Details

analyze161.0ms (4.5%)

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%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample100.0ms (2.8%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify59.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

prune5.0ms (0.1%)

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 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (-.f64 1 a)) (.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Status

Error

Program

▶

0.0b

(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (-.f64 1 a)) (*.f64 (*.f64 b b) (+.f64 3 a))))) 1)

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.3b	(.f64 (.f64 b b) (+.f64 a 3))

series90.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

35.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
35.0ms	(pow.f64 (hypot.f64 a b) 4)
12.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
5.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify81.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune201.0ms (5.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 4

Alt Table

Status	Error	Program
	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	12.7b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
▶	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))

Compiler

Compiled 4977 to 2926 computations (41.2% saved)

localize22.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4))))))
✓	0.2b	(*.f64 a (pow.f64 b 2))
✓	0.3b	(*.f64 12 (pow.f64 b 2))
✓	2.1b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series53.0ms (1.5%)

Counts

4 → 15

Calls

4 calls:

27.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4))))))
12.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
11.0ms	(*.f64 a (pow.f64 b 2))
2.0ms	(*.f64 12 (pow.f64 b 2))

rewrite42.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
26×	`add-exp-log_binary64`
24×	`associate-r_binary64`
24×	`unswap-sqr_binary64`
24×	`add-log-exp_binary64`

Counts

4 → 130

Calls

4 calls:

21.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4))))))
6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
4.0ms	(*.f64 12 (pow.f64 b 2))
4.0ms	(*.f64 a (pow.f64 b 2))

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

860×	`distribute-rgt-in_binary64`
794×	`fma-def_binary64`
222×	`fma-neg_binary64`
204×	`associate-l_binary64`
200×	`unswap-sqr_binary64`

Counts

145 → 208

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	2687
1	449	2253
2	1568	2048
3	4972	2048
4	5081	2048

prune382.0ms (10.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	0	208
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	208	4	212

Error

Counts

212 → 4

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	12.7b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))

Compiler

Compiled 10571 to 8093 computations (23.4% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.3b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
	0.3b	(.f64 (.f64 b b) (+.f64 a 3))
✓	9.6b	(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

series99.0ms (2.8%)

Counts

2 → 48

Calls

2 calls:

51.0ms

(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

48.0ms

(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`sqrt-prod_binary64`
6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`unpow-prod-down_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms

(sqrt.f64 (pow.f64 (hypot.f64 a b) 4))

0.0ms

(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (*.f64 a a) (-.f64 1 a) (*.f64 (*.f64 b b) (+.f64 a 3))) -1))

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

627×	`fma-def_binary64`
567×	`fma-neg_binary64`
532×	`cancel-sign-sub-inv_binary64`
512×	`associate-+l+_binary64`
335×	`distribute-lft-out_binary64`

Counts

79 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	1708
1	248	1553
2	746	1322
3	3076	1301
4	4889	1301
5	5008	1301

prune284.0ms (8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	190	4	194

Error

Counts

194 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
▶	12.7b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))

Compiler

Compiled 6483 to 3722 computations (42.6% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 (*.f64 b b) 12 (pow.f64 b 4))

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

704×	`distribute-rgt-in_binary64`
639×	`distribute-rgt-out_binary64`
576×	`distribute-lft-out_binary64`
334×	`associate-l_binary64`
287×	`associate-r_binary64`

Counts

22 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	277
1	32	254
2	73	254
3	239	254
4	1207	254
5	4884	254
6	4984	254

prune29.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	23	4	27

Error

Counts

27 → 4

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (sqrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	12.7b	(+.f64 -1 (fma.f64 (*.f64 b b) 12 (pow.f64 b 4)))
✓	0.0b	(-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (.f64 a (pow.f64 b 2))) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 12 (pow.f64 b 2)) (pow.f64 b 4)))))) (+.f64 1 (*.f64 4 (pow.f64 a 3))))

Compiler

Compiled 446 to 301 computations (32.5% saved)

regimes602.0ms (16.9%)

Accuracy

Total 0.0b remaining (48.1%)

Threshold costs 0.0b (48.1%)

Counts

91 → 1

Compiler

Compiled 12478 to 8851 computations (29.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	64
1	45	64
2	53	64
3	65	64
4	70	64
5	73	64
6	74	64
7	71	64

end1.0ms (0%)

Compiler: Compiled 45 to 36 computations (20% saved)

sample1.1s (29.5%)

Algorithm

1×

intervals

Results

685.0ms	8000×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 195 to 143 computations (26.7% saved)

Details

analyze161.0ms (4.5%)

sample100.0ms (2.8%)

simplify59.0ms (1.7%)

prune5.0ms (0.1%)

localize14.0ms (0.4%)

series90.0ms (2.5%)

rewrite17.0ms (0.5%)

simplify81.0ms (2.3%)

prune201.0ms (5.6%)

localize22.0ms (0.6%)

series53.0ms (1.5%)

rewrite42.0ms (1.2%)

simplify94.0ms (2.6%)

prune382.0ms (10.7%)

localize15.0ms (0.4%)

series99.0ms (2.8%)

rewrite3.0ms (0.1%)

simplify87.0ms (2.4%)

prune284.0ms (8%)

localize6.0ms (0.2%)

series4.0ms (0.1%)

rewrite1.0ms (0%)

simplify57.0ms (1.6%)

prune29.0ms (0.8%)

regimes602.0ms (16.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (29.5%)

Profiling