Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.1s (28%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify62.0ms (1.6%)

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

16.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	17.8b	(-.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)
▶	16.5b	(+.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

17.8b

(-.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)

▶

16.5b

(+.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)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a -3 1)
✓	3.7b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	6.8b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	9.6b	(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))

series65.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

39.0ms	(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))
14.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
11.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(fma.f64 a -3 1)

rewrite8.0ms (0.2%)

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×	`*-un-lft-identity_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(.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)
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))

simplify110.0ms (2.9%)

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	2832
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune138.0ms (3.6%)

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

Counts

127 → 4

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4)) -1)
	27.4b	(+.f64 (-.f64 (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
	17.8b	(-.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)
✓	16.5b	(+.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 2072 computations (42.2% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 a b)
✓	0.0b	(fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4))
✓	0.0b	(pow.f64 (hypot.f64 a b) 4)

series92.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

40.0ms	(fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4))
37.0ms	(pow.f64 (hypot.f64 a b) 4)
14.0ms	(hypot.f64 a b)

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 40

Calls

3 calls:

2.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(hypot.f64 a b)

simplify86.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
494×	`fma-neg_binary64`
325×	`unswap-sqr_binary64`
274×	`fma-def_binary64`
224×	`distribute-neg-frac_binary64`

Counts

112 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	110	1897
1	266	1788
2	732	1681
3	2868	1681
4	4955	1681
5	5110	1681

prune105.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	103	4	107

Error

Counts

107 → 4

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4)) -1)
	17.8b	(-.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)
▶	3.5b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 a 4))) -1)
✓	16.5b	(+.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 2150 to 1469 computations (31.7% saved)

localize12.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.2b	(fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 a 4))

series21.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

21.0ms

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

simplify50.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

682×	`associate-l_binary64`
557×	`associate-r_binary64`
452×	`unswap-sqr_binary64`
448×	`distribute-rgt-out_binary64`
396×	`distribute-lft-in_binary64`

Counts

34 → 28

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	743
1	54	582
2	135	582
3	499	582
4	2962	582
5	5252	582

prune41.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	28	4	32

Error

Counts

32 → 4

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4)) -1)
▶	17.8b	(-.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)
✓	3.5b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 a 4))) -1)
✓	16.5b	(+.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 784 to 510 computations (34.9% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	3.7b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	8.8b	(+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))
✓	9.6b	(+.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))))))

series75.0ms (2%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(+.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))))))
16.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))
15.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

rewrite47.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
12×	`distribute-lft-in_binary64`

Counts

4 → 106

Calls

4 calls:

22.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
9.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a))))
6.0ms	(+.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))))))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify135.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-neg_binary64`
431×	`cancel-sign-sub-inv_binary64`
307×	`associate-l_binary64`
280×	`associate-r_binary64`
263×	`fma-def_binary64`

Counts

202 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	4760
1	721	4119
2	2748	3908
3	4672	3904
4	4984	3904

prune335.0ms (8.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	210	4	214

Error

Counts

214 → 4

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (fma.f64 4 (pow.f64 b 2) (pow.f64 (hypot.f64 a b) 4)) -1)
✓	17.8b	(-.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)
✓	3.5b	(+.f64 (+.f64 (pow.f64 b 4) (fma.f64 (.f64 b b) (fma.f64 2 (.f64 a a) 4) (pow.f64 a 4))) -1)
✓	16.5b	(+.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 8217 to 4738 computations (42.3% saved)

regimes1.1s (29.4%)

Accuracy

Total 0.5b remaining (99.3%)

Threshold costs 0.5b (99.3%)

Counts

102 → 1

Compiler

Compiled 11923 to 8623 computations (27.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	12	17
2	12	17

end182.0ms (4.8%)

Compiler: Compiled 121 to 85 computations (29.8% saved)

Details

analyze2.0ms (0%)

sample1.1s (28%)

simplify62.0ms (1.6%)

prune5.0ms (0.1%)

localize16.0ms (0.4%)

series65.0ms (1.7%)

rewrite8.0ms (0.2%)

simplify110.0ms (2.9%)

prune138.0ms (3.6%)

localize7.0ms (0.2%)

series92.0ms (2.4%)

rewrite3.0ms (0.1%)

simplify86.0ms (2.3%)

prune105.0ms (2.8%)

localize12.0ms (0.3%)

series21.0ms (0.5%)

rewrite1.0ms (0%)

simplify50.0ms (1.3%)

prune41.0ms (1.1%)

localize15.0ms (0.4%)

series75.0ms (2%)

rewrite47.0ms (1.2%)

simplify135.0ms (3.5%)

prune335.0ms (8.8%)

regimes1.1s (29.4%)

simplify5.0ms (0.1%)

end182.0ms (4.8%)

Profiling