Details

analyze553.0ms (12.9%)

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)

sample90.0ms (2.1%)

Algorithm

1×

intervals

Results

11.0ms	233×	body	128	valid
1.0ms	7×	body	1024	valid
1.0ms	10×	body	256	valid
1.0ms	6×	body	512	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 36 to 28 computations (22.2% saved)

simplify225.0ms (5.2%)

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)

series13.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(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)

simplify82.0ms (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

prune45.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x))) (cbrt.f64 (fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)))
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	12.2b	(fma.f64 (-.f64 y x) (cbrt.f64 (.f64 (.f64 (fma.f64 z -6 4) (fma.f64 z -6 4)) (fma.f64 z -6 4))) x)
▶	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)))

Compiler

Compiled 835 to 507 computations (39.3% saved)

localize8.0ms (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)))
6.0ms	(*.f64 y (fma.f64 z -6 4))
2.0ms	(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)

simplify88.0ms (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

prune95.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Error

0.0b

Counts

99 → 7

Alt Table

Status	Error	Program
	12.4b	(fma.f64 x (cbrt.f64 (.f64 (.f64 (fma.f64 6 z -3) (fma.f64 6 z -3)) (fma.f64 6 z -3))) (*.f64 y (fma.f64 z -6 4)))
	12.2b	(fma.f64 (-.f64 y x) (cbrt.f64 (.f64 (.f64 (fma.f64 z -6 4) (fma.f64 z -6 4)) (fma.f64 z -6 4))) x)
	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	32.8b	(fma.f64 x (fma.f64 6 z -3) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (fma.f64 z -6 4))))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
✓	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)))

Compiler

Compiled 1682 to 1178 computations (30% saved)

localize16.0ms (0.4%)

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 y z))
✓	0.3b	(.f64 6 (.f64 z x))

series36.0ms (0.8%)

Counts

4 → 18

Calls

4 calls:

19.0ms	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))
8.0ms	(+.f64 (.f64 6 (.f64 y z)) (*.f64 3 x))
5.0ms	(.f64 6 (.f64 z x))
5.0ms	(.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 z x))
4.0ms	(.f64 6 (.f64 y z))

simplify98.0ms (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

prune158.0ms (3.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	147	8	155

Error

Counts

155 → 8

Alt Table

Status	Error	Program
	0.7b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (.f64 (.f64 (cbrt.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))) (cbrt.f64 (fma.f64 6 (.f64 z y) (.f64 x 3)))) (cbrt.f64 (fma.f64 6 (.f64 z y) (*.f64 x 3)))))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
▶	0.4b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
	46.5b	(/.f64 (.f64 (fma.f64 y 4 (.f64 z (.f64 x -6))) (-.f64 (.f64 (fma.f64 36 (.f64 (.f64 z y) (.f64 z y)) (.f64 x (fma.f64 x 9 (.f64 (.f64 z y) -18)))) (fma.f64 6 (.f64 z x) (.f64 y 4))) (fma.f64 216 (pow.f64 (.f64 z y) 3) (pow.f64 (.f64 x 3) 3)))) (.f64 (fma.f64 36 (.f64 (.f64 z y) (.f64 z y)) (.f64 x (fma.f64 x 9 (.f64 (.f64 z y) -18)))) (fma.f64 y 4 (.f64 z (*.f64 x -6)))))
	12.2b	(fma.f64 (-.f64 y x) (cbrt.f64 (.f64 (.f64 (fma.f64 z -6 4) (fma.f64 z -6 4)) (fma.f64 z -6 4))) x)
	32.8b	(fma.f64 x (fma.f64 6 z -3) (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (fma.f64 z -6 4))))
✓	0.1b	(fma.f64 (-.f64 y x) (fma.f64 z -6 4) x)
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 5186 to 3175 computations (38.8% 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 (-.f64 y x) 6)
✓	0.0b	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
✓	0.3b	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))

series33.0ms (0.8%)

Counts

4 → 108

Calls

4 calls:

14.0ms	(+.f64 x (.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z)))
13.0ms	(.f64 (.f64 (-.f64 y x) 6) (-.f64 (/.f64 2 3) z))
4.0ms	(*.f64 (-.f64 y x) 6)
1.0ms	(-.f64 (/.f64 2 3) z)

rewrite79.0ms (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:

16.0ms	(.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)))
6.0ms	(-.f64 (/.f64 2 3) z)
5.0ms	(*.f64 (-.f64 y x) 6)

simplify236.0ms (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

prune380.0ms (8.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	426	2	428
Fresh	2	2	4
Picked	1	0	1
Done	1	2	3
Total	430	6	436

Error

Counts

436 → 6

Alt Table

Status	Error	Program
	0.7b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (.f64 (.f64 (cbrt.f64 (fma.f64 6 (.f64 z y) (.f64 x 3))) (cbrt.f64 (fma.f64 6 (.f64 z y) (.f64 x 3)))) (cbrt.f64 (fma.f64 6 (.f64 z y) (*.f64 x 3)))))
	32.0b	(+.f64 (fma.f64 4 (-.f64 y x) x) (.f64 (.f64 (neg.f64 (sqrt.f64 z)) (sqrt.f64 z)) (*.f64 (-.f64 y x) 6)))
✓	0.1b	(fma.f64 x (fma.f64 6 z -3) (*.f64 y (fma.f64 z -6 4)))
	0.7b	(+.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)))
	12.2b	(fma.f64 (-.f64 y x) (cbrt.f64 (.f64 (.f64 (fma.f64 z -6 4) (fma.f64 z -6 4)) (fma.f64 z -6 4))) x)
✓	0.2b	(-.f64 (+.f64 (.f64 4 y) (.f64 6 (.f64 z x))) (+.f64 (.f64 6 (.f64 y z)) (.f64 3 x)))

Compiler

Compiled 13241 to 6914 computations (47.8% saved)

regimes1.0s (24.3%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

182 → 1

Compiler

Compiled 21237 to 15280 computations (28.1% 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)

sample940.0ms (21.9%)

Algorithm

1×

intervals

Results

417.0ms	7338×	body	128	valid
47.0ms	220×	body	1024	valid
35.0ms	257×	body	512	valid
30.0ms	600×	body	128	invalid
17.0ms	185×	body	256	valid

Compiler

Compiled 195 to 138 computations (29.2% saved)

Details

analyze553.0ms (12.9%)

sample90.0ms (2.1%)

simplify225.0ms (5.2%)

prune4.0ms (0.1%)

localize6.0ms (0.1%)

series13.0ms (0.3%)

rewrite1.0ms (0%)

simplify82.0ms (1.9%)

prune45.0ms (1%)

localize8.0ms (0.2%)

series21.0ms (0.5%)

rewrite5.0ms (0.1%)

simplify88.0ms (2%)

prune95.0ms (2.2%)

localize16.0ms (0.4%)

series36.0ms (0.8%)

rewrite28.0ms (0.7%)

simplify98.0ms (2.3%)

prune158.0ms (3.7%)

localize8.0ms (0.2%)

series33.0ms (0.8%)

rewrite79.0ms (1.8%)

simplify236.0ms (5.5%)

prune380.0ms (8.9%)

regimes1.0s (24.3%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample940.0ms (21.9%)

Profiling