.f64 3 (sqrt.f64 x))))
	0.4b	(-.f64 (-.f64 1 (pow.f64 (/.f64 1/3 (sqrt.f64 x)) 2)) (/.f64 y (*.f64 3 (sqrt.f64 x))))

Compiler

Compiled 4996 to 3484 computations (30.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
✓	0.3b	(/.f64 -1/3 (sqrt.f64 x))
✓	0.4b	(/.f64 1/9 x)

series79.0ms (2.2%)

Counts

3 → 14

Calls

3 calls:

62.0ms	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
14.0ms	(/.f64 -1/3 (sqrt.f64 x))
3.0ms	(/.f64 1/9 x)

rewrite65.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

463×	`log-prod_binary64`
407×	`prod-diff_binary64`
192×	`expm1-udef_binary64`
191×	`log1p-udef_binary64`
165×	`log-pow_binary64`

Counts

3 → 95

Calls

3 calls:

63.0ms	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (/.f64 1/9 x)))
63.0ms	(/.f64 -1/3 (sqrt.f64 x))
63.0ms	(/.f64 1/9 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	237	26
2	2672	26
3	5195	26
0	0	0
1	0	0

simplify52.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
277×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64`

Counts

109 → 103

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	225
1	40	207
2	84	207
3	145	207
4	297	207
5	419	207
6	576	207
7	676	207
8	735	207
9	742	207
10	675	207

prune114.0ms (3.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	98	5	103
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Error

0.0b

Counts

114 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (-.f64 1 (.f64 (cbrt.f64 (/.f64 1/9 x)) (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 2))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	15.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 (/.f64 1/81 (*.f64 x x)))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 1/9 (.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)))))
	0.3b	(-.f64 1 (+.f64 (.f64 1/9 (/.f64 1 x)) (.f64 1/3 (*.f64 y (sqrt.f64 (/.f64 1 x))))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
▶	0.2b	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 (.f64 (/.f64 -1/3 (sqrt.f64 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 -1/3 (sqrt.f64 x))))))

Compiler

Compiled 1905 to 1368 computations (28.2% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
	0.4b	(/.f64 1/9 x)
✓	0.4b	(*.f64 -1/3 (pow.f64 x -1/2))

series25.0ms (0.7%)

Counts

2 → 15

Calls

2 calls:

18.0ms	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
7.0ms	(*.f64 -1/3 (pow.f64 x -1/2))

rewrite61.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

489×	`log-prod_binary64`
412×	`prod-diff_binary64`
206×	`expm1-udef_binary64`
205×	`log1p-udef_binary64`
172×	`log-pow_binary64`

Counts

2 → 52

Calls

2 calls:

60.0ms	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
60.0ms	(*.f64 -1/3 (pow.f64 x -1/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	259	22
2	2792	22
3	5303	22
0	0	0
1	0	0

simplify34.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
277×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64`

Counts

67 → 60

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	226
1	40	208
2	84	208
3	145	208
4	297	208
5	419	208
6	576	208
7	676	208
8	735	208
9	742	208
10	675	208

prune95.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

0.0b

Counts

102 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (-.f64 1 (.f64 (cbrt.f64 (/.f64 1/9 x)) (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 2))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	15.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 (/.f64 1/81 (*.f64 x x)))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 1/9 (.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
✓	0.2b	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
▶	0.3b	(fma.f64 y (.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (.f64 (/.f64 1 x) 1/9)))
	0.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 (.f64 (/.f64 -1/3 (sqrt.f64 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 -1/3 (sqrt.f64 x))))))

Compiler

Compiled 1797 to 1334 computations (25.8% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (.f64 (/.f64 1 x) 1/9)))
	0.4b	(*.f64 -1/3 (pow.f64 x -1/2))
✓	0.4b	(*.f64 (/.f64 1 x) 1/9)

series18.0ms (0.5%)

Counts

2 → 27

Calls

2 calls:

16.0ms	(fma.f64 y (.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (.f64 (/.f64 1 x) 1/9)))
2.0ms	(*.f64 (/.f64 1 x) 1/9)

rewrite115.0ms (3.2%)

Algorithm

2×	batch-egg-rewrite

Rules

566×	`prod-diff_binary64`
419×	`fma-udef_binary64`
218×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
202×	`fma-def_binary64`

Counts

2 → 47

Calls

2 calls:

114.0ms	(fma.f64 y (.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (.f64 (/.f64 1 x) 1/9)))
114.0ms	(*.f64 (/.f64 1 x) 1/9)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	282	20
2	2957	20
3	4761	20
4	4796	20
5	4782	20
0	0	0
1	0	0

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Rules

341×	`fma-def_binary64`
277×	`fma-neg_binary64`
124×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-neg-in_binary64`
49×	`sub-neg_binary64`

Counts

74 → 55

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	274
1	40	256
2	84	256
3	145	256
4	297	256
5	419	256
6	576	256
7	676	256
8	735	256
9	742	256
10	675	256

prune79.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	76	7	83

Error

0.0b

Counts

83 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (-.f64 1 (.f64 (cbrt.f64 (/.f64 1/9 x)) (pow.f64 (cbrt.f64 (/.f64 1/9 x)) 2))) (/.f64 y (.f64 3 (sqrt.f64 x))))
	15.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (sqrt.f64 (/.f64 1/81 (*.f64 x x)))))
	0.3b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 1/9 (.f64 (pow.f64 x -1/2) (pow.f64 x -1/2)))))
	0.5b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (sqrt.f64 (.f64 x 9))))
✓	0.2b	(fma.f64 y (*.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (/.f64 1/9 x)))
✓	0.3b	(fma.f64 y (.f64 -1/3 (pow.f64 x -1/2)) (-.f64 1 (.f64 (/.f64 1 x) 1/9)))
	0.4b	(fma.f64 y (/.f64 -1/3 (sqrt.f64 x)) (-.f64 1 (.f64 (.f64 (/.f64 -1/3 (sqrt.f64 x)) (cbrt.f64 (/.f64 1/9 x))) (cbrt.f64 (/.f64 -1/3 (sqrt.f64 x))))))

Compiler

Compiled 1319 to 1019 computations (22.7% saved)

regimes243.0ms (6.7%)

Accuracy

Total 0.2b remaining (85.2%)

Threshold costs 0.2b (85.2%)

Counts

81 → 1

Compiler

Compiled 3995 to 3169 computations (20.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	19
1	18	19
2	24	19
3	26	19
4	27	19
5	25	19

end111.0ms (3.1%)

Compiler: Compiled 158 to 124 computations (21.5% saved)

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	19	417
1	40	399
2	84	399
3	145	399
4	297	399
5	419	399
6	576	399
7	676	399
8	735	399
9	742	399
10	675	399

Iter	Nodes	Cost
0	18	225
1	40	207
2	84	207
3	145	207
4	297	207
5	419	207
6	576	207
7	676	207
8	735	207
9	742	207
10	675	207

Iter	Nodes	Cost
0	18	226
1	40	208
2	84	208
3	145	208
4	297	208
5	419	208
6	576	208
7	676	208
8	735	208
9	742	208
10	675	208

Iter	Nodes	Cost
0	19	274
1	40	256
2	84	256
3	145	256
4	297	256
5	419	256
6	576	256
7	676	256
8	735	256
9	742	256
10	675	256

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	19	417
1	40	399
2	84	399
3	145	399
4	297	399
5	419	399
6	576	399
7	676	399
8	735	399
9	742	399
10	675	399

Iter	Nodes	Cost
0	18	225
1	40	207
2	84	207
3	145	207
4	297	207
5	419	207
6	576	207
7	676	207
8	735	207
9	742	207
10	675	207

Iter	Nodes	Cost
0	18	226
1	40	208
2	84	208
3	145	208
4	297	208
5	419	208
6	576	208
7	676	208
8	735	208
9	742	208
10	675	208

Iter	Nodes	Cost
0	19	274
1	40	256
2	84	256
3	145	256
4	297	256
5	419	256
6	576	256
7	676	256
8	735	256
9	742	256
10	675	256

Details

analyze188.0ms (5.2%)

sample1.8s (49.2%)

simplify34.0ms (1%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series59.0ms (1.6%)

rewrite89.0ms (2.5%)

simplify45.0ms (1.2%)

prune240.0ms (6.7%)

localize7.0ms (0.2%)

series79.0ms (2.2%)

rewrite65.0ms (1.8%)

simplify52.0ms (1.4%)

prune114.0ms (3.2%)

localize10.0ms (0.3%)

series25.0ms (0.7%)

rewrite61.0ms (1.7%)

simplify34.0ms (0.9%)

prune95.0ms (2.6%)

localize10.0ms (0.3%)

series18.0ms (0.5%)

rewrite115.0ms (3.2%)

simplify36.0ms (1%)

prune79.0ms (2.2%)

regimes243.0ms (6.7%)

simplify3.0ms (0.1%)

end111.0ms (3.1%)

Profiling

Iter	Nodes	Cost
0	13	21
1	27	18
2	56	18
3	112	18
4	201	16
5	339	16
6	608	16
7	856	16
8	892	16
9	907	16
10	930	16
11	837	16

Iter	Nodes	Cost
0	19	417
1	40	399
2	84	399
3	145	399
4	297	399
5	419	399
6	576	399
7	676	399
8	735	399
9	742	399
10	675	399

Iter	Nodes	Cost
0	18	225
1	40	207
2	84	207
3	145	207
4	297	207
5	419	207
6	576	207
7	676	207
8	735	207
9	742	207
10	675	207

Iter	Nodes	Cost
0	18	226
1	40	208
2	84	208
3	145	208
4	297	208
5	419	208
6	576	208
7	676	208
8	735	208
9	742	208
10	675	208

Iter	Nodes	Cost
0	19	274
1	40	256
2	84	256
3	145	256
4	297	256
5	419	256
6	576	256
7	676	256
8	735	256
9	742	256
10	675	256