Details

analyze8.0ms (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 5 computations (50% saved)

sample1.2s (33.6%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	15	4
4	15	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 9 computations (55% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(hypot.f64 x x)

rewrite94.0ms (2.7%)

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 → 40

Calls

1 calls:

93.0ms

(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

simplify19.0ms (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 (1.1%)

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
✓	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))
	33.7b	(neg.f64 (*.f64 (sqrt.f64 2) x))
	29.4b	(*.f64 (sqrt.f64 2) x)

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)

series42.0ms (1.2%)

Counts

2 → 0

Calls

2 calls:

26.0ms	(pow.f64 (sqrt.f64 (hypot.f64 x x)) 2)
16.0ms	(sqrt.f64 (hypot.f64 x x))

rewrite93.0ms (2.6%)

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:

91.0ms	(sqrt.f64 (hypot.f64 x x))
91.0ms	(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

simplify11.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune103.0ms (2.9%)

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

Compiler

Compiled 1516 to 823 computations (45.7% saved)

localize14.0ms (0.4%)

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 (31.8%)

Counts

3 → 36

Calls

3 calls:

390.0ms	(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)
362.0ms	(pow.f64 (hypot.f64 x x) 1/4)

rewrite86.0ms (2.4%)

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:

81.0ms	(pow.f64 (hypot.f64 x x) 1/4)
81.0ms	(pow.f64 (pow.f64 (pow.f64 (hypot.f64 x x) 1/4) 2) 2)
80.0ms	(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

simplify118.0ms (3.3%)

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

prune187.0ms (5.3%)

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

Compiler

Compiled 3190 to 1855 computations (41.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 0

Calls

1 calls:

6.0ms

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

rewrite102.0ms (2.9%)

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:

100.0ms

(*.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 (0.3%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune31.0ms (0.9%)

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

Compiler

Compiled 372 to 308 computations (17.2% saved)

regimes101.0ms (2.9%)

Accuracy

Total 0.1b remaining (76%)

Threshold costs 0.1b (76%)

Counts

13 → 1

Compiler

Compiled 507 to 338 computations (33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	3	4

end119.0ms (3.4%)

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

Details

analyze8.0ms (0.2%)

sample1.2s (33.6%)

simplify11.0ms (0.3%)

prune5.0ms (0.1%)

localize3.0ms (0.1%)

series9.0ms (0.2%)

rewrite94.0ms (2.7%)

simplify19.0ms (0.5%)

prune38.0ms (1.1%)

localize8.0ms (0.2%)

series42.0ms (1.2%)

rewrite93.0ms (2.6%)

simplify11.0ms (0.3%)

prune103.0ms (2.9%)

localize14.0ms (0.4%)

series1.1s (31.8%)

rewrite86.0ms (2.4%)

simplify118.0ms (3.3%)

prune187.0ms (5.3%)

localize5.0ms (0.1%)

series6.0ms (0.2%)

rewrite102.0ms (2.9%)

simplify11.0ms (0.3%)

prune31.0ms (0.9%)

regimes101.0ms (2.9%)

simplify3.0ms (0.1%)

end119.0ms (3.4%)

Profiling