Details

analyze109.0ms (4.2%)

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)

sample23.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 42 to 34 computations (19% saved)

simplify99.0ms (3.9%)

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

prune4.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	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)))
▶	0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))

Status

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)))

▶

0.0b

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

Compiler

Compiled 107 to 83 computations (22.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))
✓	0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
✓	0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
✓	14.4b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite17.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`

Counts

4 → 89

Calls

4 calls:

6.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
4.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
2.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
2.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))

series44.0ms (1.7%)

Counts

4 → 48

Calls

4 calls:

30.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
5.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))
4.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify125.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
510×	`distribute-rgt-in_binary64`
479×	`distribute-lft-in_binary64`
413×	`fma-neg_binary64`
292×	`*-commutative_binary64`

Counts

137 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2224
1	467	1694
2	1448	1673
3	4190	1663
4	4963	1663
5	4895	1663

prune178.0ms (6.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	251	3	254

Error

Counts

254 → 3

Alt Table

Status	Error	Program
	0.2b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (pow.f64 (exp.f64 (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992)) x)))) 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)))
	0.5b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (fma.f64 (sqrt.f64 162377988252285/70368744177664) (sqrt.f64 162377988252285/70368744177664) (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))

Compiler

Compiled 4690 to 3735 computations (20.4% saved)

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)
✓	0.1b	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
✓	14.4b	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms

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

0.0ms

(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)

0.0ms

(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)

series19.0ms (0.7%)

Counts

3 → 36

Calls

3 calls:

9.0ms

(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)

5.0ms

(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)

5.0ms

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

simplify141.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-neg_binary64`
462×	`fma-def_binary64`
422×	`associate-l_binary64`
367×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`

Counts

85 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1395
1	223	1254
2	550	1249
3	1399	1239
4	4641	1239
5	4993	1239
6	4999	1239
7	4900	1239

prune82.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Error

Counts

131 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

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)))

Compiler

Compiled 1772 to 1358 computations (23.4% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)
	0.1b	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1) (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)))
✓	14.3b	(/.f64 (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1) (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

2 → 107

Calls

2 calls:

5.0ms

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

2.0ms

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

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms

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

4.0ms

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

simplify150.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

872×	`fma-def_binary64`
477×	`distribute-rgt-in_binary64`
468×	`distribute-lft-in_binary64`
262×	`cancel-sign-sub-inv_binary64`
223×	`fma-neg_binary64`

Counts

131 → 228

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	162	3573
1	347	3248
2	902	3211
3	2308	3197
4	4942	3197

prune212.0ms (8.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	298	2	300

Error

Counts

300 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

▶

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)))

Compiler

Compiled 5352 to 4249 computations (20.6% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688)
✓	0.1b	(pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3)
	14.4b	(/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1))
✓	19.9b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 3881060112545747418883236907595/20282409603651670423947251286016 1034198505402457344669710228355/633825300114114700748351602688) (fma.f64 x (fma.f64 x 3228900788839551/72057594037927936 8937753748486939/9007199254740992) 1)) 3))

rewrite12.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
32×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 92

Calls

2 calls:

3.0ms

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

3.0ms

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

series11.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

6.0ms

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

4.0ms

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

simplify162.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

596×	`times-frac_binary64`
399×	`associate-/l*_binary64`
366×	`fma-def_binary64`
317×	`log-div_binary64`
284×	`unswap-sqr_binary64`

Counts

116 → 208

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	187	3313
1	470	2990
2	1369	2904
3	4493	2892
4	5170	2892

prune187.0ms (7.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	334	2	336

Error

Counts

336 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

✓

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)))

Compiler

Compiled 4712 to 3762 computations (20.2% saved)

regimes291.0ms (11.3%)

Accuracy

Total 0.0b remaining (36.4%)

Threshold costs 0.0b (36.4%)

Compiler

Compiled 5213 to 4142 computations (20.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	23
1	16	23
2	15	23

end1.0ms (0%)

Compiler: Compiled 18 to 14 computations (22.2% saved)

sample639.0ms (24.8%)

Algorithm

1×

intervals

Results

427.0ms

8000×

body

128

valid

Compiler

Compiled 77 to 61 computations (20.8% saved)

Details

analyze109.0ms (4.2%)

sample23.0ms (0.9%)

simplify99.0ms (3.9%)

prune4.0ms (0.2%)

localize10.0ms (0.4%)

rewrite17.0ms (0.7%)

series44.0ms (1.7%)

simplify125.0ms (4.8%)

prune178.0ms (6.9%)

localize9.0ms (0.3%)

rewrite5.0ms (0.2%)

series19.0ms (0.7%)

simplify141.0ms (5.5%)

prune82.0ms (3.2%)

localize10.0ms (0.4%)

rewrite13.0ms (0.5%)

series8.0ms (0.3%)

simplify150.0ms (5.8%)

prune212.0ms (8.2%)

localize12.0ms (0.5%)

rewrite12.0ms (0.5%)

series11.0ms (0.4%)

simplify162.0ms (6.3%)

prune187.0ms (7.3%)

regimes291.0ms (11.3%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample639.0ms (24.8%)

Profiling