Details

analyze91.0ms (3.7%)

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)

sample76.0ms (3%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 41 to 27 computations (34.1% saved)

simplify42.0ms (1.7%)

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
	0.1b	(-.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	(pow.f64 (hypot.f64 a b) 4)
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))

series71.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

38.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 b (*.f64 b 4) -1))
33.0ms	(pow.f64 (hypot.f64 a b) 4)

rewrite8.0ms (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:

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

simplify58.0ms (2.3%)

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 → 77

Iterations

Useful iterations: 3 (0.0ms)

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

prune80.0ms (3.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	75	4	79

Error

Counts

79 → 4

Alt Table

Status	Error	Program
	0.1b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
▶	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	0.4b	(fma.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (fma.f64 b (.f64 b 4) -1))
	14.9b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 1603 to 993 computations (38.1% saved)

localize11.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 a 4) 1)
✓	1.5b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

series24.0ms (0.9%)

Counts

2 → 27

Calls

2 calls:

21.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))
3.0ms	(-.f64 (pow.f64 a 4) 1)

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
21×	`prod-diff_binary64`
18×	`add-cube-cbrt_binary64`
15×	`unpow-prod-down_binary64`

Counts

2 → 67

Calls

2 calls:

7.0ms	(-.f64 (pow.f64 a 4) 1)
0.0ms	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))

simplify85.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-def_binary64`
592×	`distribute-rgt-in_binary64`
583×	`distribute-lft-in_binary64`
431×	`fma-neg_binary64`
346×	`*-commutative_binary64`

Counts

94 → 101

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	1542
1	153	1338
2	350	1134
3	1130	1024
4	3629	1021
5	4831	1021
6	4998	1021

prune155.0ms (6.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	101	4	105

Error

Counts

105 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	5.8b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1)))
	14.9b	(+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 4) 3)) (fma.f64 b (*.f64 b 4) -1))

Compiler

Compiled 2982 to 2017 computations (32.4% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series46.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

22.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
6.0ms	(+.f64 (.f64 a a) (.f64 b b))
2.0ms	(.f64 4 (.f64 b b))

rewrite22.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

7.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
6.0ms	(.f64 4 (.f64 b b))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
3.0ms	(+.f64 (.f64 a a) (.f64 b b))

simplify90.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-l_binary64`
617×	`fma-def_binary64`
585×	`associate-r_binary64`
564×	`fma-neg_binary64`
242×	`distribute-rgt-in_binary64`

Counts

160 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	121	2183
1	320	1975
2	966	1803
3	4484	1803
4	5000	1803

prune132.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	133	3	136

Error

Counts

136 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	14.9b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 6)) (.f64 4 (.f64 b b))) 1)
▶	5.8b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1)))

Compiler

Compiled 3070 to 1557 computations (49.3% saved)

localize15.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
	1.5b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4))
✓	5.4b	(/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

1 → 42

Calls

1 calls:

9.0ms

(/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1))

simplify76.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

470×	`div-sub_binary64`
455×	`fma-neg_binary64`
358×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
215×	`times-frac_binary64`

Counts

54 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	1099
1	180	1007
2	539	919
3	2474	883
4	4466	883
5	4927	883

prune101.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	83	3	86

Error

Counts

86 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (-.f64 (pow.f64 a 4) 1))
	14.9b	(-.f64 (+.f64 (cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 b a) 2) 6)) (.f64 4 (.f64 b b))) 1)
✓	5.8b	(+.f64 (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 b 4)) (/.f64 (+.f64 -1 (pow.f64 a 8)) (+.f64 (pow.f64 a 4) 1)))

Compiler

Compiled 2702 to 1848 computations (31.6% saved)

regimes557.0ms (22.3%)

Accuracy

Total 0.0b remaining (27.8%)

Threshold costs 0.0b (27.8%)

Counts

96 → 1

Compiler

Compiled 10556 to 7776 computations (26.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	20	27
2	21	27
3	19	27

end1.0ms (0%)

Compiler: Compiled 21 to 15 computations (28.6% saved)

sample702.0ms (28.2%)

Algorithm

1×

intervals

Results

419.0ms	8000×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 109 to 79 computations (27.5% saved)

Details

analyze91.0ms (3.7%)

sample76.0ms (3%)

simplify42.0ms (1.7%)

prune4.0ms (0.2%)

localize7.0ms (0.3%)

series71.0ms (2.9%)

rewrite8.0ms (0.3%)

simplify58.0ms (2.3%)

prune80.0ms (3.2%)

localize11.0ms (0.4%)

series24.0ms (0.9%)

rewrite10.0ms (0.4%)

simplify85.0ms (3.4%)

prune155.0ms (6.2%)

localize9.0ms (0.4%)

series46.0ms (1.8%)

rewrite22.0ms (0.9%)

simplify90.0ms (3.6%)

prune132.0ms (5.3%)

localize15.0ms (0.6%)

series4.0ms (0.2%)

rewrite12.0ms (0.5%)

simplify76.0ms (3.1%)

prune101.0ms (4.1%)

regimes557.0ms (22.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample702.0ms (28.2%)

Profiling