Details

analyze178.0ms (4.5%)

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)

sample1.3s (33.9%)

Results

1.2s	8256×	body	128	valid
1.0ms	4×	body	128	invalid

Compiler

Compiled 95 to 59 computations (37.9% saved)

simplify66.0ms (1.7%)

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 (0.4%)

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)))
✓	0.7b	(.f64 (.f64 b b) (+.f64 a 3))

series89.0ms (2.3%)

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))
32.0ms	(pow.f64 (hypot.f64 a b) 4)
11.0ms	(fma.f64 (.f64 a a) (-.f64 1 a) (.f64 (*.f64 b b) (+.f64 a 3)))
10.0ms	(.f64 (.f64 b b) (+.f64 a 3))

rewrite17.0ms (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:

7.0ms	(+.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))
6.0ms	(.f64 (.f64 b b) (+.f64 a 3))
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)))

simplify80.0ms (2%)

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

prune181.0ms (4.6%)

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))
	13.8b	(/.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)))
	14.4b	(fma.f64 (.f64 a a) 4 (+.f64 (.f64 (pow.f64 a 3) (-.f64 a 4)) -1))

Compiler

Compiled 5023 to 2936 computations (41.5% saved)

localize16.0ms (0.4%)

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))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.7b	(.f64 (.f64 b b) (+.f64 3 a))

series53.0ms (1.4%)

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)))))
12.0ms	(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))

rewrite37.0ms (0.9%)

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:

8.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
8.0ms	(.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)))))
6.0ms	(.f64 (.f64 b b) (+.f64 3 a))

simplify92.0ms (2.3%)

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

prune279.0ms (7.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	208	1	209
Fresh	1	1	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 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (*.f64 (pow.f64 a 3) (+.f64 a -4)))) 1)
	13.8b	(/.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 (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 7869 to 4051 computations (48.5% 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	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 a -4))
✓	1.4b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series29.0ms (0.8%)

Counts

4 → 60

Calls

4 calls:

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

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-l_binary64`
16×	`add-exp-log_binary64`
14×	`associate-*r/_binary64`
13×	`*-un-lft-identity_binary64`

Counts

4 → 101

Calls

4 calls:

9.0ms	(*.f64 (pow.f64 a 3) (+.f64 a -4))
8.0ms	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))
4.0ms	(.f64 a (+.f64 4 (.f64 2 a)))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 (pow.f64 a 3) (+.f64 a -4)))

simplify108.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

494×	`exp-prod_binary64`
481×	`associate-l_binary64`
439×	`associate-r_binary64`
288×	`fma-neg_binary64`
268×	`unswap-sqr_binary64`

Counts

161 → 177

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3098
1	676	2444
2	3162	2442
3	4632	2412
4	5040	2412

prune243.0ms (6.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (.f64 a (.f64 (*.f64 a a) (+.f64 a -4))))) 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 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 7280 to 4543 computations (37.6% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 4 (.f64 a a) (.f64 a (.f64 (.f64 a a) (+.f64 a -4))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 a -4))
✓	0.1b	(.f64 a (.f64 (*.f64 a a) (+.f64 a -4)))
	1.4b	(.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (*.f64 2 a)))))

series13.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(fma.f64 4 (.f64 a a) (.f64 a (.f64 (.f64 a a) (+.f64 a -4))))
3.0ms	(.f64 a (.f64 (*.f64 a a) (+.f64 a -4)))
3.0ms	(.f64 (.f64 a a) (+.f64 a -4))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

7.0ms	(.f64 a (.f64 (*.f64 a a) (+.f64 a -4)))
6.0ms	(.f64 (.f64 a a) (+.f64 a -4))
0.0ms	(fma.f64 4 (.f64 a a) (.f64 a (.f64 (.f64 a a) (+.f64 a -4))))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

813×	`associate-+r+_binary64`
509×	`distribute-rgt-in_binary64`
506×	`distribute-lft-in_binary64`
434×	`fma-def_binary64`
362×	`unswap-sqr_binary64`

Counts

101 → 110

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1431
1	241	1204
2	886	1184
3	2901	1179
4	6025	1179

prune200.0ms (5.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	169	3	172

Error

Counts

172 → 3

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 (+.f64 (.f64 (.f64 b b) (+.f64 (+.f64 (.f64 b b) 12) (.f64 a (+.f64 4 (.f64 2 a))))) (fma.f64 4 (.f64 a a) (.f64 a (.f64 (*.f64 a a) (+.f64 a -4))))) 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 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 7233 to 4148 computations (42.7% saved)

regimes658.0ms (16.8%)

Accuracy

Total 0.0b remaining (69.5%)

Threshold costs 0.0b (69.5%)

Counts

123 → 1

Compiler

Compiled 18827 to 12805 computations (32% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-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	16	33
1	21	33
2	25	33
3	27	33
4	28	33
5	28	33

end86.0ms (2.2%)

Compiler: Compiled 142 to 92 computations (35.2% saved)

Details

analyze178.0ms (4.5%)

sample1.3s (33.9%)

simplify66.0ms (1.7%)

prune5.0ms (0.1%)

localize14.0ms (0.4%)

series89.0ms (2.3%)

rewrite17.0ms (0.4%)

simplify80.0ms (2%)

prune181.0ms (4.6%)

localize16.0ms (0.4%)

series53.0ms (1.4%)

rewrite37.0ms (0.9%)

simplify92.0ms (2.3%)

prune279.0ms (7.1%)

localize17.0ms (0.4%)

series29.0ms (0.8%)

rewrite26.0ms (0.7%)

simplify108.0ms (2.8%)

prune243.0ms (6.2%)

localize17.0ms (0.4%)

series13.0ms (0.3%)

rewrite16.0ms (0.4%)

simplify67.0ms (1.7%)

prune200.0ms (5.1%)

regimes658.0ms (16.8%)

simplify3.0ms (0.1%)

end86.0ms (2.2%)

Profiling