Details

analyze169.0ms (3.9%)

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%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 32 to 20 computations (37.5% saved)

sample101.0ms (2.3%)

Algorithm

1×

intervals

Results

19.0ms

256×

body

128

valid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify58.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
556×	`cancel-sign-sub-inv_binary64`
552×	`unswap-sqr_binary64`
357×	`unsub-neg_binary64`
344×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	57	37
2	168	37
3	492	37
4	1604	33
5	2891	33
6	4309	33
7	5214	33

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

▶

0.0b

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

Compiler

Compiled 166 to 104 computations (37.3% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series94.0ms (2.2%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
36.0ms	(pow.f64 (hypot.f64 a b) 4)
13.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 78

Calls

4 calls:

6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
4.0ms	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
3.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
1.0ms	(pow.f64 (hypot.f64 a b) 4)

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
469×	`distribute-rgt-in_binary64`
453×	`distribute-lft-in_binary64`
338×	`associate--l+_binary64`
219×	`cancel-sign-sub-inv_binary64`

Counts

174 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3413
1	464	3143
2	1556	3045
3	5074	3045

prune204.0ms (4.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	159	3	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	161	3	164

Error

0.0b

Counts

164 → 3

Alt Table

Status	Error	Program
	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
	17.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
▶	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 5002 to 2925 computations (41.5% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.3b	(.f64 a (.f64 b b))
	0.3b	(.f64 (.f64 b b) (+.f64 a 3))
✓	0.3b	(.f64 a (.f64 a (*.f64 b b)))

series22.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(.f64 a (.f64 a (*.f64 b b)))
8.0ms	(.f64 a (.f64 b b))

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

2 → 44

Calls

2 calls:

7.0ms	(.f64 a (.f64 a (*.f64 b b)))
4.0ms	(.f64 a (.f64 b b))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

604×	`associate-l_binary64`
566×	`fma-def_binary64`
531×	`unswap-sqr_binary64`
469×	`*-commutative_binary64`
372×	`associate-r_binary64`

Counts

92 → 56

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	57	1003
1	125	874
2	375	832
3	1084	808
4	2147	797
5	3407	797
6	4998	797

prune170.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	129	3	132

Error

0.0b

Counts

132 → 3

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
	17.4b	(cbrt.f64 (pow.f64 (+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1)) 3))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))

Compiler

Compiled 5189 to 2738 computations (47.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
✓	0.0b	(+.f64 (*.f64 b b) 12)
✓	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	0.6b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series29.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

21.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
3.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
2.0ms	(+.f64 (*.f64 b b) 12)

rewrite32.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
25×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`associate-l_binary64`

Counts

4 → 130

Calls

4 calls:

10.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
8.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
3.0ms	(+.f64 (*.f64 b b) 12)

simplify119.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

477×	`associate-l_binary64`
442×	`associate-r_binary64`
412×	`exp-prod_binary64`
373×	`fma-neg_binary64`
223×	`unswap-sqr_binary64`

Counts

190 → 217

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	3359
1	677	2539
2	3018	2531
3	4511	2501
4	5054	2501

prune301.0ms (7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	217	3	220

Error

Counts

220 → 3

Alt Table

Status	Error	Program
	10.6b	(+.f64 (cbrt.f64 (pow.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) 3)) (fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
▶	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (.f64 a (.f64 (*.f64 a a) (-.f64 a 4))) -1)))

Compiler

Compiled 9186 to 5817 computations (36.7% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (*.f64 b b) 12)
✓	0.1b	(.f64 (.f64 a a) (-.f64 a 4))
✓	0.1b	(.f64 a (.f64 (*.f64 a a) (-.f64 a 4)))
	0.6b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(.f64 a (.f64 (*.f64 a a) (-.f64 a 4)))
3.0ms	(.f64 (.f64 a a) (-.f64 a 4))

rewrite38.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`distribute-lft-in_binary64`
65×	`distribute-rgt-in_binary64`
54×	`prod-diff_binary64`
49×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`

Counts

2 → 128

Calls

2 calls:

14.0ms	(.f64 a (.f64 (*.f64 a a) (-.f64 a 4)))
7.0ms	(.f64 (.f64 a a) (-.f64 a 4))

simplify102.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

412×	`associate-+l+_binary64`
367×	`fma-neg_binary64`
346×	`*-commutative_binary64`
335×	`unswap-sqr_binary64`
253×	`distribute-rgt-in_binary64`

Counts

152 → 163

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2345
1	303	1658
2	801	1658
3	1964	1652
4	4830	1652
5	5074	1652

prune334.0ms (7.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	249	0	249
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	249	3	252

Error

Counts

252 → 3

Alt Table

Status	Error	Program
	10.6b	(+.f64 (cbrt.f64 (pow.f64 (.f64 b (.f64 b (fma.f64 a (fma.f64 2 a 4) (fma.f64 b b 12)))) 3)) (fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))
✓	0.0b	(+.f64 (+.f64 (fma.f64 2 (.f64 a (.f64 a (.f64 b b))) (pow.f64 b 4)) (pow.f64 a 4)) (fma.f64 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (.f64 b b) (+.f64 a 3))) -1))
✓	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (.f64 a (.f64 (*.f64 a a) (-.f64 a 4))) -1)))

Compiler

Compiled 11641 to 6788 computations (41.7% saved)

regimes1.3s (29.7%)

Accuracy

Total 0.0b remaining (64.1%)

Threshold costs 0.0b (64.1%)

Counts

204 → 1

Compiler

Compiled 31942 to 22022 computations (31.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	49
1	32	49
2	35	49
3	37	49
4	38	49
5	37	49

end1.0ms (0%)

Compiler: Compiled 36 to 23 computations (36.1% saved)

sample991.0ms (22.9%)

Algorithm

1×

intervals

Results

659.0ms	8000×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 176 to 114 computations (35.2% saved)

Details

analyze169.0ms (3.9%)

sample101.0ms (2.3%)

simplify58.0ms (1.4%)

prune5.0ms (0.1%)

localize15.0ms (0.4%)

series94.0ms (2.2%)

rewrite18.0ms (0.4%)

simplify81.0ms (1.9%)

prune204.0ms (4.7%)

localize19.0ms (0.5%)

series22.0ms (0.5%)

rewrite14.0ms (0.3%)

simplify72.0ms (1.7%)

prune170.0ms (3.9%)

localize17.0ms (0.4%)

series29.0ms (0.7%)

rewrite32.0ms (0.7%)

simplify119.0ms (2.8%)

prune301.0ms (7%)

localize17.0ms (0.4%)

series7.0ms (0.2%)

rewrite38.0ms (0.9%)

simplify102.0ms (2.4%)

prune334.0ms (7.7%)

regimes1.3s (29.7%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample991.0ms (22.9%)

Profiling