Details

analyze4.0ms (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)

sample858.0ms (48.1%)

Results

773.0ms	8256×	body	128	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify60.0ms (3.4%)

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)

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

simplify67.0ms (3.7%)

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 (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	35	4	39

Error

0.0b

Counts

39 → 4

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 (-.f64 (*.f64 9 x) 12) 3)
	0.4b	(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))

Compiler

Compiled 471 to 364 computations (22.7% saved)

localize8.0ms (0.5%)

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

rewrite13.0ms (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 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))
4.0ms	(*.f64 9 (pow.f64 x 2))
2.0ms	(+.f64 3 (*.f64 9 (pow.f64 x 2)))

simplify94.0ms (5.3%)

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

prune127.0ms (7.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	113	4	117

Error

Counts

117 → 4

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 (-.f64 (*.f64 9 x) 12) 3)
	0.5b	(-.f64 (+.f64 3 (.f64 (.f64 9 (.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2)))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 2021 to 1624 computations (19.6% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

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

simplify36.0ms (2%)

Algorithm

1×	egg-herbie

Rules

724×	`associate-+r+_binary64`
699×	`associate-+l+_binary64`
269×	`distribute-lft-in_binary64`
269×	`distribute-rgt-in_binary64`
174×	`distribute-rgt-out_binary64`

Counts

22 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	26	289
1	52	213
2	92	211
3	298	211
4	1477	211
5	5477	211

prune26.0ms (1.5%)

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 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.1b	(fma.f64 x (-.f64 (*.f64 9 x) 12) 3)
	0.5b	(-.f64 (+.f64 3 (.f64 (.f64 9 (.f64 (cbrt.f64 (pow.f64 x 2)) (cbrt.f64 (pow.f64 x 2)))) (cbrt.f64 (pow.f64 x 2)))) (.f64 12 x))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 390 to 307 computations (21.3% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
✓	0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
✓	0.2b	(.f64 (.f64 x 3) x)

series8.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
2.0ms	(.f64 (.f64 x 3) x)
2.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

rewrite18.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

3 → 61

Calls

3 calls:

7.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
5.0ms	(.f64 (.f64 x 3) x)
4.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))

simplify72.0ms (4%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
363×	`fma-def_binary64`
281×	`+-commutative_binary64`
278×	`distribute-rgt-in_binary64`
273×	`distribute-lft-in_binary64`

Counts

97 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1328
1	302	1147
2	889	982
3	2422	980
4	4233	980
5	5064	980

prune91.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Error

Counts

116 → 4

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 (-.f64 (*.f64 9 x) 12) 3)
	0.2b	(.f64 (.f64 (cbrt.f64 3) (cbrt.f64 3)) (.f64 (cbrt.f64 3) (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1)))
✓	0.1b	(-.f64 (+.f64 3 (.f64 9 (pow.f64 x 2))) (.f64 12 x))

Compiler

Compiled 2108 to 1631 computations (22.6% saved)

regimes162.0ms (9.1%)

Accuracy

Total 0.1b remaining (87.8%)

Threshold costs 0.1b (87.8%)

Counts

46 → 1

Compiler

Compiled 2498 to 1987 computations (20.5% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-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	11	16
1	20	16
2	28	16
3	32	16
4	35	16
5	36	16
6	35	16

end70.0ms (3.9%)

Compiler: Compiled 80 to 66 computations (17.5% saved)

Details

analyze4.0ms (0.2%)

sample858.0ms (48.1%)

simplify60.0ms (3.4%)

prune3.0ms (0.2%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite1.0ms (0.1%)

simplify67.0ms (3.7%)

prune31.0ms (1.7%)

localize8.0ms (0.5%)

series8.0ms (0.4%)

rewrite13.0ms (0.7%)

simplify94.0ms (5.3%)

prune127.0ms (7.1%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite1.0ms (0%)

simplify36.0ms (2%)

prune26.0ms (1.5%)

localize8.0ms (0.4%)

series8.0ms (0.4%)

rewrite18.0ms (1%)

simplify72.0ms (4%)

prune91.0ms (5.1%)

regimes162.0ms (9.1%)

simplify3.0ms (0.2%)

end70.0ms (3.9%)

Profiling