Details

analyze127.0ms (4.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 21 to 17 computations (19% saved)

sample36.0ms (1.2%)

Algorithm

1×

intervals

Results

25.0ms

256×

body

128

valid

Compiler

Compiled 42 to 34 computations (19% saved)

simplify111.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

708×	`fma-def_binary64`
684×	`fma-neg_binary64`
640×	`associate-/l*_binary64`
583×	`associate-/r*_binary64`
496×	`distribute-neg-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	34	22
2	59	22
3	94	22
4	131	22
5	171	20
6	250	20
7	423	20
8	810	20
9	1376	20
10	2197	20
11	2355	20
12	3878	20
13	4822	20
14	4656	20

prune7.0ms (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

Counts

3 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
▶	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Status

Error

Program

0.0b

(*.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)) (+.f64 1 (*.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x))

▶

0.0b

(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Compiler

Compiled 107 to 83 computations (22.4% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))
✓	0.1b	(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)
✓	0.1b	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
✓	11.5b	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))

rewrite81.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-cube-cbrt_binary64`
16×	`pow1_binary64`
16×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`fma-udef_binary64`

Counts

4 → 145

Calls

4 calls:

21.0ms	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))
18.0ms	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))
17.0ms	(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)
15.0ms	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)

series35.0ms (1.1%)

Counts

4 → 48

Calls

4 calls:

10.0ms	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))
9.0ms	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
8.0ms	(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)
8.0ms	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

simplify266.0ms (8.6%)

Algorithm

1×	egg-herbie

Rules

761×	`times-frac_binary64`
549×	`fma-neg_binary64`
402×	`fma-def_binary64`
293×	`associate-/l*_binary64`
220×	`distribute-rgt-in_binary64`

Counts

193 → 270

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	2534
1	461	2346
2	1341	2289
3	4904	2281
4	5233	2281

prune293.0ms (9.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	269	1	270
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	270	2	272

Error

Counts

272 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)))
✓	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Status

Error

Program

▶

0.0b

(fma.f64 x -6369080665019903/9007199254740992 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)))

✓

0.0b

(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Compiler

Compiled 3829 to 2944 computations (23.1% saved)

localize22.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
✓	0.2b	(pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)
	11.5b	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))
✓	17.7b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3))

rewrite48.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cube-cbrt_binary64`
9×	`cube-div_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`add-exp-log_binary64`
6×	`pow1/3_binary64`

Counts

2 → 87

Calls

2 calls:

22.0ms

(pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)

19.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3))

series19.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

12.0ms

(pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)

7.0ms

(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3))

simplify183.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-l_binary64`
486×	`associate-r_binary64`
312×	`fma-neg_binary64`
291×	`log-prod_binary64`
179×	`fma-def_binary64`

Counts

111 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	1796
1	325	1595
2	980	1573
3	4502	1563
4	5187	1563

prune342.0ms (11.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	316	0	316
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	316	2	318

Error

Counts

318 → 2

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)))
✓	0.0b	(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Status

Error

Program

✓

0.0b

(fma.f64 x -6369080665019903/9007199254740992 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)))

✓

0.0b

(fma.f64 x -6369080665019903/9007199254740992 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)))

Compiler

Compiled 4923 to 3923 computations (20.3% saved)

regimes252.0ms (8.1%)

Accuracy

Total 0.0b remaining (40.8%)

Threshold costs 0.0b (40.8%)

Compiler

Compiled 1814 to 1418 computations (21.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	18	22
2	17	22

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample1.3s (40.4%)

Algorithm

1×

intervals

Results

852.0ms

8000×

body

128

valid

Compiler

Compiled 74 to 58 computations (21.6% saved)

Details

analyze127.0ms (4.1%)

sample36.0ms (1.2%)

simplify111.0ms (3.6%)

prune7.0ms (0.2%)

localize18.0ms (0.6%)

rewrite81.0ms (2.6%)

series35.0ms (1.1%)

simplify266.0ms (8.6%)

prune293.0ms (9.5%)

localize22.0ms (0.7%)

rewrite48.0ms (1.5%)

series19.0ms (0.6%)

simplify183.0ms (5.9%)

prune342.0ms (11.1%)

regimes252.0ms (8.1%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample1.3s (40.4%)

Profiling