Details

analyze357.0ms (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
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)

sample1.3s (25.8%)

Results

1.1s	8255×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify213.0ms (4.3%)

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

prune1.0ms (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

7.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	7.4b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 y z))
✓	7.4b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series33.0ms (0.7%)

Counts

2 → 42

Calls

2 calls:

29.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
4.0ms	(-.f64 1 (/.f64 y z))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-sqr-sqrt_binary64`
100×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
58×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

2 → 135

Calls

2 calls:

8.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
7.0ms	(-.f64 1 (/.f64 y z))

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

549×	`times-frac_binary64`
305×	`distribute-rgt-in_binary64`
243×	`fma-neg_binary64`
226×	`distribute-lft-in_binary64`
175×	`cancel-sign-sub-inv_binary64`

Counts

177 → 200

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	292	4046
1	754	3571
2	2276	3190
3	4701	3187
4	4818	3187

prune140.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	195	5	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	5	201

Error

0.0b

Counts

201 → 5

Alt Table

Status	Error	Program
	50.8b	(*.f64 (/.f64 1 (+.f64 1 (/.f64 (sqrt.f64 y) (sqrt.f64 z)))) (/.f64 (+.f64 y x) (-.f64 1 (/.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	33.8b	(-.f64 (neg.f64 (.f64 (+.f64 (/.f64 x y) 1) (/.f64 z (/.f64 y z)))) (+.f64 z (.f64 (/.f64 z y) (+.f64 (/.f64 z (/.f64 y z)) x))))
▶	7.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	7.6b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
	36.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 5107 to 1999 computations (60.9% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
	0.0b	(-.f64 1 (/.f64 y z))
✓	2.8b	(/.f64 x (-.f64 1 (/.f64 y z)))
✓	7.3b	(/.f64 y (-.f64 1 (/.f64 y z)))

series70.0ms (1.4%)

Counts

3 → 75

Calls

3 calls:

34.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
26.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))
9.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))

rewrite67.0ms (1.4%)

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:

38.0ms	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
7.0ms	(/.f64 y (-.f64 1 (/.f64 y z)))
6.0ms	(/.f64 x (-.f64 1 (/.f64 y z)))

simplify111.0ms (2.2%)

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

prune280.0ms (5.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	400	2	402
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	402	5	407

Error

Counts

407 → 5

Alt Table

Status	Error	Program
✓	7.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
▶	7.5b	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))
	50.8b	(*.f64 (/.f64 1 (+.f64 1 (/.f64 (sqrt.f64 y) (sqrt.f64 z)))) (/.f64 (+.f64 y x) (-.f64 1 (/.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	36.1b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))

Compiler

Compiled 12022 to 5201 computations (56.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	1.0b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x))
✓	2.6b	(/.f64 (-.f64 1 (/.f64 y z)) x)
	7.3b	(/.f64 y (-.f64 1 (/.f64 y z)))

series113.0ms (2.3%)

Counts

3 → 100

Calls

3 calls:

71.0ms	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
26.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x))
16.0ms	(/.f64 (-.f64 1 (/.f64 y z)) x)

rewrite153.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

414×	`times-frac_binary64`
358×	`add-sqr-sqrt_binary64`
270×	`*-un-lft-identity_binary64`
158×	`add-cube-cbrt_binary64`
100×	`difference-of-squares_binary64`

Counts

3 → 297

Calls

3 calls:

89.0ms	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
10.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x))
10.0ms	(/.f64 (-.f64 1 (/.f64 y z)) x)

simplify192.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
365×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
218×	`distribute-neg-in_binary64`
216×	`fma-neg_binary64`

Counts

397 → 388

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	7108
1	678	6690
2	2275	6356
3	4973	6356
4	5086	6356

prune316.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	456	1	457
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	458	4	462

Error

Counts

462 → 4

Alt Table

Status	Error	Program
✓	7.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
▶	9.1b	(+.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x)))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	7.5b	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))

Compiler

Compiled 13175 to 6936 computations (47.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x)))
✓	1.0b	(/.f64 1 (-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x))))
✓	4.7b	(/.f64 y (*.f64 z x))
	7.3b	(/.f64 y (-.f64 1 (/.f64 y z)))

series70.0ms (1.4%)

Counts

3 → 54

Calls

3 calls:

38.0ms	(/.f64 1 (-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x))))
17.0ms	(-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x)))
16.0ms	(/.f64 y (*.f64 z x))

rewrite44.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`times-frac_binary64`
137×	`add-sqr-sqrt_binary64`
122×	`*-un-lft-identity_binary64`
102×	`add-cube-cbrt_binary64`
91×	`prod-diff_binary64`

Counts

3 → 209

Calls

3 calls:

11.0ms	(-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x)))
9.0ms	(/.f64 1 (-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x))))
3.0ms	(/.f64 y (*.f64 z x))

simplify151.0ms (3%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/r*_binary64`
494×	`fma-def_binary64`
265×	`fma-neg_binary64`
229×	`associate-/l/_binary64`
219×	`exp-prod_binary64`

Counts

263 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	6084
1	547	5264
2	1603	4204
3	4413	4204
4	4921	4204

prune241.0ms (4.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	346	0	346
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	346	4	350

Error

Counts

350 → 4

Alt Table

Status	Error	Program
✓	7.4b	(+.f64 (/.f64 x (-.f64 1 (/.f64 y z))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	9.1b	(+.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 y (*.f64 z x)))) (/.f64 y (-.f64 1 (/.f64 y z))))
✓	7.5b	(+.f64 (/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) x)) (/.f64 y (-.f64 1 (/.f64 y z))))
	32.9b	(neg.f64 (fma.f64 z (/.f64 x y) z))

Compiler

Compiled 11940 to 5136 computations (57% saved)

regimes849.0ms (17.1%)

Accuracy

Total 0.6b remaining (96.5%)

Threshold costs 0.6b (96.5%)

Counts

114 → 3

Compiler

Compiled 7484 to 4862 computations (35% saved)

bsearch5.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	92
1	39	90
2	50	90
3	57	90
4	62	90
5	63	90
6	62	90

end82.0ms (1.6%)

Compiler: Compiled 198 to 115 computations (41.9% saved)

Details

analyze357.0ms (7.2%)

sample1.3s (25.8%)

simplify213.0ms (4.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series33.0ms (0.7%)

rewrite28.0ms (0.6%)

simplify138.0ms (2.8%)

prune140.0ms (2.8%)

localize7.0ms (0.1%)

series70.0ms (1.4%)

rewrite67.0ms (1.4%)

simplify111.0ms (2.2%)

prune280.0ms (5.6%)

localize9.0ms (0.2%)

series113.0ms (2.3%)

rewrite153.0ms (3.1%)

simplify192.0ms (3.9%)

prune316.0ms (6.3%)

localize13.0ms (0.3%)

series70.0ms (1.4%)

rewrite44.0ms (0.9%)

simplify151.0ms (3%)

prune241.0ms (4.8%)

regimes849.0ms (17.1%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end82.0ms (1.6%)

Profiling