Details

analyze768.0ms (10.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	17×	body	128	invalid

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify115.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1536×	`fma-neg_binary64`
909×	`div-sub_binary64`
615×	`times-frac_binary64`
547×	`fma-def_binary64`
362×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	18	13
2	29	13
3	67	13
4	136	13
5	250	13
6	551	13
7	1395	13
8	2791	13
9	2886	13
10	3210	13
11	3295	13
12	3304	13
13	3354	13
14	4929	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

2.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
✓	2.5b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

series57.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
23.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

11.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
7.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify136.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

951×	`fma-def_binary64`
905×	`times-frac_binary64`
465×	`fma-neg_binary64`
154×	`associate-/l*_binary64`
144×	`+-commutative_binary64`

Counts

190 → 193

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4749
1	800	4617
2	2672	4102
3	4971	4102
4	5241	4102

prune154.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	188	5	193
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
	8.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	2.6b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
	5.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y))) 1) (*.f64 (/.f64 (cbrt.f64 (-.f64 x y)) (-.f64 z y)) t))
	3.2b	(.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y)))) (*.f64 (cbrt.f64 (/.f64 (-.f64 x y) (-.f64 z y))) t))
▶	2.9b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

Compiler

Compiled 4604 to 1305 computations (71.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z y) (-.f64 x y))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
✓	2.5b	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)

series76.0ms (1%)

Counts

3 → 120

Calls

3 calls:

34.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
21.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
21.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

rewrite85.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
335×	`add-sqr-sqrt_binary64`
323×	`*-un-lft-identity_binary64`
157×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`

Counts

3 → 332

Calls

3 calls:

21.0ms	(*.f64 (/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y))) t)
11.0ms	(/.f64 1 (/.f64 (-.f64 z y) (-.f64 x y)))
7.0ms	(/.f64 (-.f64 z y) (-.f64 x y))

simplify238.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

543×	`sub-neg_binary64`
246×	`associate-/l*_binary64`
241×	`fma-neg_binary64`
211×	`+-commutative_binary64`
210×	`associate--l+_binary64`

Counts

452 → 498

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	10707
1	1107	10159
2	4250	9700
3	5224	9700

prune337.0ms (4.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	495	3	498
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	499	5	504

Error

Counts

504 → 5

Alt Table

Status	Error	Program
	8.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
	3.0b	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)
	32.5b	(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 x y) t) (-.f64 z y))) (sqrt.f64 (/.f64 (*.f64 (-.f64 x y) t) (-.f64 z y))))
▶	2.8b	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)

Compiler

Compiled 12508 to 4012 computations (67.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 x y))
✓	0.2b	(/.f64 1 (/.f64 1 (-.f64 x y)))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y))))
✓	2.5b	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)

series68.0ms (0.9%)

Counts

4 → 132

Calls

4 calls:

34.0ms	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)
21.0ms	(*.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y))))
9.0ms	(/.f64 1 (-.f64 x y))
4.0ms	(/.f64 1 (/.f64 1 (-.f64 x y)))

rewrite122.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

371×	`add-exp-log_binary64`
305×	`times-frac_binary64`
251×	`add-sqr-sqrt_binary64`
209×	`*-un-lft-identity_binary64`
180×	`div-exp_binary64`

Counts

4 → 427

Calls

4 calls:

35.0ms	(*.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y))))
19.0ms	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)
10.0ms	(/.f64 1 (/.f64 1 (-.f64 x y)))
4.0ms	(/.f64 1 (-.f64 x y))

simplify310.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

437×	`cancel-sign-sub-inv_binary64`
369×	`sub-neg_binary64`
272×	`fma-neg_binary64`
228×	`associate-l_binary64`
214×	`associate-/l*_binary64`

Counts

559 → 603

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	395	9412
1	915	8809
2	3375	8518
3	4881	8515
4	4987	8515
5	4966	8515

prune458.0ms (6.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	603	0	603
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	603	5	608

Error

Counts

608 → 5

Alt Table

Status	Error	Program
	8.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
▶	3.0b	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)
	32.5b	(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 x y) t) (-.f64 z y))) (sqrt.f64 (/.f64 (*.f64 (-.f64 x y) t) (-.f64 z y))))
✓	2.8b	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)

Compiler

Compiled 14587 to 7233 computations (50.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 x y))
✓	0.2b	(*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))
✓	0.3b	(/.f64 1 (*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y))))
✓	2.5b	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)

series78.0ms (1.1%)

Counts

3 → 120

Calls

3 calls:

35.0ms	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)
22.0ms	(/.f64 1 (*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y))))
21.0ms	(*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log_binary64`
44×	`prod-exp_binary64`
35×	`add-sqr-sqrt_binary64`
34×	`div-exp_binary64`
31×	`add-cbrt-cube_binary64`

Counts

3 → 147

Calls

3 calls:

15.0ms	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)
12.0ms	(*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))
9.0ms	(/.f64 1 (*.f64 (-.f64 z y) (/.f64 1 (-.f64 x y))))

simplify164.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

532×	`sub-neg_binary64`
330×	`fma-neg_binary64`
225×	`times-frac_binary64`
214×	`associate-/l*_binary64`
213×	`+-commutative_binary64`

Counts

267 → 306

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	370	6256
1	972	5732
2	3881	5342
3	4694	5340
4	5084	5340

prune227.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	364	0	364
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	364	5	369

Error

Counts

369 → 5

Alt Table

Status	Error	Program
	8.2b	(*.f64 (-.f64 x y) (/.f64 t (-.f64 z y)))
	12.1b	(-.f64 (/.f64 (.f64 t x) (-.f64 z y)) (/.f64 (.f64 y t) (-.f64 z y)))
✓	3.0b	(.f64 (/.f64 1 (.f64 (-.f64 z y) (/.f64 1 (-.f64 x y)))) t)
	32.5b	(.f64 (sqrt.f64 (/.f64 (.f64 (-.f64 x y) t) (-.f64 z y))) (sqrt.f64 (/.f64 (*.f64 (-.f64 x y) t) (-.f64 z y))))
✓	2.8b	(.f64 (.f64 (/.f64 1 (-.f64 z y)) (/.f64 1 (/.f64 1 (-.f64 x y)))) t)

Compiler

Compiled 8348 to 3576 computations (57.2% saved)

regimes3.0s (41.4%)

Accuracy

Total 1.9b remaining (98.5%)

Threshold costs 0b (0%)

Counts

263 → 3

Compiler

Compiled 33801 to 20529 computations (39.3% saved)

bsearch39.0ms (0.5%)

Steps

Iters	Range		Point
4	5.060670651257311e-292	9.694869168482788e-292	6.6024302915393845e-292
9	-7.658881820320868e-99	-8.822603904862417e-106	-1.888243183884543e-104

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	51
1	25	51
2	31	51
3	33	51
4	34	51
5	34	51

end1.0ms (0%)

Compiler: Compiled 39 to 18 computations (53.8% saved)

sample745.0ms (10.1%)

Algorithm

1×

intervals

Results

321.0ms	8000×	body	128	valid
27.0ms	661×	body	128	invalid

Compiler

Compiled 150 to 85 computations (43.3% saved)

Details

analyze768.0ms (10.4%)

sample23.0ms (0.3%)

simplify115.0ms (1.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series57.0ms (0.8%)

rewrite28.0ms (0.4%)

simplify136.0ms (1.9%)

prune154.0ms (2.1%)

localize8.0ms (0.1%)

series76.0ms (1%)

rewrite85.0ms (1.2%)

simplify238.0ms (3.2%)

prune337.0ms (4.6%)

localize10.0ms (0.1%)

series68.0ms (0.9%)

rewrite122.0ms (1.7%)

simplify310.0ms (4.2%)

prune458.0ms (6.2%)

localize9.0ms (0.1%)

series78.0ms (1.1%)

rewrite49.0ms (0.7%)

simplify164.0ms (2.2%)

prune227.0ms (3.1%)

regimes3.0s (41.4%)

bsearch39.0ms (0.5%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample745.0ms (10.1%)

Profiling