Details

analyze450.0ms (14.3%)

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
34.3%	63.2%	2.5%	9
40.6%	52.7%	6.8%	10
48.4%	42.1%	9.5%	11
56.2%	32.5%	11.4%	12
59.1%	26.9%	14%	13
63.9%	21%	15.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample886.0ms (28.1%)

Results

792.0ms	8256×	body	128	valid
59.0ms	602×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify9.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

66×	`fma-def_binary64`
8×	`associate-r_binary64`
8×	`associate-l_binary64`
7×	`+-commutative_binary64`
6×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	8
2	26	8
3	39	8
4	48	8
5	55	8
6	53	8
7	71	8
8	75	8
9	88	8
10	94	8
11	99	8
12	100	8
13	98	8

prune3.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(+.f64 x (*.f64 y (+.f64 z x)))
▶	0.0b	(fma.f64 y (+.f64 x z) x)

Compiler

Compiled 54 to 30 computations (44.4% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 y (+.f64 x z) x)

series6.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

6.0ms

(fma.f64 y (+.f64 x z) x)

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 y (+.f64 x z) x)

simplify87.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

760×	`unswap-sqr_binary64`
540×	`distribute-rgt-in_binary64`
536×	`distribute-lft-in_binary64`
456×	`*-commutative_binary64`
361×	`distribute-rgt-out_binary64`

Counts

46 → 20

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	385
1	42	368
2	96	368
3	326	368
4	1685	368
5	1904	368
6	2179	368
7	2746	368
8	4060	368
9	4552	368
10	5198	368

prune13.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	20	2	22

Error

0.0b

Counts

22 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
✓	0.0b	(fma.f64 y (+.f64 x z) x)

Compiler

Compiled 202 to 60 computations (70.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
✓	0.0b	(+.f64 (*.f64 y z) x)

series13.0ms (0.4%)

Counts

2 → 18

Calls

2 calls:

8.0ms	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
5.0ms	(+.f64 (*.f64 y z) x)

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`sum-log_binary64`
2×	`+-commutative_binary64`
2×	`flip-+_binary64`
2×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

5.0ms	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
3.0ms	(+.f64 (*.f64 y z) x)

simplify86.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

390×	`sub-neg_binary64`
356×	`fma-def_binary64`
325×	`distribute-rgt-out_binary64`
293×	`*-commutative_binary64`
229×	`fma-neg_binary64`

Counts

48 → 56

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	439
1	197	405
2	597	401
3	2006	401
4	3290	401
5	4728	401
6	4988	401
7	4970	401

prune23.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	55	3	58

Error

Counts

58 → 3

Alt Table

Status	Error	Program
▶	42.9b	(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (*.f64 y z) x)))))
✓	0.0b	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
✓	0.0b	(fma.f64 y (+.f64 x z) x)

Compiler

Compiled 907 to 230 computations (74.6% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(.f64 (.f64 y x) (+.f64 (*.f64 y z) x))
✓	3.6b	(+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3))
✓	4.3b	(-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (.f64 y z) x)))
✓	41.8b	(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (*.f64 y z) x)))))

series635.0ms (20.1%)

Counts

4 → 144

Calls

4 calls:

546.0ms	(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (*.f64 y z) x)))))
37.0ms	(+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3))
34.0ms	(-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (.f64 y z) x)))
17.0ms	(.f64 (.f64 y x) (+.f64 (*.f64 y z) x))

rewrite62.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`associate-*r/_binary64`
28×	`flip-+_binary64`
28×	`flip3-+_binary64`
26×	`*-un-lft-identity_binary64`
16×	`frac-sub_binary64`

Counts

4 → 129

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (*.f64 y z) x)))))
11.0ms	(-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (.f64 y z) x)))
8.0ms	(+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3))
5.0ms	(.f64 (.f64 y x) (+.f64 (*.f64 y z) x))

simplify246.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

354×	`distribute-rgt-in_binary64`
278×	`+-commutative_binary64`
235×	`*-commutative_binary64`
228×	`associate-+r+_binary64`
214×	`cancel-sign-sub-inv_binary64`

Counts

273 → 299

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	876	18664
1	3109	17282
2	5026	17282

prune354.0ms (11.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	299	0	299
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	299	3	302

Error

Counts

302 → 3

Alt Table

Status	Error	Program
✓	42.9b	(/.f64 (+.f64 (pow.f64 (.f64 y x) 3) (pow.f64 (+.f64 (.f64 y z) x) 3)) (+.f64 (.f64 (.f64 y x) (.f64 y x)) (-.f64 (.f64 (+.f64 (.f64 y z) x) (+.f64 (.f64 y z) x)) (.f64 (.f64 y x) (+.f64 (*.f64 y z) x)))))
✓	0.0b	(+.f64 (.f64 y x) (+.f64 (.f64 y z) x))
✓	0.0b	(fma.f64 y (+.f64 x z) x)

Compiler

Compiled 28099 to 10544 computations (62.5% saved)

regimes193.0ms (6.1%)

Accuracy

Total 0.0b remaining (53.7%)

Threshold costs 0.0b (53.7%)

Counts

38 → 1

Compiler

Compiled 4236 to 2002 computations (52.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	6	9

end50.0ms (1.6%)

Compiler: Compiled 87 to 39 computations (55.2% saved)

Iter	Nodes	Cost
0	7	10
1	16	8
2	26	8
3	39	8
4	48	8
5	55	8
6	53	8
7	71	8
8	75	8
9	88	8
10	94	8
11	99	8
12	100	8
13	98	8

Iter	Nodes	Cost
0	7	10
1	16	8
2	26	8
3	39	8
4	48	8
5	55	8
6	53	8
7	71	8
8	75	8
9	88	8
10	94	8
11	99	8
12	100	8
13	98	8

Details

analyze450.0ms (14.3%)

sample886.0ms (28.1%)

simplify9.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify87.0ms (2.8%)

prune13.0ms (0.4%)

localize5.0ms (0.2%)

series13.0ms (0.4%)

rewrite8.0ms (0.3%)

simplify86.0ms (2.7%)

prune23.0ms (0.7%)

localize15.0ms (0.5%)

series635.0ms (20.1%)

rewrite62.0ms (2%)

simplify246.0ms (7.8%)

prune354.0ms (11.2%)

regimes193.0ms (6.1%)

simplify2.0ms (0.1%)

end50.0ms (1.6%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	8
2	26	8
3	39	8
4	48	8
5	55	8
6	53	8
7	71	8
8	75	8
9	88	8
10	94	8
11	99	8
12	100	8
13	98	8