Details

analyze425.0ms (13.8%)

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)

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify224.0ms (7.3%)

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 (0.1%)

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

7.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series26.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

26.0ms

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

rewrite16.0ms (0.5%)

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:

11.0ms

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

simplify117.0ms (3.8%)

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 (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	111	4	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	111	5	116

Error

0.0b

Counts

116 → 5

Alt Table

Status	Error	Program
✓	7.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	18.2b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	36.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
▶	7.6b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	38.6b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))

Compiler

Compiled 2598 to 1127 computations (56.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	6.9b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series39.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

26.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
13.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64`
64×	`times-frac_binary64`
59×	`*-un-lft-identity_binary64`
30×	`associate-r_binary64`
28×	`difference-of-squares_binary64`

Counts

2 → 115

Calls

2 calls:

13.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
6.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

650×	`fma-def_binary64`
432×	`distribute-rgt-in_binary64`
348×	`distribute-lft-in_binary64`
312×	`associate-/l*_binary64`
303×	`times-frac_binary64`

Counts

175 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	210	3573
1	547	3405
2	1864	3177
3	5030	3177

prune124.0ms (4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	203	5	208

Error

0.0b

Counts

208 → 5

Alt Table

Status	Error	Program
✓	7.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
▶	18.2b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
	36.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	7.6b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	38.6b	(neg.f64 (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 y 2)) (+.f64 (/.f64 (pow.f64 z 2) y) (+.f64 (/.f64 (.f64 z x) y) z))))

Compiler

Compiled 4401 to 2231 computations (49.3% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 y z) (/.f64 y z))
✓	5.3b	(/.f64 (+.f64 y x) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))
✓	12.6b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))

series196.0ms (6.4%)

Counts

3 → 96

Calls

3 calls:

84.0ms	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
84.0ms	(/.f64 (+.f64 y x) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))
28.0ms	(*.f64 (/.f64 y z) (/.f64 y z))

rewrite55.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
81×	`times-frac_binary64`
79×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
39×	`associate-l_binary64`

Counts

3 → 170

Calls

3 calls:

19.0ms	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
8.0ms	(*.f64 (/.f64 y z) (/.f64 y z))
6.0ms	(/.f64 (+.f64 y x) (-.f64 1 (*.f64 (/.f64 y z) (/.f64 y z))))

simplify204.0ms (6.6%)

Algorithm

1×	egg-herbie

Rules

268×	`associate-+r+_binary64`
256×	`associate-*l/_binary64`
244×	`associate-/l*_binary64`
222×	`associate-l_binary64`
221×	`associate-*r/_binary64`

Counts

266 → 329

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	393	7531
1	1216	6991
2	4222	6708
3	4837	6708
4	4965	6708

prune201.0ms (6.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	328	1	329
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	329	5	334

Error

0.0b

Counts

334 → 5

Alt Table

Status	Error	Program
✓	7.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	18.2b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
▶	36.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	7.6b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	37.0b	(neg.f64 (+.f64 (/.f64 (.f64 x z) y) (+.f64 z (/.f64 (.f64 z z) y))))

Compiler

Compiled 9854 to 4113 computations (58.3% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 z (/.f64 y z))
✓	5.0b	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

series33.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

23.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))
10.0ms	(/.f64 z (/.f64 y z))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
44×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

2 → 82

Calls

2 calls:

6.0ms	(/.f64 z (/.f64 y z))
0.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

simplify123.0ms (4%)

Algorithm

1×	egg-herbie

Rules

522×	`associate-/l*_binary64`
499×	`associate-/r/_binary64`
359×	`associate-*l/_binary64`
320×	`distribute-rgt-in_binary64`
310×	`distribute-lft-in_binary64`

Counts

142 → 148

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	2287
1	340	2004
2	1052	1856
3	2662	1758
4	4306	1743
5	4928	1743
6	4967	1743

prune64.0ms (2.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	148	5	153

Error

Counts

153 → 5

Alt Table

Status	Error	Program
✓	7.5b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	18.2b	(.f64 (/.f64 (+.f64 y x) (-.f64 1 (.f64 (/.f64 y z) (/.f64 y z)))) (+.f64 1 (/.f64 y z)))
✓	36.5b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	7.6b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	37.5b	(neg.f64 (fma.f64 (/.f64 x y) z z))

Compiler

Compiled 2970 to 896 computations (69.8% saved)

regimes376.0ms (12.2%)

Accuracy

Total 0.2b remaining (93.6%)

Threshold costs 0.2b (93.6%)

Counts

54 → 3

Compiler

Compiled 3284 to 2132 computations (35.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	61
1	29	61
2	36	61
3	41	61
4	44	61
5	45	61
6	44	61

end1.0ms (0%)

Compiler: Compiled 44 to 24 computations (45.5% saved)

sample600.0ms (19.5%)

Algorithm

1×

intervals

Results

293.0ms	7998×	body	128	valid
0.0ms	2×	body	1024	valid

Compiler

Compiled 134 to 81 computations (39.6% saved)

Details

analyze425.0ms (13.8%)

sample18.0ms (0.6%)

simplify224.0ms (7.3%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

series26.0ms (0.8%)

rewrite16.0ms (0.5%)

simplify117.0ms (3.8%)

prune73.0ms (2.4%)

localize7.0ms (0.2%)

series39.0ms (1.3%)

rewrite28.0ms (0.9%)

simplify85.0ms (2.8%)

prune124.0ms (4%)

localize9.0ms (0.3%)

series196.0ms (6.4%)

rewrite55.0ms (1.8%)

simplify204.0ms (6.6%)

prune201.0ms (6.5%)

localize8.0ms (0.3%)

series33.0ms (1.1%)

rewrite12.0ms (0.4%)

simplify123.0ms (4%)

prune64.0ms (2.1%)

regimes376.0ms (12.2%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample600.0ms (19.5%)

Profiling