Details

analyze74.0ms (3.4%)

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)

sample31.0ms (1.4%)

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)

simplify58.0ms (2.7%)

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
	48.2b	(/.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))
✓	0.4b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

series8.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(/.f64 1 (*.f64 i i))
3.0ms	(/.f64 1/4 (-.f64 4 (/.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))

simplify126.0ms (5.7%)

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

prune97.0ms (4.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	3	116

Error

Counts

116 → 3

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	35.5b	(-.f64 (.f64 -1/4 (.f64 i i)) (pow.f64 i 4))
	14.0b	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))

Compiler

Compiled 1867 to 1404 computations (24.8% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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 (0.5%)

Counts

3 → 36

Calls

3 calls:

5.0ms	(/.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))))
3.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

rewrite50.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64`
96×	`*-un-lft-identity_binary64`
96×	`times-frac_binary64`
47×	`add-cube-cbrt_binary64`
30×	`associate-r_binary64`

Counts

3 → 167

Calls

3 calls:

23.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
6.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
6.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify128.0ms (5.8%)

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

203 → 242

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	259	4188
1	697	3891
2	2091	3770
3	4611	3768
4	5010	3768

prune178.0ms (8.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	242	3	245

Error

Counts

245 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	35.5b	(-.f64 (.f64 -1/4 (.f64 i i)) (pow.f64 i 4))
▶	14.0b	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))

Compiler

Compiled 5820 to 5026 computations (13.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))
	0.3b	(/.f64 1 (*.f64 i i))
✓	1.4b	(log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite14.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
21×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
12×	`log-pow_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))
2.0ms	(log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))

simplify97.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

458×	`fma-neg_binary64`
341×	`cancel-sign-sub-inv_binary64`
303×	`times-frac_binary64`
295×	`div-sub_binary64`
292×	`associate-/r*_binary64`

Counts

88 → 115

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	146	1399
1	260	1330
2	592	1302
3	1467	1300
4	3963	1270
5	4959	1270
6	4904	1270

prune123.0ms (5.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	155	3	158

Error

Counts

158 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	35.5b	(-.f64 (.f64 -1/4 (.f64 i i)) (pow.f64 i 4))
✓	14.0b	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))

Compiler

Compiled 2739 to 2074 computations (24.3% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 -1/4 (.f64 i i)) (pow.f64 i 4))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

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

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`cancel-sign-sub-inv_binary64`
7×	`prod-diff_binary64`
6×	`unpow-prod-down_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

1 → 28

Calls

1 calls:

6.0ms

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

simplify74.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

670×	`unsub-neg_binary64`
352×	`fma-def_binary64`
282×	`fma-neg_binary64`
270×	`cancel-sign-sub-inv_binary64`
269×	`times-frac_binary64`

Counts

40 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	90	857
1	192	653
2	683	511
3	1608	511
4	3457	511
5	4740	511

prune25.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Error

Counts

41 → 3

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	35.5b	(-.f64 (.f64 -1/4 (.f64 i i)) (pow.f64 i 4))
✓	14.0b	(/.f64 1/4 (-.f64 4 (log.f64 (exp.f64 (/.f64 1 (*.f64 i i))))))

Compiler

Compiled 766 to 514 computations (32.9% saved)

regimes99.0ms (4.5%)

Accuracy

Total 0.1b remaining (92.7%)

Threshold costs 0.1b (92.7%)

Counts

59 → 1

Compiler

Compiled 1466 to 1191 computations (18.8% saved)

simplify3.0ms (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)

sample939.0ms (42.8%)

Algorithm

1×

intervals

Results

552.0ms	8000×	body	128	valid
90.0ms	8000×	pre	128	true

Compiler

Compiled 84 to 65 computations (22.6% saved)

Details

analyze74.0ms (3.4%)

sample31.0ms (1.4%)

simplify58.0ms (2.7%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series8.0ms (0.3%)

rewrite14.0ms (0.7%)

simplify126.0ms (5.7%)

prune97.0ms (4.4%)

localize7.0ms (0.3%)

series11.0ms (0.5%)

rewrite50.0ms (2.3%)

simplify128.0ms (5.8%)

prune178.0ms (8.1%)

localize7.0ms (0.3%)

series6.0ms (0.3%)

rewrite14.0ms (0.6%)

simplify97.0ms (4.4%)

prune123.0ms (5.6%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite8.0ms (0.3%)

simplify74.0ms (3.4%)

prune25.0ms (1.1%)

regimes99.0ms (4.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample939.0ms (42.8%)

Profiling