Details

analyze335.0ms (11.8%)

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
37.4%	62.4%	0.1%	9
46.8%	47.6%	5.6%	10
54.6%	39.4%	6%	11
62.8%	31%	6.2%	12
66.9%	23.9%	9.2%	13
71.7%	19%	9.4%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample836.0ms (29.4%)

Symmetry

(sort y z)

Results

762.0ms	8256×	body	128	valid
27.0ms	307×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify13.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-def_binary64`
56×	`fma-neg_binary64`
28×	`cancel-sign-sub-inv_binary64`
18×	`sub-neg_binary64`
13×	`distribute-rgt-neg-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 24 to 15 computations (37.5% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.2%)

Counts

1 → 9

Calls

1 calls:

7.0ms

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

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-neg_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`prod-diff_binary64`

Counts

1 → 20

Calls

1 calls:

2.0ms

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

simplify88.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

520×	`fma-def_binary64`
468×	`unsub-neg_binary64`
418×	`sub-neg_binary64`
312×	`times-frac_binary64`
248×	`neg-mul-1_binary64`

Counts

29 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	321
1	106	255
2	271	237
3	937	237
4	2175	237
5	3396	237
6	4633	237
7	4756	237
8	4854	237

prune12.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Error

0.0b

Counts

28 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
▶	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))

Compiler

Compiled 369 to 119 computations (67.8% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.8b	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
✓	2.7b	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
✓	2.7b	(.f64 x (.f64 y z))
✓	38.3b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))

series135.0ms (4.8%)

Counts

4 → 144

Calls

4 calls:

70.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))
32.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
23.0ms	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
9.0ms	(.f64 x (.f64 y z))

rewrite78.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`add-sqr-sqrt_binary64`
96×	`prod-diff_binary64`
73×	`*-un-lft-identity_binary64`
63×	`add-cube-cbrt_binary64`
52×	`sqr-pow_binary64`

Counts

4 → 248

Calls

4 calls:

20.0ms	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))
9.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
5.0ms	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
3.0ms	(.f64 x (.f64 y z))

simplify236.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

634×	`fma-neg_binary64`
568×	`times-frac_binary64`
347×	`associate-l_binary64`
334×	`associate-r_binary64`
238×	`exp-prod_binary64`

Counts

392 → 280

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	9384
1	635	8417
2	3096	8201
3	4856	8201
4	4953	8201

prune305.0ms (10.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	279	1	280
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	279	3	282

Error

Counts

282 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))
▶	31.8b	(.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))))))

Compiler

Compiled 13019 to 4143 computations (68.2% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.8b	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
	2.7b	(.f64 x (.f64 y z))
✓	29.6b	(sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))))
✓	29.7b	(/.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))))

series41.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

21.0ms

(/.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z)))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z))))))

20.0ms

(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z)))))

rewrite50.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
15×	`sqrt-prod_binary64`

Counts

2 → 65

Calls

2 calls:

33.0ms

(/.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z)))) (sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z))))))

8.0ms

(sqrt.f64 (+.f64 (*.f64 x x) (+.f64 (*.f64 (*.f64 y z) (*.f64 y z)) (*.f64 x (*.f64 y z)))))

simplify118.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-neg_binary64`
538×	`fma-def_binary64`
533×	`times-frac_binary64`
367×	`distribute-rgt-in_binary64`
309×	`distribute-lft-in_binary64`

Counts

137 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	4746
1	366	3737
2	1373	3689
3	4579	3689
4	4972	3689

prune193.0ms (6.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	320	3	323

Error

Counts

323 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
✓	39.5b	(/.f64 (-.f64 (pow.f64 x 3) (pow.f64 (.f64 y z) 3)) (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))))
✓	31.8b	(.f64 (/.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))))) (/.f64 (-.f64 x (.f64 y z)) (sqrt.f64 (+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z)))))))

Compiler

Compiled 21975 to 1611 computations (92.7% saved)

regimes234.0ms (8.2%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

39 → 1

Compiler

Compiled 9787 to 3231 computations (67% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	28	7
4	32	7
5	33	7
6	33	7

end126.0ms (4.4%)

Remove: (sort y z)
Compiler: Compiled 134 to 54 computations (59.7% saved)

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7

Details

analyze335.0ms (11.8%)

sample836.0ms (29.4%)

simplify13.0ms (0.5%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series7.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify88.0ms (3.1%)

prune12.0ms (0.4%)

localize13.0ms (0.5%)

series135.0ms (4.8%)

rewrite78.0ms (2.8%)

simplify236.0ms (8.3%)

prune305.0ms (10.7%)

localize13.0ms (0.5%)

series41.0ms (1.4%)

rewrite50.0ms (1.7%)

simplify118.0ms (4.1%)

prune193.0ms (6.8%)

regimes234.0ms (8.2%)

simplify3.0ms (0.1%)

end126.0ms (4.4%)

Profiling

Iter	Nodes	Cost
0	6	7
1	12	7
2	22	7
3	39	7
4	53	7
5	83	7
6	115	7
7	142	7
8	178	7
9	186	7
10	206	7
11	212	7
12	189	7