Details

analyze11.0ms (0.2%)

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)

sample2.3s (46.5%)

Results

2.1s

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify138.0ms (2.8%)

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

prune5.0ms (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)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(hypot.f64 x x)

rewrite110.0ms (2.2%)

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 → 40

Calls

1 calls:

109.0ms

(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

simplify23.0ms (0.5%)

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

52 → 43

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

prune38.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	39	4	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	29.4b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	29.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))

Compiler

Compiled 437 to 210 computations (51.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.1b	(sqrt.f64 (hypot.f64 x x))
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

series50.0ms (1%)

Counts

2 → 0

Calls

2 calls:

32.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
17.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite210.0ms (4.2%)

Algorithm

2×	batch-egg-rewrite

Rules

688×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
339×	`pow1_binary64`
273×	`unpow-prod-down_binary64`

Counts

2 → 88

Calls

2 calls:

207.0ms	(sqrt.f64 (hypot.f64 x x))
207.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	106	10
2	1032	10
3	4509	10
4	5547	10
0	0	0
1	0	0

simplify13.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune100.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	130	6	136

Error

0.0b

Counts

136 → 6

Alt Table

Status	Error	Program
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	29.4b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
▶	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	29.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))

Compiler

Compiled 1516 to 823 computations (45.7% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 x x) 1/4)
	0.1b	(hypot.f64 x x)
✓	0.5b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
✓	0.5b	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)

series1.1s (22.8%)

Counts

3 → 36

Calls

3 calls:

380.0ms	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
378.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)
371.0ms	(pow.f64 (hypot.f64 x x) 1/4)

rewrite97.0ms (2%)

Algorithm

2×	batch-egg-rewrite

Rules

535×	`log1p-expm1-u_binary64`
535×	`expm1-log1p-u_binary64`
502×	`unpow-prod-down_binary64`
262×	`log-prod_binary64`
160×	`pow2_binary64`

Counts

3 → 159

Calls

3 calls:

92.0ms	(pow.f64 (hypot.f64 x x) 1/4)
92.0ms	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
92.0ms	(pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	174	17
2	1412	17
3	5227	17
0	0	0
1	0	0

simplify113.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

845×	`fma-neg_binary64`
483×	`fma-def_binary64`
395×	`associate-+l+_binary64`
393×	`*-commutative_binary64`
342×	`associate-+r+_binary64`

Counts

195 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	648
1	68	648
2	114	564
3	379	348
4	1568	312
5	3697	312
6	4996	312
7	4896	312

prune184.0ms (3.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	216	0	216
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	216	6	222

Error

0.0b

Counts

222 → 6

Alt Table

Status	Error	Program
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
▶	29.4b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	29.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))

Compiler

Compiled 3190 to 1855 computations (41.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 2) x)

series6.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

6.0ms

(*.f64 (sqrt.f64 2) x)

rewrite95.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

711×	`log1p-udef_binary64`
386×	`log1p-expm1-u_binary64`
386×	`expm1-log1p-u_binary64`
336×	`pow1_binary64`
245×	`unpow-prod-down_binary64`

Counts

1 → 37

Calls

1 calls:

94.0ms

(*.f64 (sqrt.f64 2) x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	99	6
2	1029	6
3	4823	6
4	5948	6
0	0	0
1	0	0

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune33.0ms (0.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	37	6	43

Error

0.0b

Counts

43 → 6

Alt Table

Status	Error	Program
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
✓	29.4b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
✓	1.0b	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
✓	0.5b	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
	29.9b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))

Compiler

Compiled 372 to 308 computations (17.2% saved)

regimes116.0ms (2.4%)

Accuracy

Total 0.1b remaining (76%)

Threshold costs 0.1b (76%)

Counts

13 → 1

Compiler

Compiled 478 to 346 computations (27.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end121.0ms (2.5%)

Compiler: Compiled 49 to 34 computations (30.6% saved)

Details

analyze11.0ms (0.2%)

sample2.3s (46.5%)

simplify138.0ms (2.8%)

prune5.0ms (0.1%)

localize3.0ms (0.1%)

series6.0ms (0.1%)

rewrite110.0ms (2.2%)

simplify23.0ms (0.5%)

prune38.0ms (0.8%)

localize8.0ms (0.2%)

series50.0ms (1%)

rewrite210.0ms (4.2%)

simplify13.0ms (0.3%)

prune100.0ms (2%)

localize14.0ms (0.3%)

series1.1s (22.8%)

rewrite97.0ms (2%)

simplify113.0ms (2.3%)

prune184.0ms (3.7%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite95.0ms (1.9%)

simplify11.0ms (0.2%)

prune33.0ms (0.7%)

regimes116.0ms (2.4%)

simplify3.0ms (0.1%)

end121.0ms (2.5%)

Profiling