Details

analyze181.0ms (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%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample79.0ms (2.4%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

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
	0.2b	(-.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 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

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 1 (*.f64 3 a)))))) 1)

▶

0.0b

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

Compiler

Compiled 172 to 108 computations (37.2% 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	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series94.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

36.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
35.0ms	(pow.f64 (hypot.f64 a b) 4)
14.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
9.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 63

Calls

4 calls:

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

simplify137.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
417×	`fma-neg_binary64`
408×	`associate-+l+_binary64`
315×	`cancel-sign-sub-inv_binary64`
250×	`exp-prod_binary64`

Counts

159 → 140

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	149	3218
1	364	2814
2	1065	2628
3	3367	2622
4	4754	2618
5	4990	2618

prune165.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	138	4	142

Error

0.0b

Counts

142 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
	2.2b	(+.f64 (expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.5b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Compiler

Compiled 4108 to 2270 computations (44.7% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series38.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

23.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`add-exp-log_binary64`
3×	`pow1_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2))

simplify102.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
590×	`unswap-sqr_binary64`
490×	`cancel-sign-sub-inv_binary64`
404×	`associate-+l+_binary64`
319×	`exp-prod_binary64`

Counts

78 → 79

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1914
1	236	1771
2	662	1521
3	2687	1517
4	4555	1517
5	4703	1517
6	5117	1517

prune163.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	145	4	149

Error

0.0b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
▶	2.2b	(+.f64 (expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
	11.5b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)

Compiler

Compiled 4704 to 2336 computations (50.3% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
	0.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	2.2b	(expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))

series37.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

37.0ms

(expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (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 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))))

simplify69.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-neg_binary64`
561×	`fma-def_binary64`
488×	`cancel-sign-sub-inv_binary64`
410×	`associate--l+_binary64`
406×	`associate-+l+_binary64`

Counts

35 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	65	1204
1	182	1113
2	548	950
3	2233	927
4	4588	901
5	5105	901

prune261.0ms (7.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	149	5	154

Error

Counts

154 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	2.2b	(+.f64 (expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
▶	11.5b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
	11.6b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)

Compiler

Compiled 4575 to 2723 computations (40.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 4 (pow.f64 a 3))
✓	0.0b	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))
✓	0.0b	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
✓	0.0b	(*.f64 4 (pow.f64 a 2))

series15.0ms (0.4%)

Counts

4 → 9

Calls

4 calls:

4.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))
4.0ms	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
4.0ms	(*.f64 4 (pow.f64 a 2))
3.0ms	(*.f64 4 (pow.f64 a 3))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
14×	`add-exp-log_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 92

Calls

4 calls:

7.0ms	(+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4)))
6.0ms	(*.f64 4 (pow.f64 a 2))
5.0ms	(+.f64 (*.f64 4 (pow.f64 a 3)) (pow.f64 a 4))
5.0ms	(*.f64 4 (pow.f64 a 3))

simplify103.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1098×	`fma-neg_binary64`
569×	`fma-def_binary64`
299×	`*-commutative_binary64`
278×	`distribute-rgt-in_binary64`
244×	`distribute-lft-in_binary64`

Counts

101 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1290
1	334	1117
2	1000	1055
3	3454	1053
4	4438	1053
5	4772	1053
6	4928	1053

prune172.0ms (5.2%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	138	0	138
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	138	5	143

Error

Counts

143 → 5

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	0.2b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)) -1)
✓	2.2b	(+.f64 (expm1.f64 (log1p.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
✓	11.5b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
	11.6b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)

Compiler

Compiled 3278 to 2625 computations (19.9% saved)

regimes488.0ms (14.6%)

Accuracy

Total 0.1b remaining (84.4%)

Threshold costs 0.1b (84.4%)

Counts

87 → 1

Compiler

Compiled 9620 to 6818 computations (29.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	14	25
2	14	25

end1.0ms (0%)

Compiler: Compiled 20 to 13 computations (35% saved)

sample1.1s (31.6%)

Algorithm

1×

intervals

Results

699.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 177 to 119 computations (32.8% saved)

Details

analyze181.0ms (5.4%)

sample79.0ms (2.4%)

simplify63.0ms (1.9%)

prune5.0ms (0.1%)

localize14.0ms (0.4%)

series94.0ms (2.8%)

rewrite9.0ms (0.3%)

simplify137.0ms (4.1%)

prune165.0ms (4.9%)

localize16.0ms (0.5%)

series38.0ms (1.1%)

rewrite7.0ms (0.2%)

simplify102.0ms (3.1%)

prune163.0ms (4.9%)

localize20.0ms (0.6%)

series37.0ms (1.1%)

rewrite1.0ms (0%)

simplify69.0ms (2.1%)

prune261.0ms (7.8%)

localize9.0ms (0.3%)

series15.0ms (0.4%)

rewrite31.0ms (0.9%)

simplify103.0ms (3.1%)

prune172.0ms (5.2%)

regimes488.0ms (14.6%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample1.1s (31.6%)

Profiling