Details

analyze81.0ms (2.2%)

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)

sample29.0ms (0.8%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify56.0ms (1.5%)

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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	47.3b	(/.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))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 4 (/.f64 1 (*.f64 i i)))
✓	0.2b	(/.f64 1 (*.f64 i i))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series8.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

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

rewrite25.0ms (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))))
5.0ms	(-.f64 4 (/.f64 1 (*.f64 i i)))
3.0ms	(/.f64 1 (*.f64 i i))

simplify137.0ms (3.8%)

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

prune150.0ms (4.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	194	2	196
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	194	4	198

Error

Counts

198 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	22.9b	(/.f64 1/4 (/.f64 (-.f64 64 (/.f64 1 (pow.f64 i 6))) (+.f64 16 (+.f64 (/.f64 1 (pow.f64 i 4)) (/.f64 4 (*.f64 i i))))))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	47.3b	(/.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))

Compiler

Compiled 3770 to 2796 computations (25.8% saved)

localize7.0ms (0.2%)

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:

3.0ms	(*.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))

rewrite64.0ms (1.7%)

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:

25.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
7.0ms	(/.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)))

simplify195.0ms (5.3%)

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

prune304.0ms (8.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	348	1	349
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	349	4	353

Error

Counts

353 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	47.3b	(/.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))
▶	15.2b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))

Compiler

Compiled 9373 to 7923 computations (15.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))
✓	0.0b	(/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i)))))
	0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
✓	0.7b	(log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))

series374.0ms (10.2%)

Counts

3 → 28

Calls

3 calls:

234.0ms

(log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))

128.0ms

(/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i)))))

12.0ms

(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))

rewrite45.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
67×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
41×	`add-cube-cbrt_binary64`
32×	`exp-prod_binary64`

Counts

3 → 141

Calls

3 calls:

21.0ms

(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))

6.0ms

(/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i)))))

5.0ms

(log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))

simplify118.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

555×	`associate-*l/_binary64`
492×	`associate-*r/_binary64`
458×	`associate-/l*_binary64`
451×	`associate-l_binary64`
395×	`fma-def_binary64`

Counts

169 → 234

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3519
1	600	3236
2	1643	3135
3	4272	3131
4	4955	3131

prune263.0ms (7.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	285	4	289

Error

Counts

289 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	47.3b	(/.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))
✓	15.2b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))

Compiler

Compiled 7543 to 6689 computations (11.3% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 i i) (*.f64 i i))
✓	19.0b	(/.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))
✓	42.7b	(/.f64 (.f64 (.f64 i i) (.f64 i i)) (.f64 (.f64 2 i) (.f64 2 i)))

series10.0ms (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))

rewrite115.0ms (3.2%)

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:

31.0ms

(/.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))

24.0ms

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

9.0ms

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

simplify157.0ms (4.3%)

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

prune206.0ms (5.6%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	277	4	281

Error

Counts

281 → 4

Alt Table

Status	Error	Program
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	47.3b	(/.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))
✓	15.2b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (log.f64 (/.f64 (exp.f64 2) (exp.f64 (/.f64 1 i))))))

Compiler

Compiled 10237 to 5855 computations (42.8% saved)

regimes277.0ms (7.6%)

Accuracy

Total 0.0b remaining (79.1%)

Threshold costs 0.0b (79.1%)

Counts

143 → 1

Compiler

Compiled 5248 to 4247 computations (19.1% 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)

sample990.0ms (27.1%)

Algorithm

1×

intervals

Results

555.0ms	8000×	body	128	valid
97.0ms	8000×	pre	128	true

Compiler

Compiled 119 to 90 computations (24.4% saved)

Details

analyze81.0ms (2.2%)

sample29.0ms (0.8%)

simplify56.0ms (1.5%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite25.0ms (0.7%)

simplify137.0ms (3.8%)

prune150.0ms (4.1%)

localize7.0ms (0.2%)

series11.0ms (0.3%)

rewrite64.0ms (1.7%)

simplify195.0ms (5.3%)

prune304.0ms (8.3%)

localize11.0ms (0.3%)

series374.0ms (10.2%)

rewrite45.0ms (1.2%)

simplify118.0ms (3.2%)

prune263.0ms (7.2%)

localize12.0ms (0.3%)

series10.0ms (0.3%)

rewrite115.0ms (3.2%)

simplify157.0ms (4.3%)

prune206.0ms (5.6%)

regimes277.0ms (7.6%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample990.0ms (27.1%)

Profiling