Details

analyze352.0ms (8.7%)

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)

sample989.0ms (24.5%)

Results

846.0ms	8255×	body	128	valid
0.0ms	1×	body	1024	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify214.0ms (5.3%)

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%)

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

7.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.6b	(/.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
✓	7.6b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series24.0ms (0.6%)

Counts

1 → 36

Calls

1 calls:

24.0ms

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

rewrite16.0ms (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:

11.0ms

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

simplify121.0ms (3%)

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

prune70.0ms (1.7%)

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
	31.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	33.8b	(+.f64 y (fma.f64 (/.f64 y z) x x))
▶	7.7b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	7.7b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.6b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 2584 to 1121 computations (56.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	7.3b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series33.0ms (0.8%)

Counts

2 → 60

Calls

2 calls:

26.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
7.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

rewrite35.0ms (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:

17.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
9.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

simplify87.0ms (2.2%)

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

prune119.0ms (2.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	203	6	209

Error

0.0b

Counts

209 → 6

Alt Table

Status	Error	Program
	31.4b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	33.8b	(+.f64 y (fma.f64 (/.f64 y z) x x))
✓	7.7b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
▶	7.7b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.6b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 4387 to 2225 computations (49.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.7b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series41.0ms (1%)

Counts

2 → 72

Calls

2 calls:

22.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
18.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite58.0ms (1.4%)

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

simplify235.0ms (5.8%)

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

prune188.0ms (4.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	309	2	311
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	311	6	317

Error

Counts

317 → 6

Alt Table

Status	Error	Program
▶	6.5b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
✓	7.7b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	7.8b	(/.f64 1 (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 x y))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	7.7b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.6b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 7898 to 3743 computations (52.6% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 z (+.f64 y x))
✓	0.0b	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
✓	0.1b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
✓	10.2b	(/.f64 y (*.f64 z (+.f64 y x)))

series101.0ms (2.5%)

Counts

4 → 111

Calls

4 calls:

49.0ms	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
28.0ms	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
15.0ms	(/.f64 y (*.f64 z (+.f64 y x)))
8.0ms	(*.f64 z (+.f64 y x))

rewrite90.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

223×	`*-un-lft-identity_binary64`
220×	`times-frac_binary64`
178×	`add-sqr-sqrt_binary64`
162×	`prod-diff_binary64`
141×	`add-cube-cbrt_binary64`

Counts

4 → 324

Calls

4 calls:

19.0ms	(-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x))))
12.0ms	(/.f64 1 (-.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 z (+.f64 y x))

simplify408.0ms (10.1%)

Algorithm

1×	egg-herbie

Rules

491×	`times-frac_binary64`
439×	`associate-/r*_binary64`
284×	`associate-/l*_binary64`
149×	`fma-def_binary64`
142×	`+-commutative_binary64`

Counts

435 → 429

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	647	20175
1	1761	16457
2	4913	16457
3	5000	16457
4	4976	16457

prune321.0ms (7.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	429	0	429
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	429	6	435

Error

Counts

435 → 6

Alt Table

Status	Error	Program
✓	6.5b	(/.f64 1 (-.f64 (/.f64 1 (+.f64 y x)) (/.f64 y (*.f64 z (+.f64 y x)))))
✓	7.7b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	7.8b	(/.f64 1 (*.f64 (-.f64 1 (/.f64 y z)) (/.f64 1 (+.f64 x y))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	7.7b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	7.6b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 19039 to 7104 computations (62.7% saved)

regimes416.0ms (10.3%)

Accuracy

Total 0.4b remaining (96.7%)

Threshold costs 0.4b (96.7%)

Counts

50 → 3

Compiler

Compiled 2721 to 1855 computations (31.8% saved)

bsearch1.0ms (0%)

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

simplify9.0ms (0.2%)

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	83
1	37	83
2	56	83
3	81	83
4	96	83
5	104	83
6	106	83
7	105	83

end88.0ms (2.2%)

Compiler: Compiled 209 to 124 computations (40.7% saved)

Details

analyze352.0ms (8.7%)

sample989.0ms (24.5%)

simplify214.0ms (5.3%)

prune2.0ms (0%)

localize6.0ms (0.2%)

series24.0ms (0.6%)

rewrite16.0ms (0.4%)

simplify121.0ms (3%)

prune70.0ms (1.7%)

localize7.0ms (0.2%)

series33.0ms (0.8%)

rewrite35.0ms (0.9%)

simplify87.0ms (2.2%)

prune119.0ms (2.9%)

localize7.0ms (0.2%)

series41.0ms (1%)

rewrite58.0ms (1.4%)

simplify235.0ms (5.8%)

prune188.0ms (4.6%)

localize8.0ms (0.2%)

series101.0ms (2.5%)

rewrite90.0ms (2.2%)

simplify408.0ms (10.1%)

prune321.0ms (7.9%)

regimes416.0ms (10.3%)

bsearch1.0ms (0%)

simplify9.0ms (0.2%)

end88.0ms (2.2%)

Profiling