Details

analyze404.0ms (13%)

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)

sample17.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 29 to 21 computations (27.6% saved)

simplify232.0ms (7.5%)

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

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

Compiler

Compiled 47 to 31 computations (34% saved)

localize7.0ms (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)))
✓	7.6b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

rewrite32.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cube-cbrt_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
8×	`add-exp-log_binary64`

Counts

2 → 92

Calls

2 calls:

14.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
12.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))

series21.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
10.0ms	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))

simplify107.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
548×	`fma-neg_binary64`
461×	`associate-/l*_binary64`
382×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-neg-in_binary64`

Counts

140 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2515
1	420	2453
2	1579	2413
3	4538	2405
4	4968	2405

prune97.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	207	3	210
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	207	4	211

Error

0.0b

Counts

211 → 4

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))
✓	0.1b	(-.f64 x (/.f64 y (fma.f64 x (/.f64 y 2) 1)))
	8.6b	(-.f64 x (.f64 (cbrt.f64 (.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.7b	(-.f64 x (/.f64 2 x))

Compiler

Compiled 3600 to 2356 computations (34.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))
✓	0.2b	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))
✓	7.5b	(*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))

rewrite104.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cube-cbrt_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
13×	`pow1_binary64`

Counts

3 → 139

Calls

3 calls:

14.0ms	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))
12.0ms	(*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))
12.0ms	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))

series32.0ms (1%)

Counts

3 → 72

Calls

3 calls:

11.0ms	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))
10.0ms	(*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1)))
10.0ms	(/.f64 1 (fma.f64 x (/.f64 y 2) 1))

simplify136.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
689×	`times-frac_binary64`
621×	`fma-neg_binary64`
203×	`unswap-sqr_binary64`
144×	`associate-r_binary64`

Counts

211 → 342

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	223	3780
1	555	3606
2	2071	3468
3	4593	3468
4	4992	3468

prune186.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	2	2
Picked	0	1	1
Done	1	0	1
Total	342	4	346

Error

Counts

346 → 4

Alt Table

Status	Error	Program
	8.6b	(-.f64 x (.f64 (cbrt.f64 (.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.7b	(-.f64 x (/.f64 2 x))
▶	0.2b	(-.f64 x (.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
✓	0.1b	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 4876 to 3325 computations (31.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	7.5b	(.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
	7.9b	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))
	7.9b	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))
✓	7.9b	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64`
12×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
6×	`clear-num_binary64`

Counts

2 → 74

Calls

2 calls:

14.0ms	(.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))
9.0ms	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))

series30.0ms (1%)

Counts

2 → 48

Calls

2 calls:

18.0ms	(cbrt.f64 (fma.f64 x (/.f64 y 2) 1))
11.0ms	(.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1))))

simplify108.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

838×	`times-frac_binary64`
465×	`fma-def_binary64`
421×	`fma-neg_binary64`
234×	`cancel-sign-sub-inv_binary64`
156×	`unswap-sqr_binary64`

Counts

122 → 196

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	205	2732
1	575	2478
2	1844	2349
3	4659	2339
4	4978	2339

prune307.0ms (9.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	442	0	442
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	442	4	446

Error

Counts

446 → 4

Alt Table

Status	Error	Program
▶	8.6b	(-.f64 x (.f64 (cbrt.f64 (.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.7b	(-.f64 x (/.f64 2 x))
✓	0.2b	(-.f64 x (.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
✓	0.1b	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 11587 to 8501 computations (26.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	7.6b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
	7.6b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
	7.6b	(/.f64 y (fma.f64 x (/.f64 y 2) 1))
✓	31.1b	(cbrt.f64 (*.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`cbrt-div_binary64`
5×	`frac-times_binary64`
5×	`pow1/3_binary64`
5×	`add-cube-cbrt_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

1 → 36

Calls

1 calls:

10.0ms

(cbrt.f64 (*.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

series25.0ms (0.8%)

Counts

1 → 24

Calls

1 calls:

25.0ms

(cbrt.f64 (*.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1))))

simplify107.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

480×	`times-frac_binary64`
315×	`associate-/r*_binary64`
304×	`associate-r_binary64`
285×	`fma-def_binary64`
277×	`associate-l_binary64`

Counts

60 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	1779
1	378	1721
2	1064	1618
3	4652	1570
4	4971	1570
5	4936	1570

prune278.0ms (9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	796	0	796
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	796	4	800

Error

Counts

800 → 4

Alt Table

Status	Error	Program
✓	8.6b	(-.f64 x (.f64 (cbrt.f64 (.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)) (/.f64 y (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (/.f64 y (fma.f64 x (/.f64 y 2) 1)))))
	21.7b	(-.f64 x (/.f64 2 x))
✓	0.2b	(-.f64 x (.f64 y (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))) (cbrt.f64 (fma.f64 x (/.f64 y 2) 1)))))
✓	0.1b	(-.f64 x (*.f64 y (/.f64 1 (fma.f64 x (/.f64 y 2) 1))))

Compiler

Compiled 8988 to 6194 computations (31.1% saved)

regimes212.0ms (6.8%)

Accuracy

Total 0.0b remaining (75.6%)

Threshold costs 0.0b (75.6%)

Compiler

Compiled 2375 to 1697 computations (28.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`distribute-rgt-neg-in_binary64`
8×	`cancel-sign-sub-inv_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	22	16
2	33	16
3	48	16
4	58	16
5	61	16
6	66	16
7	71	16
8	73	16
9	69	16

end0.0ms (0%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

sample580.0ms (18.7%)

Algorithm

1×

intervals

Results

318.0ms	7997×	body	128	valid
0.0ms	2×	body	2048	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 113 to 81 computations (28.3% saved)

Details

analyze404.0ms (13%)

sample17.0ms (0.6%)

simplify232.0ms (7.5%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

rewrite32.0ms (1%)

series21.0ms (0.7%)

simplify107.0ms (3.5%)

prune97.0ms (3.1%)

localize8.0ms (0.2%)

rewrite104.0ms (3.3%)

series32.0ms (1%)

simplify136.0ms (4.4%)

prune186.0ms (6%)

localize11.0ms (0.4%)

rewrite27.0ms (0.9%)

series30.0ms (1%)

simplify108.0ms (3.5%)

prune307.0ms (9.9%)

localize11.0ms (0.3%)

rewrite13.0ms (0.4%)

series25.0ms (0.8%)

simplify107.0ms (3.4%)

prune278.0ms (9%)

regimes212.0ms (6.8%)

simplify5.0ms (0.2%)

end0.0ms (0%)

sample580.0ms (18.7%)

Profiling