Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample98.0ms (3.1%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify57.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
510×	`distribute-rgt-in_binary64`
489×	`distribute-lft-in_binary64`
463×	`fma-neg_binary64`
415×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	40	26
2	185	17
3	915	13
4	2340	13
5	4455	13
6	4958	13
7	5077	13

prune4.0ms (0.1%)

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

0.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	45.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	0.9b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.6b	(/.f64 1 (*.f64 i i))
✓	1.0b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))
2.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-sqr-sqrt_binary64`
54×	`*-un-lft-identity_binary64`
49×	`times-frac_binary64`
34×	`add-cube-cbrt_binary64`
21×	`prod-diff_binary64`

Counts

3 → 134

Calls

3 calls:

6.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
6.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
3.0ms	(/.f64 1 (*.f64 i i))

simplify137.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
446×	`unswap-sqr_binary64`
409×	`associate-l_binary64`
361×	`fma-def_binary64`
294×	`associate-r_binary64`

Counts

170 → 196

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	203	2573
1	382	2324
2	977	2089
3	3418	2089
4	4641	2081
5	4949	2081
6	4780	2081

prune175.0ms (5.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	195	3	198

Error

Counts

198 → 3

Alt Table

Status	Error	Program
	45.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
	31.6b	(*.f64 -1/4 (pow.f64 i 2))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 3724 to 2758 computations (25.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 2 (/.f64 1 i))
✓	0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
✓	0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series11.0ms (0.3%)

Counts

4 → 39

Calls

4 calls:

4.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
3.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
3.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
1.0ms	(-.f64 2 (/.f64 1 i))

rewrite68.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

158×	`add-sqr-sqrt_binary64`
143×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
90×	`add-cube-cbrt_binary64`
39×	`prod-diff_binary64`

Counts

4 → 240

Calls

4 calls:

24.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
8.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
7.0ms	(-.f64 2 (/.f64 1 i))
6.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify198.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
446×	`fma-neg_binary64`
279×	`times-frac_binary64`
230×	`cancel-sign-sub-inv_binary64`
190×	`distribute-rgt-in_binary64`

Counts

279 → 349

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	322	5864
1	811	4962
2	2486	4702
3	4394	4700
4	4948	4700
5	4844	4700

prune291.0ms (9.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	349	3	352

Error

Counts

352 → 3

Alt Table

Status	Error	Program
	45.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
▶	31.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 9337 to 7891 computations (15.5% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 -1/4 (pow.f64 i 2))

series3.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

3.0ms

(*.f64 -1/4 (pow.f64 i 2))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`associate-r_binary64`
6×	`add-exp-log_binary64`
4×	`unswap-sqr_binary64`
4×	`unpow-prod-down_binary64`

Counts

1 → 29

Calls

1 calls:

4.0ms

(*.f64 -1/4 (pow.f64 i 2))

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
644×	`unswap-sqr_binary64`
397×	`log-prod_binary64`
394×	`sqr-pow_binary64`
337×	`*-commutative_binary64`

Counts

29 → 45

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	321
1	97	249
2	198	239
3	636	233
4	1071	233
5	2844	233
6	3957	233
7	4846	233
8	4880	233

prune28.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	45	3	48

Error

Counts

48 → 3

Alt Table

Status	Error	Program
▶	45.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	31.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 534 to 404 computations (24.3% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	12.6b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	41.9b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series9.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

3.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

3.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

rewrite108.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

302×	`add-cbrt-cube_binary64`
302×	`add-exp-log_binary64`
168×	`cbrt-unprod_binary64`
168×	`prod-exp_binary64`
114×	`pow1_binary64`

Counts

3 → 238

Calls

3 calls:

29.0ms

(/.f64 (/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i))) (-.f64 (*.f64 (*.f64 2 i) (*.f64 2 i)) 1))

20.0ms

(/.f64 (*.f64 (*.f64 i i) (*.f64 i i)) (*.f64 (*.f64 2 i) (*.f64 2 i)))

7.0ms

(*.f64 (*.f64 i i) (*.f64 i i))

simplify159.0ms (5%)

Algorithm

1×	egg-herbie

Rules

585×	`times-frac_binary64`
452×	`fma-neg_binary64`
367×	`fma-def_binary64`
294×	`associate-/l*_binary64`
236×	`associate-/r*_binary64`

Counts

274 → 277

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	7448
1	535	3595
2	2891	3441
3	4518	3441
4	4854	3441

prune204.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	277	3	280

Error

Counts

280 → 3

Alt Table

Status	Error	Program
✓	45.3b	(/.f64 (/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i))) (-.f64 (.f64 (.f64 2 i) (*.f64 2 i)) 1))
✓	31.6b	(*.f64 -1/4 (pow.f64 i 2))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 10214 to 5835 computations (42.9% saved)

regimes485.0ms (15.3%)

Accuracy

Total 0.0b remaining (88.6%)

Threshold costs 0.0b (88.6%)

Counts

239 → 1

Compiler

Compiled 8010 to 6591 computations (17.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	14	24
2	13	24

end1.0ms (0%)

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

sample995.0ms (31.3%)

Algorithm

1×

intervals

Results

563.0ms	8000×	body	128	valid
106.0ms	8000×	pre	128	true

Compiler

Compiled 96 to 70 computations (27.1% saved)

Details

analyze7.0ms (0.2%)

sample98.0ms (3.1%)

simplify57.0ms (1.8%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite23.0ms (0.7%)

simplify137.0ms (4.3%)

prune175.0ms (5.5%)

localize8.0ms (0.3%)

series11.0ms (0.3%)

rewrite68.0ms (2.1%)

simplify198.0ms (6.2%)

prune291.0ms (9.2%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite5.0ms (0.2%)

simplify76.0ms (2.4%)

prune28.0ms (0.9%)

localize8.0ms (0.3%)

series9.0ms (0.3%)

rewrite108.0ms (3.4%)

simplify159.0ms (5%)

prune204.0ms (6.4%)

regimes485.0ms (15.3%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample995.0ms (31.3%)

Profiling