Details

analyze373.0ms (11%)

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)

sample1.0s (29.5%)

Results

854.0ms	8254×	body	128	valid
0.0ms	1×	body	2048	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify212.0ms (6.2%)

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

7.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.8b	(/.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
✓	7.8b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series25.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

25.0ms

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

rewrite15.0ms (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:

8.0ms

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

simplify105.0ms (3.1%)

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

prune86.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	108	7	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
	8.0b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
▶	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	28.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (+.f64 y x))))
	35.0b	(*.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (sqrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	37.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	38.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 2646 to 1155 computations (56.3% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	3.3b	(/.f64 x (-.f64 1 (/.f64 y z)))
✓	7.8b	(/.f64 y (-.f64 1 (/.f64 y z)))

series66.0ms (2%)

Counts

3 → 75

Calls

3 calls:

32.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
24.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
10.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

rewrite64.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`
118×	`times-frac_binary64`
52×	`difference-of-squares_binary64`
43×	`add-cube-cbrt_binary64`

Counts

3 → 160

Calls

3 calls:

36.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
7.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
6.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

simplify107.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
418×	`associate-/l*_binary64`
387×	`times-frac_binary64`
295×	`distribute-rgt-in_binary64`
235×	`distribute-neg-in_binary64`

Counts

235 → 238

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	4796
1	655	4692
2	1979	4413
3	4989	4413

prune167.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	239	6	245

Error

0.0b

Counts

245 → 6

Alt Table

Status	Error	Program
▶	8.0b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	28.9b	(+.f64 y (+.f64 x (*.f64 (/.f64 y z) (+.f64 y x))))
	35.0b	(*.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (sqrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))

Compiler

Compiled 6246 to 2975 computations (52.4% saved)

localize7.0ms (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)))
✓	7.8b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series46.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

25.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
21.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite56.0ms (1.6%)

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:

12.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
11.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

simplify222.0ms (6.5%)

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

prune184.0ms (5.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	311	6	317

Error

0.0b

Counts

317 → 6

Alt Table

Status	Error	Program
▶	28.9b	(*.f64 (+.f64 x y) (+.f64 1 (/.f64 y z)))
	35.0b	(*.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (sqrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
✓	8.0b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))

Compiler

Compiled 7892 to 3732 computations (52.7% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series13.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

13.0ms

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

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`flip-+_binary64`
6×	`flip3-+_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`associate-r_binary64`

Counts

1 → 32

Calls

1 calls:

9.0ms

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

simplify62.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

732×	`distribute-rgt-in_binary64`
701×	`distribute-lft-in_binary64`
674×	`times-frac_binary64`
533×	`fma-def_binary64`
199×	`associate-*l/_binary64`

Counts

68 → 68

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	1336
1	299	1023
2	987	1011
3	4591	1011
4	5537	1011

prune35.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	68	6	74

Error

0.0b

Counts

74 → 6

Alt Table

Status	Error	Program
✓	28.9b	(*.f64 (+.f64 x y) (+.f64 1 (/.f64 y z)))
	35.0b	(*.f64 (sqrt.f64 (+.f64 y x)) (/.f64 (sqrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
✓	8.0b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.8b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	39.8b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
	36.2b	(neg.f64 (fma.f64 z (/.f64 x y) z))

Compiler

Compiled 1248 to 518 computations (58.5% saved)

regimes428.0ms (12.6%)

Accuracy

Total 0.2b remaining (95.7%)

Threshold costs 0.2b (95.7%)

Counts

70 → 3

Compiler

Compiled 4151 to 2731 computations (34.2% saved)

bsearch2.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-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	25	84
1	34	84
2	41	84
3	46	84
4	49	84
5	50	84
6	49	84

end85.0ms (2.5%)

Compiler: Compiled 204 to 117 computations (42.6% saved)

Details

analyze373.0ms (11%)

sample1.0s (29.5%)

simplify212.0ms (6.2%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series25.0ms (0.7%)

rewrite15.0ms (0.4%)

simplify105.0ms (3.1%)

prune86.0ms (2.5%)

localize7.0ms (0.2%)

series66.0ms (2%)

rewrite64.0ms (1.9%)

simplify107.0ms (3.2%)

prune167.0ms (4.9%)

localize7.0ms (0.2%)

series46.0ms (1.4%)

rewrite56.0ms (1.6%)

simplify222.0ms (6.5%)

prune184.0ms (5.4%)

localize6.0ms (0.2%)

series13.0ms (0.4%)

rewrite10.0ms (0.3%)

simplify62.0ms (1.8%)

prune35.0ms (1%)

regimes428.0ms (12.6%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end85.0ms (2.5%)

Profiling