Details

analyze474.0ms (14.2%)

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
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)

sample991.0ms (29.7%)

Symmetry

(sort y z)

Results

911.0ms	8256×	body	128	valid
29.0ms	328×	body	128	invalid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify14.0ms (0.4%)

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 9

Calls

1 calls:

6.0ms

(-.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:

3.0ms

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

simplify89.0ms (2.7%)

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

prune16.0ms (0.5%)

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
	40.1b	(/.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)))))
▶	39.9b	(cbrt.f64 (pow.f64 (-.f64 x (*.f64 y z)) 3))
✓	0.0b	(-.f64 x (*.f64 y z))

Compiler

Compiled 391 to 135 computations (65.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 x (*.f64 y z))
✓	0.1b	(pow.f64 (-.f64 x (*.f64 y z)) 3)
✓	37.9b	(cbrt.f64 (pow.f64 (-.f64 x (*.f64 y z)) 3))

series38.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

25.0ms	(pow.f64 (-.f64 x (*.f64 y z)) 3)
13.0ms	(cbrt.f64 (pow.f64 (-.f64 x (*.f64 y z)) 3))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(pow.f64 (-.f64 x (*.f64 y z)) 3)
3.0ms	(cbrt.f64 (pow.f64 (-.f64 x (*.f64 y z)) 3))

simplify98.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

577×	`cancel-sign-sub-inv_binary64`
503×	`fma-neg_binary64`
326×	`fma-def_binary64`
252×	`unswap-sqr_binary64`
233×	`*-commutative_binary64`

Counts

124 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	2048
1	267	1933
2	849	1840
3	2608	1812
4	4811	1812
5	4952	1812

prune60.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	110	3	113

Error

Counts

113 → 3

Alt Table

Status	Error	Program
	51.0b	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))
▶	40.1b	(/.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)))))
✓	0.0b	(-.f64 x (*.f64 y z))

Compiler

Compiled 1749 to 742 computations (57.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))
✓	1.6b	(.f64 x (.f64 y z))
✓	4.2b	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
✓	38.7b	(/.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)))))

series162.0ms (4.8%)

Counts

4 → 144

Calls

4 calls:

90.0ms	(/.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)))))
36.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
26.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))
9.0ms	(.f64 x (.f64 y z))

rewrite81.0ms (2.4%)

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 → 249

Calls

4 calls:

23.0ms	(/.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)))))
10.0ms	(-.f64 (pow.f64 x 3) (pow.f64 (*.f64 y z) 3))
9.0ms	(.f64 x (.f64 y z))
8.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 (.f64 y z) (.f64 y z)) (.f64 x (.f64 y z))))

simplify274.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

568×	`times-frac_binary64`
451×	`fma-neg_binary64`
314×	`associate-l_binary64`
296×	`associate-r_binary64`
243×	`exp-prod_binary64`

Counts

393 → 288

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	9946
1	620	8550
2	3001	8334
3	4771	8334
4	5017	8334

prune190.0ms (5.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	288	0	288
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	288	3	291

Error

Counts

291 → 3

Alt Table

Status	Error	Program
▶	51.0b	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))
✓	40.1b	(/.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)))))
✓	0.0b	(-.f64 x (*.f64 y z))

Compiler

Compiled 13134 to 4166 computations (68.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x 3) (.f64 y z))
✓	0.3b	(.f64 (.f64 y z) (*.f64 y z))
✓	3.0b	(.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z)))
✓	30.7b	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))

series151.0ms (4.5%)

Counts

4 → 132

Calls

4 calls:

82.0ms	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))
44.0ms	(.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z)))
17.0ms	(.f64 (.f64 y z) (*.f64 y z))
7.0ms	(-.f64 (.f64 x 3) (.f64 y z))

rewrite39.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`pow1_binary64`
34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
30×	`pow-prod-down_binary64`
21×	`cbrt-unprod_binary64`

Counts

4 → 103

Calls

4 calls:

11.0ms	(.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z)))
10.0ms	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))
5.0ms	(.f64 (.f64 y z) (*.f64 y z))
3.0ms	(-.f64 (.f64 x 3) (.f64 y z))

simplify148.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
497×	`associate-l_binary64`
486×	`associate-r_binary64`
423×	`times-frac_binary64`
254×	`associate-/r*_binary64`

Counts

235 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	348	6330
1	1022	5701
2	4727	5651
3	5378	5651

prune136.0ms (4.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	220	0	220
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	220	3	223

Error

Counts

223 → 3

Alt Table

Status	Error	Program
✓	51.0b	(cbrt.f64 (.f64 (.f64 (.f64 y z) (.f64 y z)) (-.f64 (.f64 x 3) (.f64 y z))))
✓	40.1b	(/.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)))))
✓	0.0b	(-.f64 x (*.f64 y z))

Compiler

Compiled 7228 to 3932 computations (45.6% saved)

regimes261.0ms (7.8%)

Accuracy

Total 0.0b remaining (18.2%)

Threshold costs 0.0b (18.2%)

Counts

49 → 1

Compiler

Compiled 4352 to 2661 computations (38.9% 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

end57.0ms (1.7%)

Remove: (sort y z)
Compiler: Compiled 89 to 50 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

analyze474.0ms (14.2%)

sample991.0ms (29.7%)

simplify14.0ms (0.4%)

prune1.0ms (0%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite3.0ms (0.1%)

simplify89.0ms (2.7%)

prune16.0ms (0.5%)

localize6.0ms (0.2%)

series38.0ms (1.1%)

rewrite10.0ms (0.3%)

simplify98.0ms (2.9%)

prune60.0ms (1.8%)

localize13.0ms (0.4%)

series162.0ms (4.8%)

rewrite81.0ms (2.4%)

simplify274.0ms (8.2%)

prune190.0ms (5.7%)

localize10.0ms (0.3%)

series151.0ms (4.5%)

rewrite39.0ms (1.2%)

simplify148.0ms (4.4%)

prune136.0ms (4.1%)

regimes261.0ms (7.8%)

simplify3.0ms (0.1%)

end57.0ms (1.7%)

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