Details

analyze185.0ms (8.8%)

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
31.2%	50%	18.8%	7
34.3%	43.7%	22%	8
45.3%	26.5%	28.2%	9
46.8%	23.4%	29.8%	10
48.8%	14%	37.2%	11
49.8%	12.1%	38.1%	12
52.8%	7.1%	40.1%	13
53.3%	6.1%	40.6%	14

Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.0s (48.2%)

Results

932.0ms	8256×	body	128	valid
68.0ms	589×	body	128	invalid

Compiler

Compiled 44 to 24 computations (45.5% saved)

preprocess31.0ms (1.5%)

Algorithm

2×	egg-herbie

Rules

544×	`fma-def_binary64`
352×	`fma-neg_binary64`
259×	`cancel-sign-sub-inv_binary64`
251×	`distribute-rgt-in_binary64`
248×	`associate-+l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	48
1	49	46
2	113	46
3	274	32
4	775	32
5	2542	32
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 21 to 11 computations (47.6% saved)

simplify21.0ms (1%)

Algorithm

1×	egg-herbie

Rules

578×	`fma-neg_binary64`
351×	`distribute-rgt-in_binary64`
280×	`fma-def_binary64`
251×	`cancel-sign-sub-inv_binary64`
244×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	27	23
2	63	23
3	148	16
4	416	16
5	1205	16
6	2159	16

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.2%)

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	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
	7.7b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 100 to 58 computations (42% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))
✓	0.2b	(.f64 x.im (.f64 x.re 3))

series13.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

2.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))	x.im	-inf
2.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))	x.im	0
2.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))	x.im	inf
1.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))	x.re	inf
1.0ms	(.f64 x.re (.f64 x.im (*.f64 x.re 3)))	x.re	-inf

rewrite39.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

676×	`pow1_binary64`
623×	`add-log-exp_binary64`
623×	`log1p-expm1-u_binary64`
623×	`expm1-log1p-u_binary64`
82×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1729	17

Stop Event

1×	node limit

Counts

2 → 28

simplify80.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
295×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	23	408
2	45	408
3	84	408
4	235	408
5	835	408
6	1081	408
7	1495	408
8	1595	408
9	1728	408
10	1897	408
11	2142	408
12	2455	408
13	2825	408
14	3284	408
15	3867	408
16	4575	408

Stop Event

1×	node limit

Counts

76 → 32

prune41.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	27	7	34

Error

0.0b

Counts

34 → 7

Alt Table

Status	Error	Program
	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 x.im (*.f64 x.re 3))) (pow.f64 x.im 3))
	8.2b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re))) 3) (pow.f64 x.im 3))
	7.9b	(-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 1) (pow.f64 x.im 3))
	25.9b	(-.f64 (.f64 x.re (pow.f64 (sqrt.f64 (.f64 3 (*.f64 x.im x.re))) 2)) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 x.re (.f64 3 (*.f64 x.re x.im))) (pow.f64 x.im 3))
	7.7b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 643 to 438 computations (31.9% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.re (.f64 3 (*.f64 x.re x.im)))
✓	0.2b	(.f64 3 (.f64 x.re x.im))

series20.0ms (0.9%)

Counts

2 → 24

Calls

12 calls:

5.0ms	(.f64 x.re (.f64 3 (*.f64 x.re x.im)))	x.im	0
2.0ms	(.f64 x.re (.f64 3 (*.f64 x.re x.im)))	x.im	inf
2.0ms	(.f64 3 (.f64 x.re x.im))	x.re	inf
2.0ms	(.f64 x.re (.f64 3 (*.f64 x.re x.im)))	x.im	-inf
1.0ms	(.f64 3 (.f64 x.re x.im))	x.re	-inf

rewrite40.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`pow1_binary64`
615×	`add-log-exp_binary64`
615×	`log1p-expm1-u_binary64`
615×	`expm1-log1p-u_binary64`
81×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1716	17

Stop Event

1×	node limit

Counts

2 → 26

simplify68.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
402×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
256×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	240
1	17	240
2	37	240
3	82	240
4	216	240
5	710	240
6	966	240
7	1380	240
8	1480	240
9	1613	240
10	1782	240
11	2025	240
12	2338	240
13	2710	240
14	3169	240
15	3748	240
16	4458	240

Stop Event

1×	node limit

Counts

50 → 28

prune31.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	29	6	35

Error

0.0b

Counts

35 → 6

Alt Table

Status	Error	Program
	8.2b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re))) 3) (pow.f64 x.im 3))
	7.9b	(-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 1) (pow.f64 x.im 3))
	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
▶	0.1b	(-.f64 (.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 3 (*.f64 x.re x.im))) (pow.f64 x.im 3))
	7.7b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 561 to 391 computations (30.3% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))
✓	0.2b	(.f64 x.re (.f64 x.im 3))

series17.0ms (0.8%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))	x.im	-inf
2.0ms	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))	x.im	0
2.0ms	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))	x.im	inf
1.0ms	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))	x.re	inf
1.0ms	(.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1))	x.re	-inf

rewrite42.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

708×	`pow1_binary64`
653×	`add-log-exp_binary64`
653×	`log1p-expm1-u_binary64`
653×	`expm1-log1p-u_binary64`
77×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	166	17
2	1809	17

Stop Event

1×	node limit

Counts

2 → 29

simplify81.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
295×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	408
1	23	408
2	45	408
3	84	408
4	235	408
5	835	408
6	1081	408
7	1495	408
8	1595	408
9	1728	408
10	1897	408
11	2142	408
12	2455	408
13	2825	408
14	3284	408
15	3867	408
16	4575	408

Stop Event

1×	node limit

Counts

77 → 33

prune43.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	33	6	39

Error

0.0b

Counts

39 → 6

Alt Table

Status	Error	Program
	8.2b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re))) 3) (pow.f64 x.im 3))
	7.9b	(-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 1) (pow.f64 x.im 3))
▶	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1)) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 3 (*.f64 x.re x.im))) (pow.f64 x.im 3))
	7.7b	(+.f64 (.f64 (-.f64 (.f64 x.re x.re) (.f64 x.im x.im)) x.im) (.f64 (+.f64 (.f64 x.re x.im) (.f64 x.im x.re)) x.re))

Compiler

Compiled 649 to 439 computations (32.4% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.re (.f64 x.re x.im))
✓	0.2b	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))

series18.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

4.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))	x.im	-inf
2.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))	x.im	inf
2.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))	x.im	0
2.0ms	(.f64 x.re (.f64 x.re x.im))	x.im	-inf
1.0ms	(.f64 x.re (.f64 x.re x.im))	x.im	0

rewrite36.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

663×	`pow1_binary64`
610×	`add-log-exp_binary64`
610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
80×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1673	17

Stop Event

1×	node limit

Counts

2 → 26

simplify78.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
402×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
256×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	408
1	17	408
2	37	408
3	82	408
4	216	408
5	710	408
6	966	408
7	1380	408
8	1480	408
9	1613	408
10	1782	408
11	2025	408
12	2338	408
13	2710	408
14	3169	408
15	3748	408
16	4458	408

Stop Event

1×	node limit

Counts

74 → 30

prune28.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	29	7	36

Error

0.0b

Counts

36 → 7

Alt Table

Status	Error	Program
	18.6b	(-.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 x.im (*.f64 x.re x.re)) 2) 9)) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 x.re (pow.f64 (.f64 x.re (*.f64 x.im 3)) 1)) (pow.f64 x.im 3))
	8.2b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re))) 3) (pow.f64 x.im 3))
	7.9b	(-.f64 (pow.f64 (.f64 x.im (.f64 (*.f64 x.re 3) x.re)) 1) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 3 (.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
✓	0.2b	(-.f64 (.f64 x.re (.f64 3 (*.f64 x.re x.im))) (pow.f64 x.im 3))
	7.6b	(-.f64 (pow.f64 (.f64 3 (.f64 x.im (*.f64 x.re x.re))) 1) (pow.f64 x.im 3))

Compiler

Compiled 510 to 316 computations (38% saved)

regimes46.0ms (2.2%)

Accuracy

Total 0.1b remaining (87.4%)

Threshold costs 0.1b (87.4%)

Counts

14 → 1

Compiler

Compiled 687 to 486 computations (29.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-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	11	16
1	19	16
2	23	16
3	25	16
4	26	16

Stop Event

1×

saturated

end100.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 129 to 93 computations (27.9% saved)

Details

analyze185.0ms (8.8%)

sample1.0s (48.2%)

preprocess31.0ms (1.5%)

simplify21.0ms (1%)

prune4.0ms (0.2%)

localize8.0ms (0.4%)

series13.0ms (0.6%)

rewrite39.0ms (1.9%)

simplify80.0ms (3.8%)

prune41.0ms (1.9%)

localize6.0ms (0.3%)

series20.0ms (0.9%)

rewrite40.0ms (1.9%)

simplify68.0ms (3.2%)

prune31.0ms (1.5%)

localize8.0ms (0.4%)

series17.0ms (0.8%)

rewrite42.0ms (2%)

simplify81.0ms (3.8%)

prune43.0ms (2%)

localize6.0ms (0.3%)

series18.0ms (0.9%)

rewrite36.0ms (1.7%)

simplify78.0ms (3.7%)

prune28.0ms (1.3%)

regimes46.0ms (2.2%)

simplify2.0ms (0.1%)

end100.0ms (4.7%)

Profiling