Details

analyze11.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.4s (36.7%)

Results

1.3s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify115.0ms (3%)

Algorithm

1×	egg-herbie

Rules

1333×	`fma-def_binary64`
773×	`distribute-rgt-out_binary64`
559×	`hypot-def_binary64`
453×	`associate-l_binary64`
451×	`count-2_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	12	4
2	25	4
3	46	4
4	98	4
5	245	4
6	763	4
7	1382	4
8	2673	4
9	3450	4
10	4144	4
11	4482	4
12	4395	4
13	4766	4
14	4993	4
15	4742	4

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 12 computations (40% saved)

localize2.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(hypot.f64 x x)

rewrite66.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

438×	`log1p-udef_binary64`
249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
229×	`add-cbrt-cube_binary64`
228×	`add-cube-cbrt_binary64`

Counts

1 → 41

Calls

1 calls:

65.0ms

(hypot.f64 x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	660	4
3	4745	4
4	5428	4
0	0	0
1	0	0

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

53 → 44

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune20.0ms (0.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	5	45

Error

0.0b

Counts

45 → 5

Alt Table

Status	Error	Program
▶	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
	34.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.7b	(*.f64 (sqrt.f64 2) x)

Compiler

Compiled 464 to 218 computations (53% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.5b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
✓	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)

series716.0ms (18.5%)

Counts

4 → 48

Calls

4 calls:

281.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)
264.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
166.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))

rewrite59.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

563×	`unpow-prod-down_binary64`
550×	`log1p-expm1-u_binary64`
550×	`expm1-log1p-u_binary64`
272×	`log-prod_binary64`
192×	`egg-rr`

Counts

4 → 192

Calls

4 calls:

56.0ms	(sqrt.f64 (cbrt.f64 (hypot.f64 x x)))
56.0ms	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
56.0ms	(cbrt.f64 (hypot.f64 x x))
56.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	32
1	166	23
2	1470	23
3	5384	23
0	0	0
1	0	0

simplify62.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

788×	`fma-neg_binary64`
583×	`unswap-sqr_binary64`
536×	`fma-def_binary64`
332×	`associate-+l+_binary64`
172×	`distribute-rgt-in_binary64`

Counts

240 → 210

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	692
1	95	692
2	154	632
3	410	464
4	1290	416
5	4366	416
6	5091	416

prune187.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	391	2	393
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	391	7	398

Error

0.0b

Counts

398 → 7

Alt Table

Status	Error	Program
▶	1.1b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
✓	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
	34.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.7b	(*.f64 (sqrt.f64 2) x)
	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))

Compiler

Compiled 8490 to 3947 computations (53.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))
✓	0.5b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))
	0.6b	(cbrt.f64 (hypot.f64 x x))
	0.7b	(pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3)

series10.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

6.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

4.0ms

(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))

rewrite42.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

599×	`log1p-expm1-u_binary64`
599×	`expm1-log1p-u_binary64`
308×	`log-prod_binary64`
173×	`pow2_binary64`
124×	`log-pow_binary64`

Counts

2 → 44

Calls

2 calls:

41.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x))))

41.0ms

(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (*.f64 (sqrt.f64 (sqrt.f64 (hypot.f64 x x))) (sqrt.f64 (sqrt.f64 (hypot.f64 x x)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	203	10
2	1581	10
3	4904	10
0	0	0
1	0	0

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Counts

56 → 47

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	24	80
3	25	80
4	29	80
5	47	80
6	58	80
7	63	80
8	75	80
9	72	80
10	58	80

prune72.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	169	7	176

Error

0.0b

Counts

176 → 7

Alt Table

Status	Error	Program
✓	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
	34.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.7b	(*.f64 (sqrt.f64 2) x)
	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
▶	0.8b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)

Compiler

Compiled 3807 to 1231 computations (67.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.8b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)

series552.0ms (14.3%)

Counts

2 → 24

Calls

2 calls:

327.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)
225.0ms	(pow.f64 (hypot.f64 x x) 1/4)

rewrite76.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

478×	`log1p-expm1-u_binary64`
478×	`expm1-log1p-u_binary64`
377×	`unpow-prod-down_binary64`
223×	`log-prod_binary64`
185×	`prod-diff_binary64`

Counts

2 → 88

Calls

2 calls:

74.0ms	(pow.f64 (hypot.f64 x x) 1/4)
74.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	136	11
2	1272	11
3	4921	11
4	5009	11
0	0	0
1	0	0

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

334×	`exp-prod_binary64`
315×	`distribute-rgt-in_binary64`
287×	`prod-exp_binary64`
244×	`fma-neg_binary64`
214×	`exp-sum_binary64`

Counts

112 → 97

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	420
1	58	420
2	89	372
3	235	240
4	844	204
5	2069	196
6	4321	196
7	5006	196

prune63.0ms (1.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	141	7	148

Error

0.0b

Counts

148 → 7

Alt Table

Status	Error	Program
✓	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3))
	34.4b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.3b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	0.1b	(hypot.f64 x x)
	33.7b	(*.f64 (sqrt.f64 2) x)
	1.6b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (hypot.f64 x x))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (hypot.f64 x x))) 3))
✓	0.8b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 4)

Compiler

Compiled 1901 to 1088 computations (42.8% saved)

regimes197.0ms (5.1%)

Accuracy

Total 0.1b remaining (79.8%)

Threshold costs 0.1b (79.8%)

Counts

22 → 1

Compiler

Compiled 1322 to 854 computations (35.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end79.0ms (2.1%)

Compiler: Compiled 72 to 47 computations (34.7% saved)

Details

analyze11.0ms (0.3%)

sample1.4s (36.7%)

simplify115.0ms (3%)

prune3.0ms (0.1%)

localize2.0ms (0%)

series3.0ms (0.1%)

rewrite66.0ms (1.7%)

simplify12.0ms (0.3%)

prune20.0ms (0.5%)

localize6.0ms (0.2%)

series716.0ms (18.5%)

rewrite59.0ms (1.5%)

simplify62.0ms (1.6%)

prune187.0ms (4.8%)

localize10.0ms (0.3%)

series10.0ms (0.3%)

rewrite42.0ms (1.1%)

simplify12.0ms (0.3%)

prune72.0ms (1.9%)

localize6.0ms (0.2%)

series552.0ms (14.3%)

rewrite76.0ms (2%)

simplify61.0ms (1.6%)

prune63.0ms (1.6%)

regimes197.0ms (5.1%)

simplify2.0ms (0%)

end79.0ms (2.1%)

Profiling