Details

analyze6.0ms (0.3%)

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)

sample92.0ms (4.3%)

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)

simplify55.0ms (2.6%)

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 (0.2%)

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

0.3b

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))
▶	0.3b	(/.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 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (*.f64 i i))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite14.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
35×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

2 → 85

Calls

2 calls:

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

simplify119.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

484×	`cancel-sign-sub-inv_binary64`
484×	`fma-neg_binary64`
262×	`associate-/l/_binary64`
260×	`unsub-neg_binary64`
197×	`neg-mul-1_binary64`

Counts

109 → 114

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	157	1670
1	304	1577
2	701	1474
3	1855	1474
4	4205	1414
5	4887	1414
6	4999	1414
7	4867	1414

prune112.0ms (5.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Error

Counts

116 → 4

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	32.0b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
	31.9b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))))

Compiler

Compiled 1879 to 1412 computations (24.9% saved)

localize7.0ms (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)))

series10.0ms (0.5%)

Counts

4 → 39

Calls

4 calls:

3.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
3.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
2.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
1.0ms	(+.f64 2 (/.f64 1 i))

rewrite57.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt_binary64`
101×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
49×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

4 → 185

Calls

4 calls:

24.0ms	(*.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 1/2 (+.f64 2 (/.f64 1 i)))
5.0ms	(+.f64 2 (/.f64 1 i))

simplify134.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

499×	`associate-/l*_binary64`
456×	`fma-def_binary64`
288×	`associate-/l/_binary64`
277×	`fma-neg_binary64`
200×	`associate-/r*_binary64`

Counts

224 → 263

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	265	4371
1	704	4054
2	2098	3932
3	4620	3930
4	5026	3930

prune249.0ms (11.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	263	4	267

Error

Counts

267 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	32.0b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
▶	31.9b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))))

Compiler

Compiled 6259 to 5405 computations (13.6% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4)))
✓	0.0b	(fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))

series9.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4)))
4.0ms	(fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))
0.0ms	(fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4)))

simplify56.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

764×	`associate-l_binary64`
668×	`associate-r_binary64`
667×	`unswap-sqr_binary64`
412×	`distribute-rgt-in_binary64`
408×	`distribute-lft-in_binary64`

Counts

44 → 45

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	702
1	59	626
2	135	626
3	525	626
4	3383	626
5	5107	626

prune32.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	45	4	49

Error

Counts

49 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	32.0b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
✓	31.9b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))))

Compiler

Compiled 918 to 632 computations (31.2% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/64 (*.f64 i i))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 1/64 (*.f64 i i))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
3×	`associate-/l*_binary64`
3×	`*-un-lft-identity_binary64`
3×	`times-frac_binary64`

Counts

1 → 23

Calls

1 calls:

3.0ms

(/.f64 1/64 (*.f64 i i))

simplify68.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

548×	`unsub-neg_binary64`
293×	`times-frac_binary64`
269×	`associate-/l/_binary64`
264×	`fma-def_binary64`
263×	`*-commutative_binary64`

Counts

35 → 30

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	341
1	89	296
2	172	287
3	428	287
4	1577	287
5	2187	287
6	3740	287
7	4455	287
8	5126	287

prune17.0ms (0.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	30	4	34

Error

Counts

34 → 4

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	32.0b	(+.f64 1/16 (/.f64 1/64 (*.f64 i i)))
✓	31.9b	(neg.f64 (fma.f64 4 (pow.f64 i 6) (fma.f64 (*.f64 i i) 1/4 (pow.f64 i 4))))

Compiler

Compiled 387 to 272 computations (29.7% saved)

regimes64.0ms (3%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Counts

28 → 1

Compiler

Compiled 816 to 643 computations (21.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	17	22
2	23	22
3	25	22
4	26	22
5	24	22

end1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

sample980.0ms (46.2%)

Algorithm

1×

intervals

Results

515.0ms	8000×	body	128	valid
102.0ms	8000×	pre	128	true

Compiler

Compiled 95 to 73 computations (23.2% saved)

Details

analyze6.0ms (0.3%)

sample92.0ms (4.3%)

simplify55.0ms (2.6%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series6.0ms (0.3%)

rewrite14.0ms (0.7%)

simplify119.0ms (5.6%)

prune112.0ms (5.3%)

localize7.0ms (0.3%)

series10.0ms (0.5%)

rewrite57.0ms (2.7%)

simplify134.0ms (6.3%)

prune249.0ms (11.7%)

localize8.0ms (0.4%)

series9.0ms (0.4%)

rewrite1.0ms (0.1%)

simplify56.0ms (2.7%)

prune32.0ms (1.5%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify68.0ms (3.2%)

prune17.0ms (0.8%)

regimes64.0ms (3%)

simplify2.0ms (0.1%)

end1.0ms (0%)

sample980.0ms (46.2%)

Profiling