Details

analyze287.0ms (7.2%)

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
12.5%	87.4%	0.1%	4
12.5%	87.4%	0.1%	5
15.6%	84.3%	0.1%	6
32.8%	67.1%	0.1%	7
38.2%	61.6%	0.1%	8
46%	53.8%	0.1%	9
62.6%	37.3%	0.1%	10
67.2%	32.7%	0.1%	11
71.1%	28.8%	0.1%	12
81.6%	18.2%	0.1%	13
84.1%	15.7%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample149.0ms (3.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify222.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

2674×	`fma-neg_binary64`
2270×	`div-sub_binary64`
1877×	`fma-def_binary64`
968×	`associate-/l/_binary64`
705×	`associate-/r/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	14	13
2	20	13
3	28	13
4	41	13
5	55	13
6	72	13
7	85	13
8	102	13
9	127	13
10	155	13
11	215	13
12	356	13
13	666	13
14	1204	13
15	1746	13
16	1897	13
17	2006	13
18	2246	13
19	2452	13
20	1993	13
21	2354	13
22	2400	13
23	2609	13
24	2737	13
25	2812	13
26	2982	13
27	2984	13
28	3004	13
29	3004	13
30	3850	13
31	5135	13

prune2.0ms (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

9.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series33.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

33.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`
42×	`times-frac_binary64`
20×	`difference-of-squares_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 62

Calls

1 calls:

8.0ms

(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

simplify114.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-def_binary64`
293×	`times-frac_binary64`
278×	`associate-/l*_binary64`
255×	`distribute-rgt-in_binary64`
189×	`distribute-lft-in_binary64`

Counts

98 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	178	2629
1	452	2552
2	1433	2416
3	4783	2407
4	4885	2405
5	4974	2405

prune73.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	110	6	116

Error

0.0b

Counts

116 → 6

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	20.7b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	34.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.6b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.2b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	10.1b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))

Compiler

Compiled 2602 to 1129 computations (56.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	10.0b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series45.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

23.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
22.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite58.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

316×	`times-frac_binary64`
275×	`add-sqr-sqrt_binary64`
273×	`*-un-lft-identity_binary64`
107×	`add-cube-cbrt_binary64`
84×	`difference-of-squares_binary64`

Counts

2 → 241

Calls

2 calls:

15.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
10.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

simplify214.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

942×	`times-frac_binary64`
878×	`fma-def_binary64`
191×	`associate-+r+_binary64`
167×	`+-commutative_binary64`
149×	`associate-+l+_binary64`

Counts

313 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	8808
1	793	8290
2	2783	8179
3	4999	8179
4	4985	8179

prune201.0ms (5.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	311	6	317

Error

0.0b

Counts

317 → 6

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	20.7b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	34.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.6b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	33.2b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	5.8b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))

Compiler

Compiled 7938 to 3757 computations (52.7% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
✓	0.0b	(/.f64 1 (+.f64 y x))
✓	0.2b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
✓	7.5b	(/.f64 y (*.f64 z (+.f64 y x)))

series132.0ms (3.3%)

Counts

4 → 111

Calls

4 calls:

79.0ms	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
27.0ms	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
17.0ms	(/.f64 y (*.f64 z (+.f64 y x)))
8.0ms	(/.f64 1 (+.f64 y x))

rewrite91.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

236×	`*-un-lft-identity_binary64`
232×	`times-frac_binary64`
183×	`add-sqr-sqrt_binary64`
162×	`prod-diff_binary64`
148×	`add-cube-cbrt_binary64`

Counts

4 → 338

Calls

4 calls:

16.0ms	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
15.0ms	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
4.0ms	(/.f64 y (*.f64 z (+.f64 y x)))
4.0ms	(/.f64 1 (+.f64 y x))

simplify402.0ms (10.1%)

Algorithm

1×	egg-herbie

Rules

477×	`times-frac_binary64`
409×	`associate-/r*_binary64`
272×	`associate-/l*_binary64`
147×	`sub-neg_binary64`
143×	`+-commutative_binary64`

Counts

449 → 443

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	647	20035
1	1769	16677
2	4822	16361
3	4979	16361
4	4990	16361

prune329.0ms (8.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	441	2	443
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	442	7	449

Error

Counts

449 → 7

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	20.7b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	34.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.6b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	6.9b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (.f64 z (+.f64 y x))))) (cbrt.f64 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (.f64 z (+.f64 y x))))))) (cbrt.f64 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (.f64 z (+.f64 y x))))))
▶	1.8b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))))
✓	5.8b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))

Compiler

Compiled 19444 to 7378 computations (62.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (+.f64 y x))
✓	0.0b	(/.f64 y (+.f64 y x))
✓	0.2b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))))
✓	1.8b	(*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))

series112.0ms (2.8%)

Counts

3 → 96

Calls

3 calls:

85.0ms	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))))
18.0ms	(*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))
8.0ms	(/.f64 y (+.f64 y x))

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`

Counts

3 → 137

Calls

3 calls:

12.0ms	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))))
10.0ms	(*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))
4.0ms	(/.f64 y (+.f64 y x))

simplify165.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
444×	`associate-/r*_binary64`
321×	`associate-l_binary64`
319×	`associate-/l*_binary64`
140×	`associate-*l/_binary64`

Counts

233 → 269

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	519	6718
1	1467	6489
2	4819	6396
3	5000	6396

prune270.0ms (6.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	320	7	327

Error

Counts

327 → 7

Alt Table

Status	Error	Program
✓	9.9b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	20.7b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	34.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	32.6b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	0.5b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (.f64 (.f64 (/.f64 1 z) (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))))) (/.f64 (cbrt.f64 y) (cbrt.f64 (+.f64 y x))))))
✓	1.8b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (*.f64 (/.f64 1 z) (/.f64 y (+.f64 y x)))))
✓	5.8b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))

Compiler

Compiled 10573 to 5423 computations (48.7% saved)

regimes353.0ms (8.9%)

Accuracy

Total 0.6b remaining (99.3%)

Threshold costs 0.6b (99.3%)

Counts

88 → 1

Compiler

Compiled 6119 to 3907 computations (36.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	55
1	28	55
2	43	55
3	59	55
4	73	55
5	80	55
6	82	55
7	80	55

end1.0ms (0%)

Compiler: Compiled 38 to 19 computations (50% saved)

sample643.0ms (16.2%)

Algorithm

1×

intervals

Results

313.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 192 to 111 computations (42.2% saved)

Details

analyze287.0ms (7.2%)

sample149.0ms (3.7%)

simplify222.0ms (5.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series33.0ms (0.8%)

rewrite13.0ms (0.3%)

simplify114.0ms (2.9%)

prune73.0ms (1.8%)

localize6.0ms (0.2%)

series45.0ms (1.1%)

rewrite58.0ms (1.5%)

simplify214.0ms (5.4%)

prune201.0ms (5.1%)

localize8.0ms (0.2%)

series132.0ms (3.3%)

rewrite91.0ms (2.3%)

simplify402.0ms (10.1%)

prune329.0ms (8.3%)

localize9.0ms (0.2%)

series112.0ms (2.8%)

rewrite35.0ms (0.9%)

simplify165.0ms (4.1%)

prune270.0ms (6.8%)

regimes353.0ms (8.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample643.0ms (16.2%)

Profiling