Details

analyze167.0ms (8.1%)

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)

sample24.0ms (1.2%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify46.0ms (2.3%)

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 → 1

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

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 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 80 to 54 computations (32.5% saved)

localize7.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(hypot.f64 a b)
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)

rewrite58.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

3 → 52

Calls

3 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)
0.0ms	(hypot.f64 a b)

Compiler

Compiled 946 to 568 computations (40% saved)

series206.0ms (10%)

Error

0.0b

Counts

3 → 54

Calls

3 calls:

89.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
62.0ms	(pow.f64 (hypot.f64 a b) 4)
34.0ms	(hypot.f64 a b)

Compiler

Compiled 2033 to 1579 computations (22.3% saved)

simplify88.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-neg_binary64`
459×	`fma-def_binary64`
417×	`unswap-sqr_binary64`
250×	`associate-l_binary64`
244×	`associate-r_binary64`

Counts

106 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1959
1	345	1834
2	951	1721
3	3618	1719
4	5212	1719

prune30.0ms (1.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	77	3	80

Error

Counts

80 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
	13.0b	(fma.f64 b (*.f64 b (fma.f64 b 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 726 to 445 computations (38.7% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite58.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

Rules

9×	`add-exp-log_binary64`
9×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`fma-def_binary64`
8×	`add-cbrt-cube_binary64`

Counts

3 → 62

Calls

3 calls:

6.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
4.0ms	(.f64 4 (.f64 b b))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

Compiler

Compiled 1497 to 660 computations (55.9% saved)

series103.0ms (5%)

Error

Counts

3 → 39

Calls

3 calls:

52.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
34.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1363 to 1072 computations (21.3% saved)

simplify103.0ms (5%)

Algorithm

1×	egg-herbie

Rules

719×	`unswap-sqr_binary64`
641×	`fma-neg_binary64`
482×	`fma-def_binary64`
413×	`associate-l_binary64`
337×	`associate-r_binary64`

Counts

101 → 70

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1755
1	283	1583
2	790	1382
3	2768	1379
4	4456	1379
5	5065	1379

prune26.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	70	3	73

Error

Counts

73 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
▶	13.0b	(fma.f64 b (*.f64 b (fma.f64 b 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 696 to 416 computations (40.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.1b	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
0.1b	(*.f64 b (fma.f64 b b 4))

rewrite25.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

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:

4.0ms	(*.f64 b (fma.f64 b b 4))
0.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)

Compiler

Compiled 462 to 279 computations (39.6% saved)

series33.0ms (1.6%)

Error

Counts

2 → 15

Calls

2 calls:

18.0ms	(fma.f64 b (*.f64 b (fma.f64 b b 4)) -1)
9.0ms	(*.f64 b (fma.f64 b b 4))

Compiler

Compiled 273 to 217 computations (20.5% saved)

simplify69.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-neg_binary64`
768×	`fma-def_binary64`
418×	`unswap-sqr_binary64`
404×	`associate-+l+_binary64`
358×	`associate-+r+_binary64`

Counts

47 → 36

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	62	578
1	120	517
2	306	517
3	981	517
4	2087	517
5	3984	517
6	4822	517

prune26.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	36	3	39

Error

Counts

39 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
✓	13.0b	(fma.f64 b (*.f64 b (fma.f64 b 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 363 to 252 computations (30.6% saved)

regimes228.0ms (11.1%)

Accuracy

Total 0.0b remaining (63%)

Threshold costs 0.0b (63%)

Compiler

Compiled 3307 to 2423 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	15	19
2	15	19

end1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

sample737.0ms (35.8%)

Algorithm

1×

intervals

Results

455.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 81 to 55 computations (32.1% saved)

Details

analyze167.0ms (8.1%)

sample24.0ms (1.2%)

simplify46.0ms (2.3%)

prune4.0ms (0.2%)

localize7.0ms (0.4%)

rewrite58.0ms (2.8%)

series206.0ms (10%)

simplify88.0ms (4.3%)

prune30.0ms (1.5%)

localize10.0ms (0.5%)

rewrite58.0ms (2.8%)

series103.0ms (5%)

simplify103.0ms (5%)

prune26.0ms (1.3%)

localize5.0ms (0.3%)

rewrite25.0ms (1.2%)

series33.0ms (1.6%)

simplify69.0ms (3.4%)

prune26.0ms (1.3%)

regimes228.0ms (11.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample737.0ms (35.8%)

Profiling