Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample887.0ms (38.8%)

Results

806.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify60.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

972×	`fma-def_binary64`
722×	`fma-neg_binary64`
154×	`cancel-sign-sub-inv_binary64`
107×	`distribute-rgt-in_binary64`
83×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	32	14
2	69	12
3	160	12
4	298	9
5	418	9
6	666	9
7	960	9
8	1262	9
9	1473	9
10	1531	9
11	1530	9
12	1536	9
13	1536	9
14	1401	9

prune3.0ms (0.2%)

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
▶	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

Compiler

Compiled 65 to 50 computations (23.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 9 -12)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)

series4.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(fma.f64 x (fma.f64 x 9 -12) 3)
2.0ms	(fma.f64 x 9 -12)

rewrite1.0ms (0.1%)

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 x (fma.f64 x 9 -12) 3)
0.0ms	(fma.f64 x 9 -12)

simplify63.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-+l+_binary64`
415×	`fma-neg_binary64`
321×	`distribute-lft-in_binary64`
321×	`distribute-rgt-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

44 → 37

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	431
1	63	344
2	120	342
3	378	342
4	1764	342
5	4979	342
6	5271	342

prune31.0ms (1.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Error

0.0b

Counts

39 → 6

Alt Table

Status	Error	Program
	0.2b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	52.8b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x 9 -12)) (sqrt.f64 (fma.f64 x 9 -12))) 3)
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.5b	(fma.f64 x (.f64 (.f64 (cbrt.f64 (fma.f64 x 9 -12)) (cbrt.f64 (fma.f64 x 9 -12))) (cbrt.f64 (fma.f64 x 9 -12))) 3)
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.8b	(*.f64 (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (sqrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))

Compiler

Compiled 527 to 408 computations (22.6% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (*.f64 9 (pow.f64 x 2)))
✓	0.0b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series9.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

4.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
2.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
10×	`add-log-exp_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`
8×	`associate-r_binary64`

Counts

3 → 67

Calls

3 calls:

4.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
4.0ms	(*.f64 9 (pow.f64 x 2))
3.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))

simplify97.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

623×	`fma-neg_binary64`
529×	`associate-l_binary64`
486×	`associate-r_binary64`
351×	`fma-def_binary64`
239×	`unswap-sqr_binary64`

Counts

76 → 113

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1070
1	266	827
2	737	754
3	3362	728
4	4410	728
5	4885	728
6	4829	728

prune100.0ms (4.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	3	1	4
Picked	0	1	1
Done	0	1	1
Total	113	6	119

Error

0.0b

Counts

119 → 6

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
▶	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
	15.1b	(/.f64 (fma.f64 -1728 (pow.f64 x 3) (pow.f64 (fma.f64 x (.f64 x 9) 3) 3)) (fma.f64 x (.f64 x 144) (.f64 (fma.f64 x (.f64 x 9) 3) (fma.f64 12 x (fma.f64 x (*.f64 x 9) 3)))))
	52.8b	(fma.f64 x (*.f64 (sqrt.f64 (fma.f64 x 9 -12)) (sqrt.f64 (fma.f64 x 9 -12))) 3)
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 2105 to 1688 computations (19.8% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2))))
✓	0.0b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
✓	0.1b	(*.f64 (cbrt.f64 9) (pow.f64 x 2))
✓	0.2b	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))

series53.0ms (2.3%)

Counts

4 → 36

Calls

4 calls:

30.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))
11.0ms	(+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2))))
7.0ms	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
5.0ms	(*.f64 (cbrt.f64 9) (pow.f64 x 2))

rewrite27.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`prod-exp_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

4 → 100

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))
6.0ms	(*.f64 (cbrt.f64 9) (pow.f64 x 2))
5.0ms	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (cbrt.f64 9) (pow.f64 x 2)))) (.f64 12 x))
3.0ms	(+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2))))

simplify99.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

516×	`fma-def_binary64`
482×	`fma-neg_binary64`
360×	`*-commutative_binary64`
344×	`cancel-sign-sub-inv_binary64`
303×	`distribute-rgt-neg-in_binary64`

Counts

136 → 159

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	152	1711
1	334	1461
2	1122	1360
3	3200	1328
4	4521	1328
5	5024	1328

prune177.0ms (7.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	160	5	165

Error

Counts

165 → 5

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	15.1b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (cbrt.f64 (.f64 9 (pow.f64 x 6))))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
▶	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))) (*.f64 12 x))

Compiler

Compiled 3907 to 3350 computations (14.3% saved)

localize11.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))) (*.f64 12 x))
✓	0.1b	(*.f64 (cbrt.f64 9) x)
✓	0.1b	(.f64 (.f64 (cbrt.f64 9) x) x)
✓	0.2b	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))

series31.0ms (1.3%)

Counts

4 → 36

Calls

4 calls:

12.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))
9.0ms	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))) (*.f64 12 x))
5.0ms	(.f64 (.f64 (cbrt.f64 9) x) x)
4.0ms	(*.f64 (cbrt.f64 9) x)

rewrite28.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64`
32×	`pow1_binary64`
22×	`add-cbrt-cube_binary64`
19×	`cbrt-unprod_binary64`
19×	`prod-exp_binary64`

Counts

4 → 96

Calls

4 calls:

8.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))
5.0ms	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))) (*.f64 12 x))
4.0ms	(.f64 (.f64 (cbrt.f64 9) x) x)
3.0ms	(*.f64 (cbrt.f64 9) x)

simplify73.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

907×	`distribute-rgt-in_binary64`
815×	`distribute-lft-in_binary64`
338×	`*-commutative_binary64`
330×	`fma-def_binary64`
222×	`associate-l_binary64`

Counts

132 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	2333
1	330	1354
2	1012	1197
3	2428	1195
4	5149	1195

prune153.0ms (6.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	150	5	155

Error

Counts

155 → 5

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 3 x) (.f64 3 x))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	15.1b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (cbrt.f64 (.f64 9 (pow.f64 x 6))))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.2b	(-.f64 (+.f64 3 (.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (.f64 (.f64 (cbrt.f64 9) x) x))) (*.f64 12 x))

Compiler

Compiled 3556 to 2885 computations (18.9% saved)

regimes224.0ms (9.8%)

Accuracy

Total 0.1b remaining (90.2%)

Threshold costs 0.1b (90.2%)

Counts

38 → 1

Compiler

Compiled 2372 to 1909 computations (19.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end114.0ms (5%)

Compiler: Compiled 88 to 72 computations (18.2% saved)

Details

analyze5.0ms (0.2%)

sample887.0ms (38.8%)

simplify60.0ms (2.6%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify63.0ms (2.8%)

prune31.0ms (1.4%)

localize6.0ms (0.3%)

series9.0ms (0.4%)

rewrite14.0ms (0.6%)

simplify97.0ms (4.2%)

prune100.0ms (4.4%)

localize10.0ms (0.4%)

series53.0ms (2.3%)

rewrite27.0ms (1.2%)

simplify99.0ms (4.3%)

prune177.0ms (7.8%)

localize11.0ms (0.5%)

series31.0ms (1.3%)

rewrite28.0ms (1.2%)

simplify73.0ms (3.2%)

prune153.0ms (6.7%)

regimes224.0ms (9.8%)

simplify2.0ms (0.1%)

end114.0ms (5%)

Profiling