Details

analyze109.0ms (6.2%)

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
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample712.0ms (40.4%)

Results

670.0ms	8256×	body	128	valid
14.0ms	186×	body	128	invalid

Compiler

Compiled 29 to 20 computations (31% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

13×	`fma-def_binary64`
7×	`associate-r_binary64`
7×	`associate-l_binary64`
4×	`*-commutative_binary64`
4×	`*-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	17	8
2	29	8
3	55	8
4	59	8
5	61	8

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

5.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.1b	(fma.f64 x (*.f64 y y) x)

Compiler

Compiled 31 to 15 computations (51.6% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.8b	(fma.f64 x (*.f64 y y) x)

series7.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

7.0ms

(fma.f64 x (*.f64 y y) x)

rewrite29.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

418×	`log1p-expm1-u_binary64`
418×	`expm1-log1p-u_binary64`
266×	`unpow-prod-down_binary64`
221×	`log-prod_binary64`
148×	`pow-prod-down_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1177	8

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

28.0ms

(fma.f64 x (*.f64 y y) x)

simplify62.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
412×	`fabs-mul_binary64`
390×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	22	183
2	40	183
3	74	183
4	167	183
5	462	183
6	687	183
7	1108	183
8	1228	183
9	1363	183
10	1535	183
11	1778	183
12	2093	183
13	2465	183
14	2922	183
15	3509	183
16	4219	183

Stop Event

1×	node limit

Counts

64 → 46

prune22.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	42	5	47

Error

0.0b

Counts

47 → 5

Alt Table

Status	Error	Program
	35.0b	(.f64 (cbrt.f64 (fma.f64 x (.f64 y y) x)) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 2)))
▶	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(fma.f64 x (*.f64 y y) x)
	44.1b	(cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 3))
	35.0b	(pow.f64 (sqrt.f64 (fma.f64 x (*.f64 y y) x)) 2)

Compiler

Compiled 651 to 237 computations (63.6% saved)

localize3.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (*.f64 y x) x)

series6.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

6.0ms

(fma.f64 y (*.f64 y x) x)

rewrite30.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`log1p-expm1-u_binary64`
443×	`expm1-log1p-u_binary64`
303×	`unpow-prod-down_binary64`
252×	`log-prod_binary64`
153×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1207	8

Stop Event

1×	node limit

Counts

1 → 36

Calls

1 calls:

29.0ms

(fma.f64 y (*.f64 y x) x)

simplify59.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

775×	`sqr-pow_binary64`
405×	`fabs-mul_binary64`
390×	`cube-prod_binary64`
381×	`pow-sqr_binary64`
242×	`unswap-sqr_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	183
1	22	183
2	40	183
3	74	183
4	167	183
5	454	183
6	675	183
7	1096	183
8	1216	183
9	1349	183
10	1521	183
11	1764	183
12	2077	183
13	2449	183
14	2908	183
15	3483	183
16	4195	183

Stop Event

1×	node limit

Counts

60 → 42

prune21.0ms (1.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	41	6	47

Error

0.0b

Counts

47 → 6

Alt Table

Status	Error	Program
	35.0b	(.f64 (cbrt.f64 (fma.f64 x (.f64 y y) x)) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 2)))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 y (*.f64 y x) x)) 2)
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)
✓	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(fma.f64 x (*.f64 y y) x)
	44.1b	(cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 3))

Compiler

Compiled 627 to 230 computations (63.3% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (*.f64 y x) x)
✓	0.6b	(cbrt.f64 (fma.f64 y (*.f64 y x) x))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)

series38.0ms (2.2%)

Counts

2 → 8

Calls

2 calls:

30.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)
9.0ms	(cbrt.f64 (fma.f64 y (*.f64 y x) x))

rewrite48.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

611×	`log1p-expm1-u_binary64`
611×	`expm1-log1p-u_binary64`
321×	`log-prod_binary64`
153×	`prod-diff_binary64`
123×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	160	18
2	1709	18

Stop Event

1×	node limit

Counts

2 → 74

Calls

2 calls:

43.0ms	(cbrt.f64 (fma.f64 y (*.f64 y x) x))
43.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)

simplify27.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-def_binary64`
627×	`cancel-sign-sub-inv_binary64`
610×	`fma-neg_binary64`
292×	`*-commutative_binary64`
202×	`unswap-sqr_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	125
1	93	122
2	295	104
3	1225	97
4	3975	97

Stop Event

1×	node limit

Counts

82 → 87

prune60.0ms (3.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	127	8	135

Error

0.0b

Counts

135 → 8

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (cbrt.f64 (*.f64 y x)) x)
	35.0b	(.f64 (cbrt.f64 (fma.f64 x (.f64 y y) x)) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 2)))
	30.4b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 y x)) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 y (*.f64 y x) x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)
✓	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(fma.f64 x (*.f64 y y) x)
	44.1b	(cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 3))

Compiler

Compiled 2018 to 787 computations (61% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (cbrt.f64 (*.f64 y x)) x)
✓	0.2b	(.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
✓	9.1b	(cbrt.f64 (*.f64 y x))

series143.0ms (8.1%)

Counts

4 → 6

Calls

4 calls:

44.0ms	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (cbrt.f64 (*.f64 y x)) x)
43.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
36.0ms	(.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2))
19.0ms	(cbrt.f64 (*.f64 y x))

rewrite47.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`log1p-expm1-u_binary64`
728×	`expm1-log1p-u_binary64`
149×	`log1p-udef_binary64`
86×	`add-sqr-sqrt_binary64`
84×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	48
1	181	37
2	2081	37

Stop Event

1×	node limit

Counts

4 → 84

Calls

4 calls:

45.0ms	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (cbrt.f64 (*.f64 y x)) x)
45.0ms	(.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2))
45.0ms	(pow.f64 (cbrt.f64 (*.f64 y x)) 2)
45.0ms	(cbrt.f64 (*.f64 y x))

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	6

Stop Event

1×

saturated

Counts

90 → 85

prune85.0ms (4.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	108	10	118

Error

0.0b

Counts

118 → 10

Alt Table

Status	Error	Program
	44.1b	(cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 3))
	0.5b	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (.f64 (cbrt.f64 (cbrt.f64 (.f64 y x))) (cbrt.f64 (pow.f64 (cbrt.f64 (*.f64 y x)) 2))) x)
	35.0b	(.f64 (cbrt.f64 (fma.f64 x (.f64 y y) x)) (cbrt.f64 (pow.f64 (fma.f64 x (*.f64 y y) x) 2)))
	30.4b	(fma.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (.f64 y x)) x)
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 y (*.f64 y x) x)) 2)
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 y (*.f64 y x) x)) 3)
✓	0.1b	(fma.f64 y (*.f64 y x) x)
✓	5.1b	(fma.f64 x (*.f64 y y) x)
	0.5b	(fma.f64 (.f64 y (pow.f64 (.f64 (cbrt.f64 y) (cbrt.f64 x)) 2)) (cbrt.f64 (*.f64 y x)) x)
	0.4b	(fma.f64 (.f64 y (pow.f64 (cbrt.f64 (.f64 y x)) 2)) (*.f64 (cbrt.f64 y) (cbrt.f64 x)) x)

Compiler

Compiled 1958 to 725 computations (63% saved)

regimes116.0ms (6.5%)

Accuracy

Total 0.1b remaining (81.8%)

Threshold costs 0.1b (81.8%)

Counts

26 → 1

Compiler

Compiled 1776 to 998 computations (43.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	6	8

Stop Event

1×

saturated

end103.0ms (5.9%)

Compiler: Compiled 155 to 87 computations (43.9% saved)

Details

analyze109.0ms (6.2%)

sample712.0ms (40.4%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize7.0ms (0.4%)

series7.0ms (0.4%)

rewrite29.0ms (1.6%)

simplify62.0ms (3.5%)

prune22.0ms (1.2%)

localize3.0ms (0.2%)

series6.0ms (0.3%)

rewrite30.0ms (1.7%)

simplify59.0ms (3.3%)

prune21.0ms (1.2%)

localize6.0ms (0.3%)

series38.0ms (2.2%)

rewrite48.0ms (2.7%)

simplify27.0ms (1.5%)

prune60.0ms (3.4%)

localize7.0ms (0.4%)

series143.0ms (8.1%)

rewrite47.0ms (2.6%)

simplify7.0ms (0.4%)

prune85.0ms (4.8%)

regimes116.0ms (6.5%)

simplify2.0ms (0.1%)

end103.0ms (5.9%)

Profiling