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)

sample961.0ms (48.2%)

Results

850.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify63.0ms (3.2%)

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

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

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

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)
1.0ms	(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)

simplify60.0ms (3%)

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

prune32.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	36	3	39

Error

0.0b

Counts

39 → 3

Alt Table

Status	Error	Program
	0.1b	(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
	0.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3))) (cbrt.f64 (fma.f64 x (fma.f64 x 9 -12) 3)))

Compiler

Compiled 455 to 350 computations (23.1% saved)

localize7.0ms (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))

series8.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

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

rewrite14.0ms (0.7%)

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:

5.0ms	(*.f64 9 (pow.f64 x 2))
4.0ms	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
2.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))

simplify96.0ms (4.8%)

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

prune138.0ms (6.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	112	4	116

Error

Counts

116 → 4

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12))) (fma.f64 (neg.f64 x) 12 (*.f64 x 12)))
	0.4b	(-.f64 (+.f64 3 (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))) (.f64 12 x))
	0.1b	(-.f64 (+.f64 3 (.f64 (sqrt.f64 9) (.f64 3 (.f64 x x)))) (.f64 12 x))
	0.1b	(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)

Compiler

Compiled 2045 to 1640 computations (19.8% saved)

localize13.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 3 (*.f64 9 (pow.f64 x 2)))
✓	0.0b	(fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12)))
	0.2b	(*.f64 9 (pow.f64 x 2))
✓	36.8b	(fma.f64 (neg.f64 x) 12 (*.f64 x 12))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12)))
3.0ms	(fma.f64 (neg.f64 x) 12 (*.f64 x 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 (neg.f64 x) 12 (*.f64 x 12))
0.0ms	(fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12)))

simplify63.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

672×	`distribute-rgt-in_binary64`
647×	`distribute-lft-in_binary64`
440×	`associate-l_binary64`
381×	`unsub-neg_binary64`
365×	`associate-r_binary64`

Counts

44 → 46

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	457
1	75	372
2	164	307
3	594	255
4	3141	255
5	4739	255
6	4838	255

prune125.0ms (6.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Error

Counts

119 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12))) (fma.f64 (neg.f64 x) 12 (*.f64 x 12)))
	0.4b	(-.f64 (+.f64 3 (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))) (.f64 12 x))
	0.1b	(-.f64 (+.f64 3 (.f64 (sqrt.f64 9) (.f64 3 (.f64 x x)))) (.f64 12 x))
▶	0.1b	(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)

Compiler

Compiled 2968 to 2267 computations (23.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)

simplify37.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-+r+_binary64`
700×	`associate-+l+_binary64`
271×	`distribute-lft-in_binary64`
271×	`distribute-rgt-in_binary64`
174×	`distribute-rgt-out_binary64`

Counts

22 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	289
1	57	213
2	91	211
3	299	211
4	1476	211
5	5477	211

prune23.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	27	4	31

Error

Counts

31 → 4

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (fma.f64 1 (+.f64 3 (.f64 9 (pow.f64 x 2))) (neg.f64 (.f64 x 12))) (fma.f64 (neg.f64 x) 12 (*.f64 x 12)))
	0.4b	(-.f64 (+.f64 3 (.f64 (.f64 9 (.f64 x (cbrt.f64 x))) (pow.f64 (cbrt.f64 x) 2))) (.f64 12 x))
	0.1b	(-.f64 (+.f64 3 (.f64 (sqrt.f64 9) (.f64 3 (.f64 x x)))) (.f64 12 x))
✓	0.1b	(fma.f64 x (+.f64 (*.f64 x 9) -12) 3)

Compiler

Compiled 359 to 280 computations (22% saved)

regimes239.0ms (12%)

Accuracy

Total 0.1b remaining (81%)

Threshold costs 0.1b (81%)

Counts

66 → 1

Compiler

Compiled 3856 to 3133 computations (18.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`
2×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	27	26
2	33	26
3	35	26
4	34	26

end81.0ms (4%)

Compiler: Compiled 102 to 78 computations (23.5% saved)

Details

analyze5.0ms (0.2%)

sample961.0ms (48.2%)

simplify63.0ms (3.2%)

prune4.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify60.0ms (3%)

prune32.0ms (1.6%)

localize7.0ms (0.3%)

series8.0ms (0.4%)

rewrite14.0ms (0.7%)

simplify96.0ms (4.8%)

prune138.0ms (6.9%)

localize13.0ms (0.7%)

series7.0ms (0.3%)

rewrite1.0ms (0.1%)

simplify63.0ms (3.2%)

prune125.0ms (6.3%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite1.0ms (0%)

simplify37.0ms (1.8%)

prune23.0ms (1.2%)

regimes239.0ms (12%)

simplify3.0ms (0.1%)

end81.0ms (4%)

Profiling