Details

analyze932.0ms (13.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
13.3%	86.5%	0.2%	9
17.5%	82.3%	0.2%	10
23.6%	75.2%	1.2%	11
25%	72%	2.9%	12
35.8%	59.6%	4.6%	13
40.3%	54.3%	5.4%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (18.7%)

Results

902.0ms	8256×	body	128	valid
227.0ms	2143×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify65.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

938×	`fma-def_binary64`
721×	`fma-neg_binary64`
220×	`cancel-sign-sub-inv_binary64`
144×	`distribute-rgt-in_binary64`
108×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	16	11
2	37	11
3	72	11
4	140	11
5	242	11
6	395	11
7	682	11
8	1049	11
9	1368	11
10	1492	11
11	1530	11
12	1536	11
13	1541	11
14	1541	11
15	1456	11

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

2.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	2.0b	(fma.f64 (/.f64 x y) (-.f64 z t) t)
▶	2.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 71 to 39 computations (45.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)
✓	7.8b	(*.f64 (/.f64 x y) (-.f64 z t))

series45.0ms (0.6%)

Counts

2 → 96

Calls

2 calls:

23.0ms	(*.f64 (/.f64 x y) (-.f64 z t))
22.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
38×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
26×	`associate-+l+_binary64`

Counts

2 → 106

Calls

2 calls:

8.0ms	(*.f64 (/.f64 x y) (-.f64 z t))
7.0ms	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-def_binary64`
553×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
208×	`fma-neg_binary64`
175×	`cancel-sign-sub-inv_binary64`

Counts

202 → 175

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2602
1	472	2504
2	1658	2387
3	5048	2387

prune119.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	168	7	175
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	169	8	177

Error

0.0b

Counts

177 → 8

Alt Table

Status	Error	Program
▶	1.0b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t))) t)
	8.1b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	7.2b	(+.f64 (.f64 x (.f64 (/.f64 1 y) (-.f64 z t))) t)
	36.5b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	7.0b	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
	28.5b	(+.f64 (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) (-.f64 z t))) t)
	2.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
✓	2.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 3827 to 952 computations (75.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.5b	(cbrt.f64 x)
✓	0.5b	(cbrt.f64 y)
✓	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))

series162.0ms (2.3%)

Counts

4 → 84

Calls

4 calls:

59.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))
41.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
33.0ms	(cbrt.f64 y)
29.0ms	(cbrt.f64 x)

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-exp-log_binary64`
52×	`distribute-lft-in_binary64`
52×	`distribute-rgt-in_binary64`
51×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`

Counts

4 → 179

Calls

4 calls:

16.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t)))
5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 x)

simplify139.0ms (2%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
529×	`unswap-sqr_binary64`
440×	`associate-l_binary64`
421×	`associate-r_binary64`
293×	`associate-*l/_binary64`

Counts

263 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	338	6281
1	656	3018
2	3027	2838
3	4548	2838
4	4950	2838

prune205.0ms (2.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	307	8	315

Error

0.0b

Counts

315 → 8

Alt Table

Status	Error	Program
✓	1.0b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t))) t)
	8.1b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	7.2b	(+.f64 (.f64 x (.f64 (/.f64 1 y) (-.f64 z t))) t)
	36.5b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
	7.0b	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
	28.5b	(+.f64 (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) (-.f64 z t))) t)
▶	2.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
✓	2.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 10380 to 1920 computations (81.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
✓	1.2b	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))
✓	11.7b	(cbrt.f64 (/.f64 x y))

series1.5s (21.6%)

Counts

4 → 144

Calls

4 calls:

547.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
491.0ms	(cbrt.f64 (/.f64 x y))
450.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))
46.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))

rewrite70.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
94×	`add-cube-cbrt_binary64`
92×	`cbrt-prod_binary64`
65×	`distribute-lft-in_binary64`

Counts

4 → 271

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t)))
11.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))
9.0ms	(*.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y)))
2.0ms	(cbrt.f64 (/.f64 x y))

simplify213.0ms (3%)

Algorithm

1×	egg-herbie

Rules

754×	`fma-def_binary64`
664×	`associate-l_binary64`
562×	`associate-r_binary64`
538×	`times-frac_binary64`
286×	`*-commutative_binary64`

Counts

415 → 390

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	452	7839
1	866	7175
2	3012	6928
3	4930	6928
4	4807	6928

prune336.0ms (4.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	462	0	462
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	462	8	470

Error

0.0b

Counts

470 → 8

Alt Table

Status	Error	Program
✓	1.0b	(+.f64 (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (.f64 (/.f64 (cbrt.f64 x) (cbrt.f64 y)) (-.f64 z t))) t)
	8.1b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
	7.2b	(+.f64 (.f64 x (.f64 (/.f64 1 y) (-.f64 z t))) t)
	36.5b	(*.f64 (-.f64 (/.f64 z y) (/.f64 t y)) x)
▶	7.0b	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
	28.5b	(+.f64 (.f64 (sqrt.f64 (/.f64 x y)) (.f64 (sqrt.f64 (/.f64 x y)) (-.f64 z t))) t)
✓	2.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
✓	2.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 14254 to 2894 computations (79.7% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 t z))
✓	0.0b	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
✓	7.1b	(/.f64 (neg.f64 x) (/.f64 y (-.f64 t z)))

series60.0ms (0.8%)

Counts

3 → 120

Calls

3 calls:

22.0ms	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
22.0ms	(/.f64 (neg.f64 x) (/.f64 y (-.f64 t z)))
15.0ms	(/.f64 y (-.f64 t z))

rewrite135.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

750×	`times-frac_binary64`
468×	`*-un-lft-identity_binary64`
466×	`add-sqr-sqrt_binary64`
332×	`add-cube-cbrt_binary64`
215×	`fma-def_binary64`

Counts

3 → 529

Calls

3 calls:

51.0ms	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
9.0ms	(/.f64 (neg.f64 x) (/.f64 y (-.f64 t z)))
4.0ms	(/.f64 y (-.f64 t z))

simplify233.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-def_binary64`
412×	`associate-/r/_binary64`
315×	`associate-/l/_binary64`
276×	`*-commutative_binary64`
276×	`associate-*l/_binary64`

Counts

649 → 608

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	484	9768
1	1199	9604
2	4822	9442
3	5414	9442

prune411.0ms (5.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	606	2	608
Fresh	2	2	4
Picked	0	1	1
Done	1	2	3
Total	609	7	616

Error

0.0b

Counts

616 → 7

Alt Table

Status	Error	Program
	7.2b	(+.f64 (.f64 x (.f64 (/.f64 1 y) (-.f64 z t))) t)
	8.2b	(fma.f64 (/.f64 -1 y) (/.f64 x (/.f64 1 (-.f64 t z))) t)
✓	7.0b	(+.f64 (/.f64 (neg.f64 x) (/.f64 y (-.f64 t z))) t)
	8.1b	(+.f64 (/.f64 (*.f64 (-.f64 z t) x) y) t)
✓	2.5b	(+.f64 (.f64 (.f64 (cbrt.f64 (/.f64 x y)) (cbrt.f64 (/.f64 x y))) (*.f64 (cbrt.f64 (/.f64 x y)) (-.f64 z t))) t)
	7.2b	(*.f64 1 (fma.f64 x (/.f64 (fma.f64 -1 t z) y) t))
✓	2.0b	(+.f64 (*.f64 (/.f64 x y) (-.f64 z t)) t)

Compiler

Compiled 13444 to 2800 computations (79.2% saved)

regimes870.0ms (12.2%)

Accuracy

Total 0.9b remaining (99.1%)

Threshold costs 0.9b (99.1%)

Counts

135 → 1

Compiler

Compiled 16787 to 9972 computations (40.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	21	35
2	26	35
3	28	35
4	29	35
5	29	35

end81.0ms (1.1%)

Compiler: Compiled 162 to 97 computations (40.1% saved)

Details

analyze932.0ms (13.1%)

sample1.3s (18.7%)

simplify65.0ms (0.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series45.0ms (0.6%)

rewrite26.0ms (0.4%)

simplify70.0ms (1%)

prune119.0ms (1.7%)

localize12.0ms (0.2%)

series162.0ms (2.3%)

rewrite44.0ms (0.6%)

simplify139.0ms (2%)

prune205.0ms (2.9%)

localize10.0ms (0.1%)

series1.5s (21.6%)

rewrite70.0ms (1%)

simplify213.0ms (3%)

prune336.0ms (4.7%)

localize7.0ms (0.1%)

series60.0ms (0.8%)

rewrite135.0ms (1.9%)

simplify233.0ms (3.3%)

prune411.0ms (5.8%)

regimes870.0ms (12.2%)

simplify3.0ms (0%)

end81.0ms (1.1%)

Profiling