Details

analyze154.0ms (5.4%)

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)

sample22.0ms (0.8%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify46.0ms (1.6%)

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 (0.1%)

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

Compiler

Compiled 97 to 64 computations (34% saved)

localize7.0ms (0.3%)

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)

series89.0ms (3.1%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
41.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify70.0ms (2.4%)

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

prune74.0ms (2.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (fma.f64 b (*.f64 b 4) (pow.f64 (hypot.f64 a b) 4)) -1)
	10.1b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 b b (.f64 2 (.f64 a a))) (pow.f64 a 4)) (fma.f64 b (.f64 b 4) -1))

Compiler

Compiled 1496 to 938 computations (37.3% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series45.0ms (1.6%)

Counts

1 → 24

Calls

1 calls:

45.0ms

(fma.f64 b (*.f64 b 4) (pow.f64 (hypot.f64 a b) 4))

simplify100.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

480×	`distribute-lft-in_binary64`
480×	`distribute-rgt-in_binary64`
463×	`associate-l_binary64`
458×	`fma-def_binary64`
420×	`unswap-sqr_binary64`

Counts

34 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	726
1	66	659
2	177	595
3	519	571
4	1854	571
5	4832	571
6	4841	571
7	4992	571
8	4965	571

prune63.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	136	3	139

Error

Counts

139 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 b (*.f64 b 4) (pow.f64 (hypot.f64 a b) 4)) -1)
	10.1b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
▶	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 a (.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 4)) -1)

Compiler

Compiled 1225 to 767 computations (37.4% saved)

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 b b) (fma.f64 a (.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 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) (fma.f64 a (*.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 4))

series36.0ms (1.2%)

Counts

1 → 24

Calls

1 calls:

35.0ms

(fma.f64 (*.f64 b b) (fma.f64 a (*.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 4))

simplify76.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

851×	`associate-l_binary64`
715×	`associate-r_binary64`
570×	`fma-def_binary64`
532×	`unswap-sqr_binary64`
473×	`exp-prod_binary64`

Counts

34 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	839
1	69	666
2	185	662
3	759	662
4	3517	662
5	5026	662

prune112.0ms (3.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	61	3	64

Error

Counts

64 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 b (*.f64 b 4) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	10.1b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 a (.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 4)) -1)

Compiler

Compiled 773 to 496 computations (35.8% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8))
	0.0b	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(pow.f64 (hypot.f64 a b) 8)
✓	9.4b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`

Counts

3 → 77

Calls

3 calls:

7.0ms

(/.f64 (fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

1.0ms

(pow.f64 (hypot.f64 a b) 8)

0.0ms

(fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8))

series281.0ms (9.8%)

Counts

3 → 72

Calls

3 calls:

220.0ms

(/.f64 (fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))

35.0ms

(fma.f64 (fma.f64 b (*.f64 b 4) -1) (fma.f64 b (*.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8))

25.0ms

(pow.f64 (hypot.f64 a b) 8)

simplify147.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

509×	`fma-def_binary64`
356×	`associate-+l+_binary64`
326×	`times-frac_binary64`
315×	`associate-/l*_binary64`
221×	`associate-/r*_binary64`

Counts

149 → 268

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	492	8911
1	1486	8554
2	5206	8554

prune362.0ms (12.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	418	0	418
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	418	3	421

Error

Counts

421 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 b (*.f64 b 4) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	10.1b	(/.f64 (fma.f64 (fma.f64 b (.f64 b 4) -1) (fma.f64 b (.f64 b -4) 1) (pow.f64 (hypot.f64 a b) 8)) (-.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1)))
✓	0.1b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 a (.f64 a 2) (fma.f64 b b 4)) (pow.f64 a 4)) -1)

Compiler

Compiled 13696 to 9432 computations (31.1% saved)

regimes354.0ms (12.3%)

Accuracy

Total 0.0b remaining (73.9%)

Threshold costs 0.0b (73.9%)

Compiler

Compiled 6843 to 5019 computations (26.7% saved)

simplify4.0ms (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)

sample776.0ms (26.9%)

Algorithm

1×

intervals

Results

435.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 103 to 70 computations (32% saved)

Details

analyze154.0ms (5.4%)

sample22.0ms (0.8%)

simplify46.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.3%)

rewrite7.0ms (0.3%)

series89.0ms (3.1%)

simplify70.0ms (2.4%)

prune74.0ms (2.6%)

localize7.0ms (0.3%)

rewrite1.0ms (0%)

series45.0ms (1.6%)

simplify100.0ms (3.5%)

prune63.0ms (2.2%)

localize11.0ms (0.4%)

rewrite1.0ms (0%)

series36.0ms (1.2%)

simplify76.0ms (2.6%)

prune112.0ms (3.9%)

localize15.0ms (0.5%)

rewrite15.0ms (0.5%)

series281.0ms (9.8%)

simplify147.0ms (5.1%)

prune362.0ms (12.6%)

regimes354.0ms (12.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample776.0ms (26.9%)

Profiling