Details

analyze579.0ms (16.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
31.2%	68.6%	0.1%	9
35.9%	55.4%	8.7%	10
42.9%	47.6%	9.5%	11
51.5%	38.2%	10.3%	12
55%	30%	15%	13
59.5%	25.3%	15.3%	14

Compiler

Compiled 17 to 13 computations (23.5% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	238×	body	128	valid
2.0ms	12×	body	1024	valid
1.0ms	19×	body	128	invalid
0.0ms	3×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify227.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

5304×	`fma-neg_binary64`
679×	`unsub-neg_binary64`
400×	`sub-neg_binary64`
376×	`fma-def_binary64`
289×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	16
1	23	14
2	59	14
3	157	12
4	438	12
5	1253	12
6	2078	12
7	2563	12
8	2777	12
9	2907	12
10	2949	12
11	2964	12
12	2967	12
13	2967	12
14	2967	12
15	3141	12
16	3015	12
17	3015	12
18	8062	12

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series12.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
1.0ms	(fma.f64 z -6 4)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
0.0ms	(fma.f64 z -6 4)

simplify85.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-def_binary64`
445×	`associate-l_binary64`
416×	`exp-prod_binary64`
398×	`distribute-rgt-in_binary64`
387×	`associate-r_binary64`

Counts

68 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	1086
1	149	928
2	343	874
3	949	793
4	4177	793
5	4989	793
6	4976	793

prune46.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	30.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))

Compiler

Compiled 755 to 453 computations (40% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 6 z -3)
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(*.f64 y (fma.f64 z -6 4))

series20.0ms (0.6%)

Counts

3 → 72

Calls

3 calls:

12.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
6.0ms	(*.f64 y (fma.f64 z -6 4))
1.0ms	(fma.f64 6 z -3)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 42

Calls

3 calls:

3.0ms	(*.f64 y (fma.f64 z -6 4))
0.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
0.0ms	(fma.f64 6 z -3)

simplify75.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

798×	`neg-mul-1_binary64`
520×	`distribute-rgt-neg-out_binary64`
469×	`distribute-lft-neg-out_binary64`
296×	`fma-neg_binary64`
289×	`associate-l_binary64`

Counts

114 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1600
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune80.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Error

Counts

98 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	30.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	30.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (fma.f64 z -6 4))))

Compiler

Compiled 1643 to 1144 computations (30.4% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.0b	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
✓	0.2b	(.f64 6 (.f64 z x))
✓	0.3b	(.f64 6 (.f64 y z))

series31.0ms (0.9%)

Counts

4 → 18

Calls

4 calls:

15.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
7.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
5.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-log-exp_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
4.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
4.0ms	(.f64 6 (.f64 y z))
4.0ms	(.f64 6 (.f64 z x))

simplify97.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

443×	`times-frac_binary64`
372×	`cancel-sign-sub-inv_binary64`
279×	`associate-l_binary64`
278×	`distribute-rgt-neg-in_binary64`
271×	`associate-r_binary64`

Counts

111 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	2856
1	619	2159
2	2427	1906
3	4509	1906
4	5450	1906

prune127.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Error

Counts

151 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
▶	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	30.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	30.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (fma.f64 z -6 4))))

Compiler

Compiled 4900 to 2996 computations (38.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.0b	(*.f64 (-.f64 y x) 6)
✓	0.3b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series34.0ms (1%)

Counts

3 → 96

Calls

3 calls:

18.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
11.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
4.0ms	(*.f64 (-.f64 y x) 6)

rewrite61.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`prod-diff_binary64`
156×	`add-sqr-sqrt_binary64`
151×	`*-un-lft-identity_binary64`
147×	`add-cube-cbrt_binary64`
109×	`times-frac_binary64`

Counts

3 → 243

Calls

3 calls:

13.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
9.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
5.0ms	(*.f64 (-.f64 y x) 6)

simplify204.0ms (6%)

Algorithm

1×	egg-herbie

Rules

862×	`fma-neg_binary64`
372×	`associate-l_binary64`
344×	`associate-r_binary64`
266×	`*-commutative_binary64`
238×	`cancel-sign-sub-inv_binary64`

Counts

339 → 339

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	419	8699
1	713	7701
2	2829	6017
3	3995	5936
4	4850	5936

prune321.0ms (9.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	339	0	339
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	339	5	344

Error

Counts

344 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
✓	0.3b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	30.4b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	30.1b	(fma.f64 x (fma.f64 6 z -3) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (fma.f64 z -6 4))))

Compiler

Compiled 10796 to 5564 computations (48.5% saved)

regimes475.0ms (13.9%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Counts

102 → 1

Compiler

Compiled 7700 to 5579 computations (27.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	18	21
2	18	21

end1.0ms (0%)

Compiler: Compiled 18 to 13 computations (27.8% saved)

sample845.0ms (24.7%)

Algorithm

1×

intervals

Results

369.0ms	7337×	body	128	valid
42.0ms	236×	body	1024	valid
36.0ms	248×	body	512	valid
28.0ms	585×	body	128	invalid
15.0ms	179×	body	256	valid

Compiler

Compiled 134 to 96 computations (28.4% saved)

Details

analyze579.0ms (16.9%)

sample24.0ms (0.7%)

simplify227.0ms (6.6%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series12.0ms (0.4%)

rewrite1.0ms (0%)

simplify85.0ms (2.5%)

prune46.0ms (1.4%)

localize8.0ms (0.2%)

series20.0ms (0.6%)

rewrite5.0ms (0.1%)

simplify75.0ms (2.2%)

prune80.0ms (2.3%)

localize14.0ms (0.4%)

series31.0ms (0.9%)

rewrite28.0ms (0.8%)

simplify97.0ms (2.8%)

prune127.0ms (3.7%)

localize8.0ms (0.2%)

series34.0ms (1%)

rewrite61.0ms (1.8%)

simplify204.0ms (6%)

prune321.0ms (9.4%)

regimes475.0ms (13.9%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample845.0ms (24.7%)

Profiling