Details

analyze391.0ms (10.2%)

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
12.5%	71.8%	15.7%	8
25%	56.2%	18.9%	9
31.2%	43.7%	25.1%	10
39%	34.7%	26.3%	11
44.9%	27.9%	27.3%	12
47.8%	22%	30.2%	13
52.6%	16.8%	30.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample983.0ms (25.8%)

Symmetry

(sort y z)

Results

865.0ms	8256×	body	128	valid
56.0ms	543×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (0.5%)

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

prune4.0ms (0.1%)

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))

series9.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

9.0ms

(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))

simplify77.0ms (2%)

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

prune18.0ms (0.5%)

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

0.0b

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 1 expressions with local error:

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

series10.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

10.0ms

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

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

simplify86.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

702×	`fma-neg_binary64`
491×	`*-commutative_binary64`
334×	`neg-sub0_binary64`
314×	`neg-mul-1_binary64`
287×	`associate-l_binary64`

Counts

46 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	508
1	41	485
2	86	485
3	301	485
4	1385	485
5	3037	485
6	4879	485
7	4982	485
8	4927	485

prune10.0ms (0.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

0.0b

Counts

24 → 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 349 to 162 computations (53.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 -4 (.f64 y z) (.f64 x x))
✓	0.4b	(.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))))
✓	2.5b	(cbrt.f64 (fma.f64 -4 (.f64 y z) (.f64 x x)))

series135.0ms (3.5%)

Counts

3 → 108

Calls

3 calls:

70.0ms

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

52.0ms

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

11.0ms

(*.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))))

rewrite18.0ms (0.5%)

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:

7.0ms

(*.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)))

simplify174.0ms (4.6%)

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

prune378.0ms (9.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	448	3	451

Error

Counts

451 → 3

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))
▶	19.5b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (*.f64 y z) -4)))) 3))

Compiler

Compiled 20481 to 11185 computations (45.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4))))
✓	0.1b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (*.f64 y z) -4)))) 3))
✓	0.5b	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3)
✓	2.5b	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))

series249.0ms (6.5%)

Counts

4 → 144

Calls

4 calls:

122.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3)
63.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))
53.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4))))
11.0ms	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (*.f64 y z) -4)))) 3))

rewrite62.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

184×	`add-sqr-sqrt_binary64`
162×	`sqrt-prod_binary64`
119×	`cube-prod_binary64`
119×	`unpow-prod-down_binary64`
81×	`cbrt-prod_binary64`

Counts

4 → 260

Calls

4 calls:

15.0ms	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (*.f64 y z) -4)))) 3))
2.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3)
1.0ms	(sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4))))
1.0ms	(cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))

simplify288.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

426×	`times-frac_binary64`
373×	`associate-/r*_binary64`
308×	`associate-/l*_binary64`
283×	`fma-def_binary64`
168×	`associate-*l/_binary64`

Counts

404 → 372

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	558	15040
1	1676	13154
2	4961	13154

prune624.0ms (16.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	628	0	628
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	628	3	631

Error

Counts

631 → 3

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))
✓	19.5b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (.f64 y z) -4)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 x x (.f64 (*.f64 y z) -4)))) 3))

Compiler

Compiled 28707 to 19306 computations (32.7% saved)

regimes178.0ms (4.7%)

Accuracy

Total 0.0b remaining (14.1%)

Threshold costs 0.0b (14.1%)

Counts

19 → 1

Compiler

Compiled 2732 to 1794 computations (34.3% 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

end70.0ms (1.8%)

Remove: (sort y z)
Compiler: Compiled 115 to 70 computations (39.1% 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

analyze391.0ms (10.2%)

sample983.0ms (25.8%)

simplify20.0ms (0.5%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify77.0ms (2%)

prune18.0ms (0.5%)

localize5.0ms (0.1%)

series10.0ms (0.3%)

rewrite1.0ms (0%)

simplify86.0ms (2.2%)

prune10.0ms (0.3%)

localize10.0ms (0.3%)

series135.0ms (3.5%)

rewrite18.0ms (0.5%)

simplify174.0ms (4.6%)

prune378.0ms (9.9%)

localize10.0ms (0.3%)

series249.0ms (6.5%)

rewrite62.0ms (1.6%)

simplify288.0ms (7.5%)

prune624.0ms (16.3%)

regimes178.0ms (4.7%)

simplify2.0ms (0%)

end70.0ms (1.8%)

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