Details

analyze594.0ms (14.4%)

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
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)

sample1.2s (29.3%)

Results

867.0ms	7582×	body	128	valid
97.0ms	254×	body	1024	valid
68.0ms	255×	body	512	valid
66.0ms	604×	body	128	invalid
30.0ms	165×	body	256	valid

Compiler

Compiled 50 to 38 computations (24% saved)

simplify220.0ms (5.3%)

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

prune4.0ms (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
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
▶	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

Compiler

Compiled 81 to 56 computations (30.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 z -6 4)
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)

series15.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

13.0ms	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
2.0ms	(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)

simplify80.0ms (1.9%)

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 (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	5	51

Error

0.0b

Counts

51 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	45.6b	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 z -6 4) (-.f64 y x) x) 3))

Compiler

Compiled 749 to 453 computations (39.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 z -6 4)
✓	0.0b	(fma.f64 6 z -3)
✓	0.1b	(*.f64 y (fma.f64 z -6 4))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))

series21.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

14.0ms	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
5.0ms	(*.f64 y (fma.f64 z -6 4))
1.0ms	(fma.f64 6 z -3)

rewrite7.0ms (0.2%)

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

simplify81.0ms (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 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1678
1	209	1387
2	553	1252
3	1824	1252
4	4279	1252
5	5516	1252

prune76.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	92	6	98

Error

0.0b

Counts

98 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	14.4b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 6 z -3) 3)) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	45.6b	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 z -6 4) (-.f64 y x) x) 3))

Compiler

Compiled 1612 to 1128 computations (30% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series31.0ms (0.8%)

Counts

4 → 18

Calls

4 calls:

13.0ms	(-.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))
7.0ms	(.f64 6 (.f64 z x))
4.0ms	(.f64 6 (.f64 y z))

rewrite28.0ms (0.7%)

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:

12.0ms	(-.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))
3.0ms	(.f64 6 (.f64 z x))

simplify93.0ms (2.3%)

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 → 148

Iterations

Useful iterations: 2 (0.0ms)

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

prune138.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
▶	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	14.4b	(fma.f64 x (cbrt.f64 (pow.f64 (fma.f64 6 z -3) 3)) (*.f64 y (fma.f64 z -6 4)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	45.6b	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 z -6 4) (-.f64 y x) x) 3))

Compiler

Compiled 4920 to 3015 computations (38.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 2 3) z)
✓	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))

series39.0ms (1%)

Counts

4 → 108

Calls

4 calls:

15.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
12.0ms	(*.f64 (-.f64 y x) 6)
11.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite72.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`add-sqr-sqrt_binary64`
196×	`*-un-lft-identity_binary64`
195×	`prod-diff_binary64`
190×	`add-cube-cbrt_binary64`
146×	`times-frac_binary64`

Counts

4 → 314

Calls

4 calls:

12.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
11.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
6.0ms	(-.f64 (/.f64 2 3) z)
4.0ms	(*.f64 (-.f64 y x) 6)

simplify227.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

422 → 428

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	427	9776
1	723	8689
2	2854	6627
3	4047	6546
4	4842	6546

prune343.0ms (8.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	426	2	428
Fresh	1	1	2
Picked	1	0	1
Done	0	3	3
Total	428	6	434

Error

0.0b

Counts

434 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
	0.6b	(+.f64 (fma.f64 (.f64 6 (-.f64 y x)) (-.f64 (/.f64 (/.f64 2 (sqrt.f64 3)) (sqrt.f64 3)) z) x) (.f64 (fma.f64 (neg.f64 z) 1 (.f64 z 1)) (.f64 (-.f64 y x) 6)))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	45.6b	(cbrt.f64 (pow.f64 (fma.f64 (fma.f64 z -6 4) (-.f64 y x) x) 3))
	28.6b	(+.f64 x (/.f64 (.f64 (-.f64 2/3 z) (.f64 6 (-.f64 (.f64 y y) (.f64 x x)))) (+.f64 y x)))

Compiler

Compiled 13203 to 6889 computations (47.8% saved)

regimes653.0ms (15.9%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

133 → 1

Compiler

Compiled 12445 to 9182 computations (26.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	20	18
2	28	18
3	32	18
4	35	18
5	36	18
6	35	18

end105.0ms (2.5%)

Compiler: Compiled 151 to 108 computations (28.5% saved)

Details

analyze594.0ms (14.4%)

sample1.2s (29.3%)

simplify220.0ms (5.3%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series15.0ms (0.4%)

rewrite1.0ms (0%)

simplify80.0ms (1.9%)

prune46.0ms (1.1%)

localize9.0ms (0.2%)

series21.0ms (0.5%)

rewrite7.0ms (0.2%)

simplify81.0ms (2%)

prune76.0ms (1.8%)

localize11.0ms (0.3%)

series31.0ms (0.8%)

rewrite28.0ms (0.7%)

simplify93.0ms (2.3%)

prune138.0ms (3.4%)

localize8.0ms (0.2%)

series39.0ms (1%)

rewrite72.0ms (1.8%)

simplify227.0ms (5.5%)

prune343.0ms (8.3%)

regimes653.0ms (15.9%)

simplify2.0ms (0.1%)

end105.0ms (2.5%)

Profiling