Details

analyze66.0ms (2.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	24.9%	13
75%	0%	25%	14

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample28.0ms (0.9%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 22 to 18 computations (18.2% saved)

simplify48.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

271×	`fma-def_binary64`
257×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
55×	`sub-neg_binary64`
32×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	25	11
2	54	11
3	122	11
4	222	9
5	361	9
6	423	9
7	587	9
8	645	9
9	664	9
10	593	9

prune6.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(-.f64 1 (.f64 x (+.f64 2278821411449471/9007199254740992 (.f64 x 1080863910568919/9007199254740992))))
▶	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

Compiler

Compiled 53 to 41 computations (22.6% saved)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

series11.0ms (0.4%)

Counts

1 → 12

Calls

1 calls:

11.0ms

(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

450×	`exp-prod_binary64`
447×	`fma-neg_binary64`
392×	`neg-mul-1_binary64`
337×	`cancel-sign-sub-inv_binary64`
335×	`times-frac_binary64`

Counts

22 → 36

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	277
1	57	213
2	117	210
3	376	210
4	1865	210
5	3696	210
6	5001	210

prune39.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	34	4	38

Error

0.0b

Counts

38 → 4

Alt Table

Status	Error	Program
	0.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)) (cbrt.f64 (fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1))) (cbrt.f64 (fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)))
	14.7b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1) 3))
▶	0.1b	(-.f64 1 (+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

Compiler

Compiled 321 to 248 computations (22.7% saved)

localize12.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x))
✓	0.2b	(*.f64 1080863910568919/9007199254740992 (pow.f64 x 2))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
7×	`add-exp-log_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 43

Calls

2 calls:

8.0ms	(*.f64 1080863910568919/9007199254740992 (pow.f64 x 2))
7.0ms	(+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x))

series41.0ms (1.3%)

Counts

2 → 3

Calls

2 calls:

21.0ms	(+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x))
20.0ms	(*.f64 1080863910568919/9007199254740992 (pow.f64 x 2))

simplify111.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

926×	`fma-neg_binary64`
448×	`distribute-rgt-out_binary64`
438×	`associate-l_binary64`
356×	`associate-r_binary64`
350×	`cancel-sign-sub-inv_binary64`

Counts

46 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	79	575
1	193	481
2	520	452
3	2083	449
4	4173	448
5	4966	448

prune130.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	2	0	2
Picked	0	1	1
Done	0	1	1
Total	84	4	88

Error

Counts

88 → 4

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x)))
	14.6b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2)))) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

Compiler

Compiled 1279 to 1019 computations (20.3% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x))
✓	0.1b	(*.f64 x (sqrt.f64 1080863910568919/9007199254740992))
✓	0.2b	(.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (*.f64 x (sqrt.f64 1080863910568919/9007199254740992))))
✓	0.2b	(.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))

rewrite51.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
20×	`pow1_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`

Counts

4 → 84

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (*.f64 x (sqrt.f64 1080863910568919/9007199254740992))))
13.0ms	(+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x))
10.0ms	(.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))
7.0ms	(*.f64 x (sqrt.f64 1080863910568919/9007199254740992))

series125.0ms (4.1%)

Counts

4 → 48

Calls

4 calls:

40.0ms	(.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (*.f64 x (sqrt.f64 1080863910568919/9007199254740992))))
33.0ms	(+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x))
29.0ms	(.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))
23.0ms	(*.f64 x (sqrt.f64 1080863910568919/9007199254740992))

simplify170.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

652×	`fma-neg_binary64`
493×	`unswap-sqr_binary64`
358×	`*-commutative_binary64`
348×	`fma-def_binary64`
300×	`cancel-sign-sub-inv_binary64`

Counts

132 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1360
1	274	1253
2	1004	1182
3	2247	1170
4	4837	1170
5	5187	1170

prune210.0ms (6.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	232	4	236

Error

Counts

236 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x)))
▶	14.6b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2)))) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

Compiler

Compiled 2604 to 2045 computations (21.5% saved)

localize25.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))
✓	0.2b	(*.f64 (pow.f64 x 2) (pow.f64 x 2))
✓	1.0b	(.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992)
✓	25.2b	(cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (*.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))))

rewrite78.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-exp-log_binary64`
69×	`prod-exp_binary64`
34×	`pow-exp_binary64`
34×	`pow-to-exp_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

4 → 169

Calls

4 calls:

27.0ms	(cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (*.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))))
16.0ms	(.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))
12.0ms	(*.f64 (pow.f64 x 2) (pow.f64 x 2))
9.0ms	(.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992)

series85.0ms (2.8%)

Counts

4 → 36

Calls

4 calls:

31.0ms	(.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))
31.0ms	(cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (*.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2))))
23.0ms	(*.f64 (pow.f64 x 2) (pow.f64 x 2))
0.0ms	(.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992)

simplify221.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-def_binary64`
384×	`sqr-pow_binary64`
294×	`times-frac_binary64`
251×	`*-commutative_binary64`
239×	`log-prod_binary64`

Counts

205 → 367

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	150	2096
1	207	1272
2	530	1172
3	786	1145
4	1379	1099
5	3061	1099
6	4742	1099
7	4825	1099

prune402.0ms (13.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	367	0	367
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	367	4	371

Error

Counts

371 → 4

Alt Table

Status	Error	Program
✓	0.2b	(-.f64 1 (+.f64 (.f64 (sqrt.f64 1080863910568919/9007199254740992) (.f64 x (.f64 x (sqrt.f64 1080863910568919/9007199254740992)))) (.f64 2278821411449471/9007199254740992 x)))
✓	14.6b	(-.f64 1 (+.f64 (cbrt.f64 (.f64 (.f64 (.f64 1080863910568919/9007199254740992 1080863910568919/9007199254740992) 1080863910568919/9007199254740992) (.f64 (.f64 (pow.f64 x 2) (pow.f64 x 2)) (pow.f64 x 2)))) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(-.f64 1 (+.f64 (.f64 1080863910568919/9007199254740992 (pow.f64 x 2)) (.f64 2278821411449471/9007199254740992 x)))
✓	0.1b	(fma.f64 x (fma.f64 x -1080863910568919/9007199254740992 -2278821411449471/9007199254740992) 1)

Compiler

Compiled 5200 to 4291 computations (17.5% saved)

regimes259.0ms (8.5%)

Accuracy

Total 0.1b remaining (91.3%)

Threshold costs 0.1b (91.3%)

Compiler

Compiled 1898 to 1568 computations (17.4% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	15	14
2	19	14
3	21	14
4	22	14
5	21	14

end1.0ms (0%)

Compiler: Compiled 11 to 9 computations (18.2% saved)

sample811.0ms (26.5%)

Algorithm

1×

intervals

Results

426.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 84 to 69 computations (17.9% saved)

Details

analyze66.0ms (2.2%)

sample28.0ms (0.9%)

simplify48.0ms (1.6%)

prune6.0ms (0.2%)

localize8.0ms (0.3%)

rewrite2.0ms (0.1%)

series11.0ms (0.4%)

simplify79.0ms (2.6%)

prune39.0ms (1.3%)

localize12.0ms (0.4%)

rewrite19.0ms (0.6%)

series41.0ms (1.3%)

simplify111.0ms (3.6%)

prune130.0ms (4.3%)

localize16.0ms (0.5%)

rewrite51.0ms (1.7%)

series125.0ms (4.1%)

simplify170.0ms (5.6%)

prune210.0ms (6.9%)

localize25.0ms (0.8%)

rewrite78.0ms (2.6%)

series85.0ms (2.8%)

simplify221.0ms (7.2%)

prune402.0ms (13.1%)

regimes259.0ms (8.5%)

simplify7.0ms (0.2%)

end1.0ms (0%)

sample811.0ms (26.5%)

Profiling