Details

analyze250.0ms (12.9%)

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
18.7%	81.1%	0.1%	7
21.8%	78%	0.1%	8
43.7%	56.2%	0.1%	9
54.6%	39.8%	5.6%	10
58.5%	35.5%	6%	11
67.3%	26.5%	6.2%	12
71.7%	19.1%	9.2%	13
74.1%	16.6%	9.4%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample47.0ms (2.4%)

Algorithm

1×

intervals

Symmetry

(sort y z)

Results

6.0ms	256×	body	128	valid
0.0ms	14×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify13.0ms (0.7%)

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

prune5.0ms (0.3%)

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 (0.2%)

Local error

Found 1 expressions with local error:

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

series5.0ms (0.3%)

Counts

1 → 9

Calls

1 calls:

5.0ms

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

rewrite3.0ms (0.2%)

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))

simplify85.0ms (4.4%)

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

prune11.0ms (0.5%)

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))
▶	33.6b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))

Compiler

Compiled 341 to 103 computations (69.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.0b	(sqrt.f64 (-.f64 x (*.f64 y z)))
✓	0.3b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))

series54.0ms (2.8%)

Counts

2 → 44

Calls

2 calls:

39.0ms	(sqrt.f64 (-.f64 x (*.f64 y z)))
15.0ms	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))

rewrite17.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
18×	`pow1_binary64`
14×	`sqrt-div_binary64`
11×	`*-un-lft-identity_binary64`

Counts

2 → 78

Calls

2 calls:

9.0ms	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))
2.0ms	(sqrt.f64 (-.f64 x (*.f64 y z)))

simplify65.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

525×	`times-frac_binary64`
446×	`unswap-sqr_binary64`
396×	`cancel-sign-sub-inv_binary64`
298×	`fma-neg_binary64`
252×	`*-commutative_binary64`

Counts

122 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	126	1860
1	283	1702
2	909	1656
3	2524	1631
4	4992	1631

prune64.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	196	3	199

Error

Counts

199 → 3

Alt Table

Status	Error	Program
▶	33.8b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (.f64 y z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	33.6b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))

Compiler

Compiled 4302 to 950 computations (77.9% saved)

localize7.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (-.f64 x (*.f64 y z)))
✓	0.1b	(sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z))))
✓	0.2b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (.f64 y z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3))
✓	0.3b	(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3)

series197.0ms (10.1%)

Counts

3 → 96

Calls

3 calls:

128.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3)

52.0ms

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

17.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3))

rewrite37.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`sqrt-prod_binary64`
69×	`add-sqr-sqrt_binary64`
32×	`sqrt-div_binary64`
27×	`cube-prod_binary64`
27×	`unpow-prod-down_binary64`

Counts

3 → 147

Calls

3 calls:

13.0ms

(*.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3))

4.0ms

(pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3)

3.0ms

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

simplify270.0ms (13.9%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
463×	`associate-l_binary64`
430×	`times-frac_binary64`
328×	`associate-/r*_binary64`
209×	`associate-/l*_binary64`

Counts

243 → 238

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	420	7617
1	1288	7078
2	4969	7078
3	5433	7078

prune227.0ms (11.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	377	0	377
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	377	3	380

Error

Counts

380 → 3

Alt Table

Status	Error	Program
✓	33.8b	(.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (.f64 y z)))) (pow.f64 (sqrt.f64 (sqrt.f64 (-.f64 x (*.f64 y z)))) 3))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	33.6b	(.f64 (sqrt.f64 (-.f64 x (.f64 y z))) (sqrt.f64 (-.f64 x (*.f64 y z))))

Compiler

Compiled 13966 to 5933 computations (57.5% saved)

regimes73.0ms (3.8%)

Accuracy

Total 0.0b remaining (20%)

Threshold costs 0.0b (20%)

Counts

13 → 1

Compiler

Compiled 867 to 606 computations (30.1% saved)

simplify2.0ms (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

end5.0ms (0.3%)

Remove: (sort y z)
Compiler: Compiled 24 to 15 computations (37.5% saved)

sample496.0ms (25.5%)

Algorithm

1×

intervals

Results

211.0ms	8000×	body	128	valid
6.0ms	266×	body	128	invalid

Compiler

Compiled 64 to 36 computations (43.8% 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

analyze250.0ms (12.9%)

sample47.0ms (2.4%)

simplify13.0ms (0.7%)

prune5.0ms (0.3%)

localize4.0ms (0.2%)

series5.0ms (0.3%)

rewrite3.0ms (0.2%)

simplify85.0ms (4.4%)

prune11.0ms (0.5%)

localize6.0ms (0.3%)

series54.0ms (2.8%)

rewrite17.0ms (0.9%)

simplify65.0ms (3.4%)

prune64.0ms (3.3%)

localize7.0ms (0.4%)

series197.0ms (10.1%)

rewrite37.0ms (1.9%)

simplify270.0ms (13.9%)

prune227.0ms (11.7%)

regimes73.0ms (3.8%)

simplify2.0ms (0.1%)

end5.0ms (0.3%)

sample496.0ms (25.5%)

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