Details

analyze366.0ms (8.8%)

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
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 (24.6%)

Results

882.0ms	8254×	body	128	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify222.0ms (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

8.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.0b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (/.f64 y z))
✓	8.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series37.0ms (0.9%)

Counts

2 → 42

Calls

2 calls:

32.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
5.0ms	(-.f64 1 (/.f64 y z))

rewrite99.0ms (2.4%)

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:

78.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
9.0ms	(-.f64 1 (/.f64 y z))

simplify126.0ms (3%)

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

prune139.0ms (3.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	194	6	200
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	194	7	201

Error

Counts

201 → 7

Alt Table

Status	Error	Program
	37.1b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
▶	8.1b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	9.2b	(.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
	34.7b	(-.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))))
	8.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
	8.5b	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
✓	8.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 5131 to 2015 computations (60.7% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (/.f64 y z))
✓	0.3b	(/.f64 1 (-.f64 1 (/.f64 y z)))
✓	7.8b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

series53.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

28.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))
25.0ms	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))

rewrite31.0ms (0.7%)

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))))
7.0ms	(/.f64 1 (-.f64 1 (/.f64 y z)))

simplify87.0ms (2.1%)

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

prune197.0ms (4.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	285	7	292

Error

Counts

292 → 7

Alt Table

Status	Error	Program
	37.1b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
✓	8.1b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	9.2b	(.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
▶	8.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
	33.8b	(-.f64 (neg.f64 (fma.f64 (/.f64 z y) x (/.f64 z (/.f64 y z)))) z)
	8.5b	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
✓	8.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 6990 to 3228 computations (53.8% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 1 (/.f64 y z))
✓	0.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
✓	8.1b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

series57.0ms (1.4%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
25.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite63.0ms (1.5%)

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:

15.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
13.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

simplify233.0ms (5.6%)

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

prune300.0ms (7.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	393	0	393
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	393	7	400

Error

Counts

400 → 7

Alt Table

Status	Error	Program
	37.1b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
✓	8.1b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	9.2b	(.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
✓	8.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
	33.8b	(-.f64 (neg.f64 (fma.f64 (/.f64 z y) x (/.f64 z (/.f64 y z)))) z)
▶	8.5b	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
✓	8.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 10487 to 4732 computations (54.9% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3))))
✓	0.7b	(cbrt.f64 z)
✓	0.8b	(pow.f64 (cbrt.f64 z) 3)
✓	8.0b	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))

series147.0ms (3.5%)

Counts

4 → 84

Calls

4 calls:

60.0ms	(pow.f64 (cbrt.f64 z) 3)
34.0ms	(cbrt.f64 z)
31.0ms	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
21.0ms	(+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3))))

rewrite60.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`

Counts

4 → 112

Calls

4 calls:

25.0ms	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
25.0ms	(+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3))))
2.0ms	(pow.f64 (cbrt.f64 z) 3)
1.0ms	(cbrt.f64 z)

simplify87.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-/l*_binary64`
307×	`distribute-rgt-in_binary64`
231×	`distribute-lft-in_binary64`
157×	`distribute-neg-in_binary64`
148×	`associate-+r+_binary64`

Counts

196 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	220	2792
1	560	2650
2	1920	2552
3	4847	2552

prune122.0ms (2.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	37.1b	(.f64 -1 (/.f64 (.f64 z (+.f64 y x)) y))
✓	8.1b	(*.f64 (+.f64 x y) (/.f64 1 (-.f64 1 (/.f64 y z))))
	9.2b	(.f64 (.f64 (cbrt.f64 (+.f64 y x)) (cbrt.f64 (+.f64 y x))) (/.f64 (cbrt.f64 (+.f64 y x)) (-.f64 1 (/.f64 y z))))
✓	8.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
	33.8b	(-.f64 (neg.f64 (fma.f64 (/.f64 z y) x (/.f64 z (/.f64 y z)))) z)
✓	8.5b	(/.f64 (+.f64 x y) (+.f64 1 (neg.f64 (/.f64 y (pow.f64 (cbrt.f64 z) 3)))))
✓	8.0b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

Compiler

Compiled 3769 to 2018 computations (46.5% saved)

regimes578.0ms (13.9%)

Accuracy

Total 0.6b remaining (97.6%)

Threshold costs 0.6b (97.6%)

Counts

75 → 3

Compiler

Compiled 5399 to 3403 computations (37% saved)

bsearch2.0ms (0.1%)

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

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
15×	`*-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	87
1	46	87
2	65	87
3	94	87
4	117	87
5	135	87
6	141	87
7	142	87
8	141	87

end102.0ms (2.4%)

Compiler: Compiled 229 to 140 computations (38.9% saved)

Details

analyze366.0ms (8.8%)

sample1.0s (24.6%)

simplify222.0ms (5.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series37.0ms (0.9%)

rewrite99.0ms (2.4%)

simplify126.0ms (3%)

prune139.0ms (3.3%)

localize7.0ms (0.2%)

series53.0ms (1.3%)

rewrite31.0ms (0.7%)

simplify87.0ms (2.1%)

prune197.0ms (4.7%)

localize7.0ms (0.2%)

series57.0ms (1.4%)

rewrite63.0ms (1.5%)

simplify233.0ms (5.6%)

prune300.0ms (7.2%)

localize10.0ms (0.3%)

series147.0ms (3.5%)

rewrite60.0ms (1.4%)

simplify87.0ms (2.1%)

prune122.0ms (2.9%)

regimes578.0ms (13.9%)

bsearch2.0ms (0.1%)

simplify6.0ms (0.2%)

end102.0ms (2.4%)

Profiling