Details

analyze181.0ms (6.7%)

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%	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)

sample77.0ms (2.8%)

Algorithm

1×

intervals

Results

23.0ms

256×

body

128

valid

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify60.0ms (2.2%)

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 (0.2%)

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
	0.2b	(-.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)

localize25.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	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)))
✓	0.9b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series58.0ms (2.1%)

Counts

4 → 84

Calls

4 calls:

33.0ms	(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))
13.0ms	(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))
2.0ms	(fma.f64 a -3 1)

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

4.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
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))
0.0ms	(fma.f64 a -3 1)

simplify103.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune146.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Error

0.0b

Counts

127 → 4

Alt Table

Status	Error	Program
	13.3b	(+.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (pow.f64 a 4))) -1)
	14.7b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -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 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 3586 to 2013 computations (43.9% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.9b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series60.0ms (2.2%)

Counts

4 → 84

Calls

4 calls:

30.0ms	(+.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))))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
11.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
7.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite31.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
8.0ms	(+.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))))))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify91.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

870×	`distribute-rgt-in_binary64`
807×	`distribute-lft-in_binary64`
278×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
213×	`associate-r_binary64`

Counts

186 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3661
1	577	3211
2	1997	3007
3	5819	3007

prune184.0ms (6.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	192	2	194

Error

0.0b

Counts

194 → 2

Alt Table

Status	Error	Program
▶	13.3b	(-.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4))) 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

▶

13.3b

(-.f64 (+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) 4))) 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 7093 to 4010 computations (43.5% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
✓	0.0b	(.f64 2 (.f64 b b))
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 a 4))
✓	2.2b	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))

series50.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

27.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
16.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))
5.0ms	(*.f64 (pow.f64 a 3) (+.f64 a 4))
2.0ms	(.f64 2 (.f64 b b))

rewrite38.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64`
16×	`associate-l_binary64`
16×	`add-cbrt-cube_binary64`
14×	`pow1_binary64`

Counts

4 → 106

Calls

4 calls:

9.0ms	(*.f64 (pow.f64 a 3) (+.f64 a 4))
8.0ms	(.f64 (.f64 a a) (+.f64 (.f64 2 (.f64 b b)) 4))
8.0ms	(+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4)))
4.0ms	(.f64 2 (.f64 b b))

simplify139.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

439×	`associate-l_binary64`
406×	`fma-neg_binary64`
380×	`exp-prod_binary64`
341×	`associate-r_binary64`
333×	`unswap-sqr_binary64`

Counts

178 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	3129
1	590	2888
2	2787	2870
3	4507	2846
4	4803	2846
5	4940	2846

prune149.0ms (5.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	163	0	163
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	163	2	165

Error

0.0b

Counts

165 → 2

Alt Table

Status	Error	Program
✓	13.3b	(-.f64 (+.f64 (.f64 (pow.f64 a 3) (+.f64 a 4)) (.f64 (.f64 a a) (+.f64 (.f64 2 (*.f64 b b)) 4))) 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

✓

13.3b

(-.f64 (+.f64 (*.f64 (pow.f64 a 3) (+.f64 a 4)) (*.f64 (*.f64 a a) (+.f64 (*.f64 2 (*.f64 b b)) 4))) 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 4921 to 3183 computations (35.3% saved)

regimes315.0ms (11.5%)

Accuracy

Total 0.0b remaining (61.1%)

Threshold costs 0.0b (61.1%)

Counts

55 → 1

Compiler

Compiled 6191 to 4425 computations (28.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	13	25
2	13	25

end1.0ms (0%)

Compiler: Compiled 20 to 12 computations (40% saved)

sample972.0ms (35.7%)

Algorithm

1×

intervals

Results

691.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 104 to 69 computations (33.7% saved)

Details

analyze181.0ms (6.7%)

sample77.0ms (2.8%)

simplify60.0ms (2.2%)

prune5.0ms (0.2%)

localize25.0ms (0.9%)

series58.0ms (2.1%)

rewrite9.0ms (0.3%)

simplify103.0ms (3.8%)

prune146.0ms (5.3%)

localize19.0ms (0.7%)

series60.0ms (2.2%)

rewrite31.0ms (1.1%)

simplify91.0ms (3.3%)

prune184.0ms (6.7%)

localize13.0ms (0.5%)

series50.0ms (1.8%)

rewrite38.0ms (1.4%)

simplify139.0ms (5.1%)

prune149.0ms (5.5%)

regimes315.0ms (11.5%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample972.0ms (35.7%)

Profiling