Details

analyze192.0ms (8.7%)

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 (46.9%)

Results

946.0ms	8256×	body	128	valid
67.0ms	589×	body	128	invalid

Compiler

Compiled 44 to 24 computations (45.5% saved)

preprocess32.0ms (1.4%)

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)

simplify22.0ms (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

prune3.0ms (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)

localize7.0ms (0.3%)

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))

series14.0ms (0.6%)

Counts

2 → 48

Calls

12 calls:

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
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

rewrite37.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

623×	`log1p-expm1-u_binary64`
623×	`expm1-log1p-u_binary64`
383×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1743	17

Stop Event

1×	node limit

Counts

2 → 36

simplify88.0ms (4%)

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

84 → 40

prune44.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	33	7	40
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	34	8	42

Error

0.0b

Counts

42 → 8

Alt Table

Status	Error	Program
	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))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 3) (pow.f64 x.im 3))
	17.8b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
	15.4b	(-.f64 (pow.f64 (sqrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 2) (pow.f64 x.im 3))
	0.6b	(-.f64 (.f64 x.re (pow.f64 (cbrt.f64 (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
▶	0.1b	(-.f64 (.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im)))) (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))

Compiler

Compiled 864 to 602 computations (30.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im))))
✓	0.2b	(.f64 x.re (.f64 3 x.im))

series16.0ms (0.7%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(.f64 x.re (.f64 3 x.im))	x.re	inf
2.0ms	(.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im))))	x.im	inf
2.0ms	(.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im))))	x.im	-inf
2.0ms	(.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im))))	x.im	0
1.0ms	(.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im))))	x.re	-inf

rewrite38.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

723×	`log1p-expm1-u_binary64`
723×	`expm1-log1p-u_binary64`
133×	`log1p-udef_binary64`
82×	`add-sqr-sqrt_binary64`
77×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	195	17
2	2202	17

Stop Event

1×	node limit

Counts

2 → 54

simplify80.0ms (3.7%)

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

102 → 58

prune66.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Error

0.0b

Counts

66 → 8

Alt Table

Status	Error	Program
	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))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 3) (pow.f64 x.im 3))
	17.8b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
	15.4b	(-.f64 (pow.f64 (sqrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 2) (pow.f64 x.im 3))
	0.6b	(-.f64 (.f64 x.re (pow.f64 (cbrt.f64 (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im)))) (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))

Compiler

Compiled 1241 to 895 computations (27.9% saved)

localize8.0ms (0.4%)

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))

series14.0ms (0.6%)

Counts

2 → 24

Calls

12 calls:

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

rewrite38.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

615×	`log1p-expm1-u_binary64`
615×	`expm1-log1p-u_binary64`
382×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	143	17
2	1730	17

Stop Event

1×	node limit

Counts

2 → 34

simplify68.0ms (3.1%)

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

58 → 36

prune42.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	36	8	44

Error

0.0b

Counts

44 → 8

Alt Table

Status	Error	Program
	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))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 3) (pow.f64 x.im 3))
	17.8b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
	15.4b	(-.f64 (pow.f64 (sqrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 2) (pow.f64 x.im 3))
	0.6b	(-.f64 (.f64 x.re (pow.f64 (cbrt.f64 (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im)))) (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))

Compiler

Compiled 782 to 508 computations (35% 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)))

series19.0ms (0.9%)

Counts

2 → 48

Calls

12 calls:

3.0ms	(.f64 x.re (.f64 x.re x.im))	x.re	0
2.0ms	(.f64 3 (.f64 x.re (*.f64 x.re x.im)))	x.im	0
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	inf
2.0ms	(.f64 x.re (.f64 x.re x.im))	x.im	-inf

rewrite35.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

610×	`log1p-expm1-u_binary64`
610×	`expm1-log1p-u_binary64`
379×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	142	17
2	1687	17

Stop Event

1×	node limit

Counts

2 → 34

simplify80.0ms (3.6%)

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

82 → 38

prune45.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	36	2	38
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	39	7	46

Error

0.0b

Counts

46 → 7

Alt Table

Status	Error	Program
	17.8b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im))) 3)) (pow.f64 x.im 3))
	0.6b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x.re (.f64 x.re (*.f64 3 x.im)))) 3) (pow.f64 x.im 3))
✓	0.1b	(-.f64 (.f64 x.re (+.f64 0 (.f64 x.re (*.f64 3 x.im)))) (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))
	18.6b	(-.f64 (sqrt.f64 (.f64 (pow.f64 (.f64 x.im (*.f64 x.re x.re)) 2) 9)) (pow.f64 x.im 3))
	7.6b	(-.f64 (+.f64 0 (.f64 3 (.f64 x.im (*.f64 x.re x.re)))) (pow.f64 x.im 3))

Compiler

Compiled 681 to 394 computations (42.1% saved)

regimes63.0ms (2.9%)

Accuracy

Total 0.1b remaining (83.2%)

Threshold costs 0.1b (83.2%)

Counts

20 → 1

Compiler

Compiled 960 to 687 computations (28.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`+-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	22	16
3	24	16
4	25	16

Stop Event

1×

saturated

end102.0ms (4.6%)

Stop Event

1×

fuel

Compiler

Compiled 130 to 94 computations (27.7% saved)

Details

analyze192.0ms (8.7%)

sample1.0s (46.9%)

preprocess32.0ms (1.4%)

simplify22.0ms (1%)

prune3.0ms (0.2%)

localize7.0ms (0.3%)

series14.0ms (0.6%)

rewrite37.0ms (1.7%)

simplify88.0ms (4%)

prune44.0ms (2%)

localize7.0ms (0.3%)

series16.0ms (0.7%)

rewrite38.0ms (1.7%)

simplify80.0ms (3.7%)

prune66.0ms (3%)

localize8.0ms (0.4%)

series14.0ms (0.6%)

rewrite38.0ms (1.7%)

simplify68.0ms (3.1%)

prune42.0ms (1.9%)

localize6.0ms (0.3%)

series19.0ms (0.9%)

rewrite35.0ms (1.6%)

simplify80.0ms (3.6%)

prune45.0ms (2%)

regimes63.0ms (2.9%)

simplify2.0ms (0.1%)

end102.0ms (4.6%)

Profiling