Details

analyze342.0ms (7.3%)

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
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)

sample46.0ms (1%)

Algorithm

1×

intervals

Symmetry

(sort y z)

Results

6.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify14.0ms (0.3%)

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

prune1.0ms (0%)

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))

series5.0ms (0.1%)

Counts

1 → 9

Calls

1 calls:

5.0ms

(-.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))

simplify90.0ms (1.9%)

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

prune13.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Error

0.0b

Counts

28 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (*.f64 y z))
	39.4b	(/.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)))))
▶	39.2b	(cbrt.f64 (.f64 (.f64 (-.f64 x (.f64 y z)) (-.f64 x (.f64 y z))) (-.f64 x (*.f64 y z))))

Compiler

Compiled 411 to 135 computations (67.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.1b	(.f64 (.f64 (-.f64 x (.f64 y z)) (-.f64 x (.f64 y z))) (-.f64 x (*.f64 y z)))
✓	0.1b	(.f64 (-.f64 x (.f64 y z)) (-.f64 x (*.f64 y z)))
✓	37.3b	(cbrt.f64 (.f64 (.f64 (-.f64 x (.f64 y z)) (-.f64 x (.f64 y z))) (-.f64 x (*.f64 y z))))

series47.0ms (1%)

Counts

3 → 108

Calls

3 calls:

23.0ms

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

13.0ms

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

11.0ms

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

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip--_binary64`
60×	`frac-times_binary64`
60×	`flip3--_binary64`
30×	`associate-*l/_binary64`
29×	`pow1_binary64`

Counts

3 → 150

Calls

3 calls:

15.0ms

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

8.0ms

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

6.0ms

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

simplify198.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-def_binary64`
657×	`fma-neg_binary64`
347×	`cancel-sign-sub-inv_binary64`
273×	`associate-l_binary64`
244×	`associate-r_binary64`

Counts

258 → 230

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	234	8072
1	484	6489
2	1806	5840
3	4182	5805
4	4995	5805
5	4947	5805

prune131.0ms (2.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	311	3	314

Error

0.0b

Counts

314 → 3

Alt Table

Status	Error	Program
▶	39.2b	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))
✓	0.0b	(-.f64 x (*.f64 y z))
	39.4b	(/.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 9467 to 1904 computations (79.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z)))
✓	0.3b	(fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x))))
✓	3.4b	(.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))
✓	37.3b	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))

series2.0s (42.5%)

Counts

4 → 144

Calls

4 calls:

1.9s	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))
27.0ms	(.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z)))
22.0ms	(fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x))))
22.0ms	(.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))

rewrite20.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`*-un-lft-identity_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))
4.0ms	(.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z)))
3.0ms	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))
0.0ms	(fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x))))

simplify143.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
469×	`cancel-sign-sub-inv_binary64`
294×	`associate-l_binary64`
282×	`fma-neg_binary64`
257×	`times-frac_binary64`

Counts

227 → 180

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	238	5941
1	586	5116
2	2131	4987
3	4615	4945
4	4914	4945

prune93.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	180	3	183

Error

0.0b

Counts

183 → 3

Alt Table

Status	Error	Program
✓	39.2b	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))
✓	0.0b	(-.f64 x (*.f64 y z))
▶	39.4b	(/.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 5260 to 2180 computations (58.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.2b	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))
✓	1.6b	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
✓	3.3b	(.f64 x (.f64 y z))
✓	38.2b	(/.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)))))

series132.0ms (2.8%)

Counts

4 → 144

Calls

4 calls:

79.0ms	(/.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)))))
23.0ms	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
21.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))
8.0ms	(.f64 x (.f64 y z))

rewrite54.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
32×	`difference-of-squares_binary64`
31×	`*-un-lft-identity_binary64`
24×	`sqr-pow_binary64`

Counts

4 → 125

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)))))
7.0ms	(+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (*.f64 y z)))
7.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))
4.0ms	(.f64 x (.f64 y z))

simplify162.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-neg_binary64`
460×	`cancel-sign-sub-inv_binary64`
275×	`distribute-rgt-out_binary64`
234×	`distribute-rgt-neg-in_binary64`
210×	`distribute-lft-neg-in_binary64`

Counts

269 → 202

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	6039
1	579	5816
2	2311	5648
3	4575	5647
4	5057	5647

prune113.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	202	3	205

Error

0.0b

Counts

205 → 3

Alt Table

Status	Error	Program
✓	39.2b	(cbrt.f64 (.f64 (fma.f64 x x (.f64 (.f64 y z) (-.f64 (.f64 y z) (.f64 2 x)))) (-.f64 x (.f64 y z))))
✓	0.0b	(-.f64 x (*.f64 y z))
✓	39.4b	(/.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 8178 to 2346 computations (71.3% saved)

regimes344.0ms (7.4%)

Accuracy

Total 0.0b remaining (26.6%)

Threshold costs 0.0b (26.6%)

Counts

67 → 1

Compiler

Compiled 7177 to 3656 computations (49.1% 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

end5.0ms (0.1%)

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

sample638.0ms (13.7%)

Algorithm

1×

intervals

Results

239.0ms	8000×	body	128	valid
7.0ms	301×	body	128	invalid

Compiler

Compiled 82 to 46 computations (43.9% 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

analyze342.0ms (7.3%)

sample46.0ms (1%)

simplify14.0ms (0.3%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite3.0ms (0.1%)

simplify90.0ms (1.9%)

prune13.0ms (0.3%)

localize8.0ms (0.2%)

series47.0ms (1%)

rewrite48.0ms (1%)

simplify198.0ms (4.3%)

prune131.0ms (2.8%)

localize11.0ms (0.2%)

series2.0s (42.5%)

rewrite20.0ms (0.4%)

simplify143.0ms (3.1%)

prune93.0ms (2%)

localize13.0ms (0.3%)

series132.0ms (2.8%)

rewrite54.0ms (1.2%)

simplify162.0ms (3.5%)

prune113.0ms (2.4%)

regimes344.0ms (7.4%)

simplify3.0ms (0.1%)

end5.0ms (0.1%)

sample638.0ms (13.7%)

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