Details

analyze5.0ms (0.3%)

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)

sample1.0s (55%)

Results

926.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify61.0ms (3.3%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(.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)

series5.0ms (0.3%)

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)

simplify62.0ms (3.4%)

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

prune30.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	35	4	39

Error

0.0b

Counts

39 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
✓	0.1b	(fma.f64 x (fma.f64 x 9 -12) 3)
	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
	0.9b	(*.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 455 to 350 computations (23.1% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 9 (pow.f64 x 2))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 9 (pow.f64 x 2))

rewrite8.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

7.0ms

(*.f64 9 (pow.f64 x 2))

simplify75.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`unswap-sqr_binary64`
397×	`log-prod_binary64`
394×	`sqr-pow_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	303
1	98	231
2	198	221
3	636	215
4	1072	215
5	2844	215
6	3956	215
7	4840	215
8	4876	215

prune42.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	45	4	49

Error

Counts

49 → 4

Alt Table

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

Compiler

Compiled 837 to 663 computations (20.8% saved)

localize7.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (.f64 9 x) x)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (*.f64 9 x) x)

rewrite5.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
6×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`

Counts

1 → 20

Calls

1 calls:

4.0ms

(*.f64 (*.f64 9 x) x)

simplify54.0ms (3%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
343×	`associate-l_binary64`
269×	`associate-*r/_binary64`
230×	`associate-/l*_binary64`
222×	`associate-*l/_binary64`

Counts

32 → 29

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	41	296
1	94	260
2	302	251
3	576	249
4	815	249
5	1385	249
6	3511	249
7	4898	249

prune29.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	29	4	33

Error

Counts

33 → 4

Alt Table

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

Compiler

Compiled 549 to 399 computations (27.3% saved)

localize9.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(*.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)))

series23.0ms (1.2%)

Counts

2 → 12

Calls

2 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 9) (cbrt.f64 9)) (*.f64 (cbrt.f64 9) (pow.f64 x 2)))
5.0ms	(*.f64 (cbrt.f64 9) (pow.f64 x 2))

rewrite17.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64`
21×	`prod-exp_binary64`
18×	`add-sqr-sqrt_binary64`
9×	`associate-r_binary64`
9×	`cbrt-unprod_binary64`

Counts

2 → 62

Calls

2 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))

simplify97.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

515×	`times-frac_binary64`
386×	`unswap-sqr_binary64`
383×	`fma-def_binary64`
303×	`log-prod_binary64`
302×	`associate-+l+_binary64`

Counts

74 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	90	911
1	166	706
2	490	696
3	811	675
4	1371	675
5	3566	675
6	4297	675
7	4966	675
8	4913	675

prune100.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	89	4	93

Error

Counts

93 → 4

Alt Table

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

Compiler

Compiled 2120 to 1814 computations (14.4% saved)

regimes100.0ms (5.4%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

Counts

25 → 1

Compiler

Compiled 1292 to 1013 computations (21.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	7	9

end73.0ms (4%)

Compiler: Compiled 77 to 62 computations (19.5% saved)

Details

analyze5.0ms (0.3%)

sample1.0s (55%)

simplify61.0ms (3.3%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite1.0ms (0.1%)

simplify62.0ms (3.4%)

prune30.0ms (1.6%)

localize6.0ms (0.3%)

series3.0ms (0.1%)

rewrite8.0ms (0.5%)

simplify75.0ms (4.1%)

prune42.0ms (2.3%)

localize7.0ms (0.4%)

series3.0ms (0.2%)

rewrite5.0ms (0.3%)

simplify54.0ms (3%)

prune29.0ms (1.6%)

localize9.0ms (0.5%)

series23.0ms (1.2%)

rewrite17.0ms (0.9%)

simplify97.0ms (5.3%)

prune100.0ms (5.5%)

regimes100.0ms (5.4%)

simplify2.0ms (0.1%)

end73.0ms (4%)

Profiling