Details

analyze409.0ms (8.6%)

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
6.2%	93.6%	0.1%	6
20.3%	79.6%	0.1%	7
28.9%	71%	0.1%	8
39.8%	60.1%	0.1%	9
57.5%	42.3%	0.1%	10
63.9%	36%	0.1%	11
68.6%	31.3%	0.1%	12
79.5%	20.3%	0.1%	13
82.9%	17%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample1.1s (23.1%)

Results

932.0ms	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify221.0ms (4.6%)

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

8.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.8b	(/.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
✓	8.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series29.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

28.0ms

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

rewrite18.0ms (0.4%)

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:

12.0ms

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

simplify121.0ms (2.5%)

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

prune75.0ms (1.6%)

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
▶	8.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
✓	8.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
	20.3b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
	36.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	35.5b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 2574 to 1115 computations (56.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	8.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series37.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

27.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
10.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

rewrite30.0ms (0.6%)

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))))
8.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

simplify83.0ms (1.8%)

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

prune129.0ms (2.7%)

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
✓	8.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
✓	8.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
▶	20.3b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
	36.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	35.5b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 4377 to 2219 computations (49.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z))))
✓	0.1b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
✓	4.7b	(sqrt.f64 (-.f64 1 (/.f64 y z)))

series142.0ms (3%)

Counts

3 → 72

Calls

3 calls:

87.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z))))
31.0ms	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
21.0ms	(sqrt.f64 (-.f64 1 (/.f64 y z)))

rewrite273.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Rules

1332×	`times-frac_binary64`
1209×	`add-sqr-sqrt_binary64`
1076×	`*-un-lft-identity_binary64`
840×	`sqrt-prod_binary64`
420×	`difference-of-squares_binary64`

Counts

3 → 729

Calls

3 calls:

29.0ms	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
13.0ms	(/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z))))
8.0ms	(sqrt.f64 (-.f64 1 (/.f64 y z)))

simplify872.0ms (18.3%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
560×	`associate-/l/_binary64`
236×	`distribute-rgt-in_binary64`
230×	`associate-+r+_binary64`
181×	`associate-/r*_binary64`

Counts

801 → 680

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	559	38350
1	1338	35993
2	3167	34820
3	4820	34532
4	5033	34532

prune483.0ms (10.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	711	0	711
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	711	5	716

Error

0.0b

Counts

716 → 5

Alt Table

Status	Error	Program
✓	8.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
✓	8.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	20.3b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))
	36.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
▶	35.5b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 25291 to 12246 computations (51.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 (pow.f64 z 2) y) z)
✓	3.9b	(+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z))
✓	3.9b	(/.f64 (*.f64 z x) y)
✓	6.8b	(/.f64 (pow.f64 z 2) y)

series55.0ms (1.1%)

Counts

4 → 45

Calls

4 calls:

24.0ms	(+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z))
12.0ms	(/.f64 (*.f64 z x) y)
10.0ms	(/.f64 (pow.f64 z 2) y)
8.0ms	(+.f64 (/.f64 (pow.f64 z 2) y) z)

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
40×	`add-cube-cbrt_binary64`
35×	`fma-def_binary64`

Counts

4 → 142

Calls

4 calls:

19.0ms	(+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z))
9.0ms	(+.f64 (/.f64 (pow.f64 z 2) y) z)
3.0ms	(/.f64 (pow.f64 z 2) y)
3.0ms	(/.f64 (*.f64 z x) y)

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Rules

725×	`times-frac_binary64`
461×	`fma-def_binary64`
397×	`distribute-rgt-in_binary64`
357×	`distribute-lft-in_binary64`
319×	`associate-/l/_binary64`

Counts

187 → 215

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2371
1	434	2160
2	1418	2080
3	4744	2080
4	4978	2080

prune129.0ms (2.7%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	0	1
Picked	0	1	1
Done	0	3	3
Total	215	5	220

Error

Counts

220 → 5

Alt Table

Status	Error	Program
✓	8.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
✓	8.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
✓	35.5b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	35.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))
✓	20.3b	(/.f64 (/.f64 (+.f64 x y) (sqrt.f64 (-.f64 1 (/.f64 y z)))) (sqrt.f64 (-.f64 1 (/.f64 y z))))

Compiler

Compiled 4595 to 1932 computations (58% saved)

regimes288.0ms (6%)

Accuracy

Total 0.2b remaining (91.5%)

Threshold costs 0.2b (91.5%)

Counts

45 → 3

Compiler

Compiled 2744 to 1744 computations (36.4% saved)

bsearch1.0ms (0%)

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
11×	`*-commutative_binary64`
11×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	72
1	40	72
2	59	72
3	84	72
4	99	72
5	107	72
6	109	72
7	108	72

end89.0ms (1.9%)

Compiler: Compiled 175 to 106 computations (39.4% saved)

Details

analyze409.0ms (8.6%)

sample1.1s (23.1%)

simplify221.0ms (4.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series29.0ms (0.6%)

rewrite18.0ms (0.4%)

simplify121.0ms (2.5%)

prune75.0ms (1.6%)

localize7.0ms (0.1%)

series37.0ms (0.8%)

rewrite30.0ms (0.6%)

simplify83.0ms (1.8%)

prune129.0ms (2.7%)

localize8.0ms (0.2%)

series142.0ms (3%)

rewrite273.0ms (5.7%)

simplify872.0ms (18.3%)

prune483.0ms (10.1%)

localize9.0ms (0.2%)

series55.0ms (1.1%)

rewrite44.0ms (0.9%)

simplify96.0ms (2%)

prune129.0ms (2.7%)

regimes288.0ms (6%)

bsearch1.0ms (0%)

simplify7.0ms (0.1%)

end89.0ms (1.9%)

Profiling