Details

analyze421.0ms (10.3%)

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
12.5%	87.4%	0.1%	4
12.5%	87.4%	0.1%	5
15.6%	84.3%	0.1%	6
32.8%	67.1%	0.1%	7
38.2%	61.6%	0.1%	8
46%	53.8%	0.1%	9
62.6%	37.3%	0.1%	10
67.2%	32.7%	0.1%	11
71.1%	28.8%	0.1%	12
81.6%	18.2%	0.1%	13
84.1%	15.7%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample18.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify215.0ms (5.2%)

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

6.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	6.2b	(/.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))
✓	6.2b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

series31.0ms (0.8%)

Counts

2 → 42

Calls

2 calls:

27.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
5.0ms	(-.f64 1 (/.f64 y z))

rewrite29.0ms (0.7%)

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:

9.0ms	(-.f64 1 (/.f64 y z))
8.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

simplify134.0ms (3.3%)

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

prune154.0ms (3.8%)

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
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	6.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
▶	6.3b	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))
	35.2b	(-.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))))

Compiler

Compiled 5113 to 2009 computations (60.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z)))
✓	0.2b	(*.f64 (neg.f64 y) (/.f64 1 z))
✓	6.2b	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))

series39.0ms (1%)

Counts

3 → 84

Calls

3 calls:

28.0ms	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
6.0ms	(*.f64 (neg.f64 y) (/.f64 1 z))
5.0ms	(+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z)))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
23×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`

Counts

3 → 100

Calls

3 calls:

11.0ms	(*.f64 (neg.f64 y) (/.f64 1 z))
5.0ms	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
3.0ms	(+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z)))

simplify100.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary64`
842×	`fma-def_binary64`
285×	`fma-neg_binary64`
157×	`distribute-neg-in_binary64`
148×	`associate-+r+_binary64`

Counts

184 → 192

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	226	2861
1	601	2738
2	1961	2625
3	4961	2625
4	5104	2625

prune135.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	192	5	197

Error

0.0b

Counts

197 → 5

Alt Table

Status	Error	Program
	33.1b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	6.3b	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
▶	6.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))

Compiler

Compiled 3994 to 2003 computations (49.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))
✓	0.3b	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
✓	1.8b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
✓	6.4b	(cbrt.f64 (-.f64 1 (/.f64 y z)))

series96.0ms (2.3%)

Counts

4 → 108

Calls

4 calls:

27.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
27.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
23.0ms	(*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))
19.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

rewrite106.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`add-sqr-sqrt_binary64`
104×	`*-un-lft-identity_binary64`
83×	`cbrt-prod_binary64`
80×	`times-frac_binary64`
62×	`add-exp-log_binary64`

Counts

4 → 240

Calls

4 calls:

38.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
15.0ms	(*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))
13.0ms	(/.f64 1 (*.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
7.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

simplify229.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-def_binary64`
313×	`associate-r_binary64`
275×	`associate-/l*_binary64`
274×	`associate-/r*_binary64`
274×	`times-frac_binary64`

Counts

348 → 430

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	539	12243
1	1436	10422
2	4731	10266
3	5291	10266

prune453.0ms (11%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	532	0	532
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	532	5	537

Error

0.0b

Counts

537 → 5

Alt Table

Status	Error	Program
▶	33.1b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	6.3b	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
✓	6.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))

Compiler

Compiled 22127 to 12538 computations (43.3% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 z (/.f64 z (/.f64 y z)))
✓	0.1b	(/.f64 z (/.f64 y z))
✓	5.9b	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

series45.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

25.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))
10.0ms	(/.f64 z (/.f64 y z))
9.0ms	(+.f64 z (/.f64 z (/.f64 y z)))

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
49×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
46×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

3 → 101

Calls

3 calls:

10.0ms	(+.f64 z (/.f64 z (/.f64 y z)))
4.0ms	(/.f64 z (/.f64 y z))
0.0ms	(fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z))))

simplify165.0ms (4%)

Algorithm

1×	egg-herbie

Rules

576×	`associate-/l*_binary64`
513×	`associate-/r/_binary64`
418×	`fma-neg_binary64`
379×	`distribute-rgt-out_binary64`
377×	`associate-l_binary64`

Counts

185 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	2697
1	403	2375
2	1232	2221
3	3439	2197
4	4720	2197
5	4992	2197
6	4996	2197
7	4955	2197

prune86.0ms (2.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	177	1	178
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	177	6	183

Error

Counts

183 → 6

Alt Table

Status	Error	Program
✓	33.1b	(neg.f64 (fma.f64 (/.f64 z y) x (+.f64 z (/.f64 z (/.f64 y z)))))
✓	6.3b	(/.f64 (+.f64 x y) (+.f64 1 (*.f64 (neg.f64 y) (/.f64 1 z))))
	34.7b	(neg.f64 (+.f64 (/.f64 (*.f64 z x) y) (+.f64 (/.f64 (pow.f64 z 2) y) z)))
	33.9b	(neg.f64 (*.f64 (+.f64 (/.f64 x y) 1) z))
✓	6.7b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z))))) (/.f64 (+.f64 x y) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
	35.1b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 y x) (-.f64 1 (/.f64 y z))) 3))

Compiler

Compiled 3586 to 1067 computations (70.2% saved)

regimes875.0ms (21.3%)

Accuracy

Total 0.1b remaining (88.4%)

Threshold costs 0.1b (88.4%)

Counts

114 → 3

Compiler

Compiled 7947 to 5193 computations (34.7% saved)

bsearch3.0ms (0.1%)

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
9×	`*-commutative_binary64`
8×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	24	83
1	39	83
2	56	81
3	70	81
4	79	81
5	83	81
6	84	81
7	82	81

end1.0ms (0%)

Compiler: Compiled 58 to 31 computations (46.6% saved)

sample678.0ms (16.5%)

Algorithm

1×

intervals

Results

338.0ms	7998×	body	128	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 177 to 112 computations (36.7% saved)

Details

analyze421.0ms (10.3%)

sample18.0ms (0.4%)

simplify215.0ms (5.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series31.0ms (0.8%)

rewrite29.0ms (0.7%)

simplify134.0ms (3.3%)

prune154.0ms (3.8%)

localize8.0ms (0.2%)

series39.0ms (1%)

rewrite24.0ms (0.6%)

simplify100.0ms (2.4%)

prune135.0ms (3.3%)

localize11.0ms (0.3%)

series96.0ms (2.3%)

rewrite106.0ms (2.6%)

simplify229.0ms (5.6%)

prune453.0ms (11%)

localize8.0ms (0.2%)

series45.0ms (1.1%)

rewrite21.0ms (0.5%)

simplify165.0ms (4%)

prune86.0ms (2.1%)

regimes875.0ms (21.3%)

bsearch3.0ms (0.1%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample678.0ms (16.5%)

Profiling