Details

analyze1.4s (23.9%)

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
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	97.5%	2.5%	10
0%	97.5%	2.5%	11
0.4%	97.1%	2.5%	12
0.6%	95.7%	3.8%	13
0.9%	95.3%	3.9%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample3.1s (54.8%)

Symmetry

(sort y z)

Results

2.0s	3541×	body	8192	exit
1.0s	8256×	body	128	valid
30.0ms	217×	body	128	invalid

Compiler

Compiled 25 to 17 computations (32% saved)

simplify20.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-def_binary64`
126×	`fma-neg_binary64`
60×	`cancel-sign-sub-inv_binary64`
40×	`distribute-rgt-neg-in_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 -4 (.f64 y z) (.f64 x x))

Compiler

Compiled 42 to 25 computations (40.5% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 -4 (.f64 y z) (.f64 x x))

series13.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(fma.f64 -4 (*.f64 y z) (*.f64 x 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 -4 (*.f64 y z) (*.f64 x x))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

490×	`*-commutative_binary64`
334×	`neg-sub0_binary64`
314×	`neg-mul-1_binary64`
290×	`times-frac_binary64`
288×	`associate-l_binary64`

Counts

46 → 24

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	565
1	40	488
2	87	488
3	294	488
4	1369	488
5	2959	488
6	4609	488
7	5240	488

prune16.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	22	2	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	2	25

Error

Counts

25 → 2

Alt Table

Status	Error	Program
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))))
▶	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))

Compiler

Compiled 374 to 171 computations (54.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
✓	0.0b	(.f64 (.f64 y z) -4)

series15.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

10.0ms	(fma.f64 x x (.f64 (.f64 y z) -4))
5.0ms	(.f64 (.f64 y z) -4)

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 (.f64 y z) -4)
0.0ms	(fma.f64 x x (.f64 (.f64 y z) -4))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

692×	`neg-mul-1_binary64`
552×	`associate-l_binary64`
501×	`distribute-rgt-neg-in_binary64`
483×	`neg-sub0_binary64`
388×	`associate-r_binary64`

Counts

90 → 49

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	888
1	124	829
2	407	829
3	1391	829
4	3156	829
5	4399	829
6	4915	829

prune24.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	49	2	51

Error

Counts

51 → 2

Alt Table

Status	Error	Program
▶	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))))
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))

Compiler

Compiled 698 to 344 computations (50.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 -4 (.f64 y z) (.f64 x x))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (*.f64 x x))))
✓	3.0b	(cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))

series154.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

72.0ms

(*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))))

66.0ms

(cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x)))

15.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x)))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

6.0ms

(*.f64 (*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x)))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))))

4.0ms

(*.f64 (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))) (cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x))))

1.0ms

(cbrt.f64 (fma.f64 -4 (*.f64 y z) (*.f64 x x)))

simplify173.0ms (3%)

Algorithm

1×	egg-herbie

Rules

338×	`fma-neg_binary64`
294×	`associate-r_binary64`
232×	`sub-neg_binary64`
227×	`associate-/r*_binary64`
222×	`associate-l_binary64`

Counts

201 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	6977
1	1109	6577
2	4158	6181
3	4923	6181
4	5050	6181

prune393.0ms (6.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	449	0	449
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	449	2	451

Error

Counts

451 → 2

Alt Table

Status	Error	Program
✓	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))) (cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x))))
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))

Compiler

Compiled 20425 to 11147 computations (45.4% saved)

regimes145.0ms (2.5%)

Accuracy

Total 0.0b remaining (12.3%)

Threshold costs 0.0b (12.3%)

Counts

16 → 1

Compiler

Compiled 2295 to 1476 computations (35.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end51.0ms (0.9%)

Remove: (sort y z)
Compiler: Compiled 87 to 51 computations (41.4% saved)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Details

analyze1.4s (23.9%)

sample3.1s (54.8%)

simplify20.0ms (0.3%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series13.0ms (0.2%)

rewrite1.0ms (0%)

simplify76.0ms (1.3%)

prune16.0ms (0.3%)

localize5.0ms (0.1%)

series15.0ms (0.3%)

rewrite6.0ms (0.1%)

simplify84.0ms (1.5%)

prune24.0ms (0.4%)

localize10.0ms (0.2%)

series154.0ms (2.7%)

rewrite20.0ms (0.3%)

simplify173.0ms (3%)

prune393.0ms (6.9%)

regimes145.0ms (2.5%)

simplify2.0ms (0%)

end51.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11