Details

analyze168.0ms (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%	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)

sample1.2s (29.6%)

Results

1.2s	8256×	body	128	valid
1.0ms	8×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify59.0ms (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)

localize14.0ms (0.3%)

Local error

Found 4 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 4 (fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3))) -1))
✓	0.1b	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
✓	0.4b	(.f64 (.f64 b b) (+.f64 a 3))

series95.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

40.0ms	(+.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)
10.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
8.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite16.0ms (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))
1.0ms	(pow.f64 (hypot.f64 a b) 4)
0.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))

simplify79.0ms (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

prune197.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	4	164

Error

Counts

164 → 4

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))
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.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)))
	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 5059 to 2958 computations (41.5% saved)

localize14.0ms (0.3%)

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 3 a)))))
✓	0.1b	(.f64 (.f64 a a) (-.f64 1 a))
✓	0.4b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.4b	(.f64 (.f64 b b) (+.f64 3 a))

series54.0ms (1.3%)

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 3 a)))))
14.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.f64 (.f64 b b) (+.f64 3 a))
3.0ms	(.f64 (.f64 a a) (-.f64 1 a))

rewrite33.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
15×	`distribute-lft-in_binary64`

Counts

4 → 121

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (+.f64 3 a))
7.0ms	(.f64 (.f64 a a) (-.f64 1 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 3 a)))))
3.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify92.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-+l+_binary64`
383×	`associate-l_binary64`
299×	`associate-r_binary64`
268×	`cancel-sign-sub-inv_binary64`
211×	`unswap-sqr_binary64`

Counts

205 → 209

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	3743
1	600	3419
2	2388	3054
3	4882	3054

prune288.0ms (6.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	209	4	213

Error

Counts

213 → 4

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))
	10.4b	(/.f64 (-.f64 (pow.f64 (hypot.f64 a b) 8) (.f64 (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1) (fma.f64 (-.f64 (fma.f64 a a (.f64 (+.f64 3 a) (.f64 b b))) (pow.f64 a 3)) 4 -1))) (-.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)))
▶	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 7869 to 4051 computations (48.5% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
✓	0.0b	(.f64 a (+.f64 4 (.f64 2 a)))
✓	0.1b	(*.f64 (pow.f64 a 3) (-.f64 a 4))
✓	1.2b	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))

series29.0ms (0.7%)

Counts

4 → 60

Calls

4 calls:

20.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))
3.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
3.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))
2.0ms	(.f64 a (+.f64 4 (.f64 2 a)))

rewrite31.0ms (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 → 126

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))
7.0ms	(*.f64 (pow.f64 a 3) (-.f64 a 4))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
0.0ms	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

simplify111.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

483×	`associate-l_binary64`
452×	`fma-neg_binary64`
443×	`associate-r_binary64`
240×	`cancel-sign-sub-inv_binary64`
217×	`unswap-sqr_binary64`

Counts

186 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	3659
1	703	2717
2	3163	2701
3	4741	2695
4	4886	2695

prune318.0ms (7.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	219	3	222

Error

Counts

222 → 3

Alt Table

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

Compiler

Compiled 9184 to 5824 computations (36.6% 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)))
✓	0.1b	(.f64 (.f64 a a) (-.f64 a 4))
✓	0.2b	(.f64 a (.f64 (*.f64 a a) (-.f64 a 4)))
	1.2b	(.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (*.f64 2 a)))))

series6.0ms (0.1%)

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))

rewrite30.0ms (0.7%)

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:

9.0ms	(.f64 (.f64 a a) (-.f64 a 4))
9.0ms	(.f64 a (.f64 (*.f64 a a) (-.f64 a 4)))

simplify100.0ms (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

prune320.0ms (7.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	268	3	271

Error

Counts

271 → 3

Alt Table

Status	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))
✓	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (.f64 a (.f64 (*.f64 a a) (-.f64 a 4))) -1)))
✓	0.2b	(+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 12 (.f64 b b)) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 (.f64 a a) 4 (+.f64 (*.f64 (pow.f64 a 3) (-.f64 a 4)) -1)))

Compiler

Compiled 12412 to 7217 computations (41.9% saved)

regimes784.0ms (18.6%)

Accuracy

Total 0.0b remaining (58.9%)

Threshold costs 0.0b (58.9%)

Counts

142 → 1

Compiler

Compiled 21485 to 14626 computations (31.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	37
1	33	37
2	37	37
3	39	37
4	40	37
5	38	37

end83.0ms (2%)

Compiler: Compiled 149 to 100 computations (32.9% saved)

Details

analyze168.0ms (4%)

sample1.2s (29.6%)

simplify59.0ms (1.4%)

prune5.0ms (0.1%)

localize14.0ms (0.3%)

series95.0ms (2.3%)

rewrite16.0ms (0.4%)

simplify79.0ms (1.9%)

prune197.0ms (4.7%)

localize14.0ms (0.3%)

series54.0ms (1.3%)

rewrite33.0ms (0.8%)

simplify92.0ms (2.2%)

prune288.0ms (6.9%)

localize16.0ms (0.4%)

series29.0ms (0.7%)

rewrite31.0ms (0.7%)

simplify111.0ms (2.6%)

prune318.0ms (7.6%)

localize17.0ms (0.4%)

series6.0ms (0.1%)

rewrite30.0ms (0.7%)

simplify100.0ms (2.4%)

prune320.0ms (7.6%)

regimes784.0ms (18.6%)

simplify3.0ms (0.1%)

end83.0ms (2%)

Profiling