Details

analyze583.0ms (11.3%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
50%	50%	0.1%	5
62.4%	37.5%	0.1%	6
74.9%	25%	0.1%	7
81.2%	18.7%	0.1%	8
87.4%	12.5%	0.1%	9
90.5%	9.4%	0.1%	10
93.7%	6.2%	0.1%	11
95.2%	4.7%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 14 to 10 computations (28.6% saved)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

22.0ms

256×

body

128

valid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify321.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

2174×	`fma-neg_binary64`
1504×	`div-sub_binary64`
895×	`associate-/l/_binary64`
827×	`fma-def_binary64`
818×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	16
2	28	14
3	41	14
4	57	14
5	91	14
6	134	14
7	193	14
8	356	14
9	521	14
10	825	14
11	1475	14
12	2002	14
13	1877	14
14	1931	14
15	1961	14
16	1967	14
17	1967	14
18	2590	14
19	2366	14
20	2366	14
21	3254	14
22	4052	14
23	4024	14
24	4504	14
25	4470	14
26	4706	14
27	4913	14

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 47 to 31 computations (34% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	7.4b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series34.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
13.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
46×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

2 → 100

Calls

2 calls:

13.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
4.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

simplify232.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
422×	`fma-neg_binary64`
414×	`associate-/l*_binary64`
273×	`cancel-sign-sub-inv_binary64`
190×	`times-frac_binary64`

Counts

148 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4990
1	637	3475
2	1683	2934
3	4633	2926
4	4994	2926
5	4994	2926
6	4795	2926

prune260.0ms (5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	4	150

Error

Counts

150 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
	10.0b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
	0.6b	(-.f64 x (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (fma.f64 x (/.f64 y 2) 1) (cbrt.f64 y))))
▶	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 4913 to 3115 computations (36.6% saved)

localize17.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
✓	7.3b	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

series41.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

16.0ms	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))
15.0ms	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
10.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

rewrite131.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

354×	`times-frac_binary64`
252×	`add-sqr-sqrt_binary64`
243×	`*-un-lft-identity_binary64`
238×	`add-cube-cbrt_binary64`
132×	`prod-diff_binary64`

Counts

3 → 306

Calls

3 calls:

26.0ms	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))
5.0ms	(/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y))
3.0ms	(/.f64 (fma.f64 x (/.f64 y 2) 1) y)

simplify646.0ms (12.5%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-neg_binary64`
519×	`times-frac_binary64`
405×	`cancel-sign-sub-inv_binary64`
233×	`distribute-rgt-out_binary64`
211×	`distribute-rgt-neg-in_binary64`

Counts

378 → 397

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	315	15274
1	764	10817
2	2261	8904
3	4298	8522
4	4986	8522
5	4972	8522
6	4618	8522

prune730.0ms (14.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	396	1	397
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	397	4	401

Error

Counts

401 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
	10.0b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
▶	0.0b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 17383 to 12196 computations (29.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/2 x (/.f64 1 y))
✓	0.0b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(/.f64 1 (fma.f64 1/2 x (/.f64 1 y)))

series28.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

13.0ms	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
10.0ms	(/.f64 1 (fma.f64 1/2 x (/.f64 1 y)))
5.0ms	(fma.f64 1/2 x (/.f64 1 y))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
53×	`add-cube-cbrt_binary64`
47×	`times-frac_binary64`
39×	`prod-diff_binary64`

Counts

3 → 116

Calls

3 calls:

6.0ms	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
2.0ms	(/.f64 1 (fma.f64 1/2 x (/.f64 1 y)))
0.0ms	(fma.f64 1/2 x (/.f64 1 y))

simplify145.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
522×	`times-frac_binary64`
513×	`associate-l_binary64`
479×	`associate-r_binary64`
225×	`cancel-sign-sub-inv_binary64`

Counts

188 → 167

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	4341
1	402	3476
2	1164	2956
3	4376	2956
4	4927	2956

prune213.0ms (4.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	167	4	171

Error

Counts

171 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
▶	10.0b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
✓	0.0b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 5033 to 3776 computations (25% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
✓	0.2b	(pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)
	7.4b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
✓	37.5b	(cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3))

series109.0ms (2.1%)

Counts

3 → 72

Calls

3 calls:

39.0ms	(pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)
36.0ms	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
33.0ms	(cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3))

rewrite120.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`cbrt-prod_binary64`
148×	`add-sqr-sqrt_binary64`
135×	`*-un-lft-identity_binary64`
133×	`add-cube-cbrt_binary64`
110×	`times-frac_binary64`

Counts

3 → 256

Calls

3 calls:

35.0ms	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
7.0ms	(pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)
6.0ms	(cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3))

simplify363.0ms (7%)

Algorithm

1×	egg-herbie

Rules

430×	`unswap-sqr_binary64`
392×	`fma-neg_binary64`
285×	`log-prod_binary64`
247×	`exp-prod_binary64`
195×	`sub-neg_binary64`

Counts

328 → 290

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	427	11462
1	972	8604
2	2944	7093
3	4342	7061
4	4906	7061

prune344.0ms (6.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	336	4	340

Error

Counts

340 → 4

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
✓	10.0b	(-.f64 x (cbrt.f64 (pow.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) 3)))
✓	0.0b	(-.f64 x (/.f64 1 (fma.f64 1/2 x (/.f64 1 y))))
✓	0.1b	(-.f64 x (/.f64 1 (/.f64 (fma.f64 x (/.f64 y 2) 1) y)))

Compiler

Compiled 11947 to 8425 computations (29.5% saved)

regimes98.0ms (1.9%)

Accuracy

Total 0.0b remaining (84.4%)

Threshold costs 0.0b (84.4%)

Counts

30 → 1

Compiler

Compiled 1256 to 887 computations (29.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	13	14
2	19	14
3	23	14
4	26	14
5	27	14
6	26	14

end0.0ms (0%)

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

sample615.0ms (11.9%)

Algorithm

1×

intervals

Results

324.0ms	7998×	body	128	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 81 to 58 computations (28.4% saved)

Details

analyze583.0ms (11.3%)

sample37.0ms (0.7%)

simplify321.0ms (6.2%)

prune6.0ms (0.1%)

localize13.0ms (0.2%)

series34.0ms (0.7%)

rewrite27.0ms (0.5%)

simplify232.0ms (4.5%)

prune260.0ms (5%)

localize17.0ms (0.3%)

series41.0ms (0.8%)

rewrite131.0ms (2.5%)

simplify646.0ms (12.5%)

prune730.0ms (14.1%)

localize6.0ms (0.1%)

series28.0ms (0.5%)

rewrite17.0ms (0.3%)

simplify145.0ms (2.8%)

prune213.0ms (4.1%)

localize20.0ms (0.4%)

series109.0ms (2.1%)

rewrite120.0ms (2.3%)

simplify363.0ms (7%)

prune344.0ms (6.7%)

regimes98.0ms (1.9%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample615.0ms (11.9%)

Profiling