Details

analyze186.0ms (8.9%)

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%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 20 to 13 computations (35% saved)

sample23.0ms (1.1%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify47.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

770×	`unswap-sqr_binary64`
631×	`associate-l_binary64`
623×	`fma-def_binary64`
311×	`fma-neg_binary64`
283×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	30	21
2	60	21
3	159	21
4	518	17
5	1687	17
6	3597	17
7	5026	17

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)

Compiler

Compiled 97 to 64 computations (34% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
7×	`fma-def_binary64`
6×	`add-sqr-sqrt_binary64`
6×	`unpow-prod-down_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 42

Calls

2 calls:

4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
2.0ms	(pow.f64 (hypot.f64 a b) 4)

series86.0ms (4.1%)

Counts

2 → 48

Calls

2 calls:

46.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
40.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify70.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

593×	`associate-+l+_binary64`
307×	`fma-def_binary64`
295×	`cancel-sign-sub-inv_binary64`
264×	`fma-neg_binary64`
253×	`unswap-sqr_binary64`

Counts

90 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1576
1	194	1474
2	523	1381
3	2044	1379
4	5169	1379

prune64.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

0.0b

Counts

147 → 3

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1424 to 894 computations (37.2% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
✓	0.0b	(pow.f64 (hypot.f64 a b) 2)
✓	0.3b	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

rewrite16.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`unpow-prod-down_binary64`
14×	`*-un-lft-identity_binary64`
12×	`fma-def_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 77

Calls

3 calls:

7.0ms	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
3.0ms	(pow.f64 (hypot.f64 a b) 2)
3.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

series140.0ms (6.7%)

Counts

3 → 72

Calls

3 calls:

57.0ms	(pow.f64 (hypot.f64 a b) 2)
45.0ms	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
38.0ms	(pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4))

simplify164.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

444×	`log-prod_binary64`
413×	`exp-prod_binary64`
342×	`cancel-sign-sub-inv_binary64`
321×	`fma-def_binary64`
284×	`fma-neg_binary64`

Counts

149 → 261

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	111	2194
1	252	1935
2	640	1839
3	2392	1834
4	4109	1834
5	4473	1828
6	4971	1828
7	4924	1828

prune102.0ms (4.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	261	0	261
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	261	3	264

Error

0.0b

Counts

264 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
▶	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2708 to 1817 computations (32.9% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.1b	(*.f64 b (fma.f64 b b 4))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 b (fma.f64 b b 4))
0.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

series22.0ms (1%)

Counts

2 → 24

Calls

2 calls:

11.0ms	(*.f64 b (fma.f64 b b 4))
10.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

simplify89.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

784×	`fma-neg_binary64`
764×	`fma-def_binary64`
404×	`associate-+l+_binary64`
395×	`unswap-sqr_binary64`
359×	`associate-+r+_binary64`

Counts

56 → 98

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	59	650
1	111	579
2	299	579
3	963	579
4	2085	579
5	3908	579
6	4988	579
7	4818	579

prune46.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	98	3	101

Error

0.0b

Counts

101 → 3

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) (sqrt.f64 4)) (fma.f64 b (*.f64 b 4) -1))
✓	11.7b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 869 to 562 computations (35.3% saved)

regimes184.0ms (8.8%)

Accuracy

Total 0.0b remaining (37%)

Threshold costs 0.0b (37%)

Compiler

Compiled 2274 to 1672 computations (26.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	12	17
2	12	17

end1.0ms (0%)

Compiler: Compiled 14 to 10 computations (28.6% saved)

sample815.0ms (38.9%)

Algorithm

1×

intervals

Results

532.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 78 to 55 computations (29.5% saved)

Details

analyze186.0ms (8.9%)

sample23.0ms (1.1%)

simplify47.0ms (2.2%)

prune4.0ms (0.2%)

localize8.0ms (0.4%)

rewrite7.0ms (0.3%)

series86.0ms (4.1%)

simplify70.0ms (3.4%)

prune64.0ms (3%)

localize10.0ms (0.5%)

rewrite16.0ms (0.7%)

series140.0ms (6.7%)

simplify164.0ms (7.8%)

prune102.0ms (4.9%)

localize5.0ms (0.3%)

rewrite4.0ms (0.2%)

series22.0ms (1%)

simplify89.0ms (4.2%)

prune46.0ms (2.2%)

regimes184.0ms (8.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample815.0ms (38.9%)

Profiling