Details

analyze8.0ms (0.4%)

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)

sample95.0ms (5.3%)

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)

simplify56.0ms (3.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	49.0b	(/.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))
▶	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

Compiler

Compiled 107 to 73 computations (31.8% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.4b	(/.f64 1 (*.f64 i i))

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite19.0ms (1%)

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:

10.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
4.0ms	(/.f64 1 (*.f64 i i))

simplify123.0ms (6.9%)

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

prune83.0ms (4.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	0	1
Picked	0	1	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))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1873 to 1406 computations (24.9% saved)

localize7.0ms (0.4%)

Local error

Found 2 expressions with local error:

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

series6.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

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

rewrite19.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
47×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
13×	`associate-/r*_binary64`

Counts

2 → 90

Calls

2 calls:

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

simplify98.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

732×	`fma-neg_binary64`
618×	`cancel-sign-sub-inv_binary64`
323×	`sub-neg_binary64`
285×	`fma-def_binary64`
257×	`times-frac_binary64`

Counts

114 → 117

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	169	1963
1	372	1859
2	886	1847
3	2135	1840
4	4352	1834
5	4935	1834

prune136.0ms (7.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	117	3	120

Error

Counts

120 → 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))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
▶	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 2729 to 2347 computations (14% saved)

localize12.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
✓	0.0b	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))

series10.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
5.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))

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 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))
0.0ms	(fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))

simplify37.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

961×	`distribute-lft-in_binary64`
961×	`distribute-rgt-in_binary64`
509×	`fma-def_binary64`
97×	`exp-prod_binary64`
95×	`associate-+r+_binary64`

Counts

44 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	886
1	83	796
2	196	790
3	782	790
4	5006	790

prune40.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	43	3	46

Error

Counts

46 → 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))))
✓	0.1b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	31.6b	(neg.f64 (fma.f64 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8)))))

Compiler

Compiled 1062 to 735 computations (30.8% saved)

regimes77.0ms (4.3%)

Accuracy

Total 0.3b remaining (98.9%)

Threshold costs 0.3b (98.9%)

Counts

34 → 1

Compiler

Compiled 1064 to 841 computations (21% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	19	13
3	21	13
4	22	13
5	20	13

end0.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample943.0ms (52.7%)

Algorithm

1×

intervals

Results

533.0ms	8000×	body	128	valid
94.0ms	8000×	pre	128	true

Compiler

Compiled 86 to 64 computations (25.6% saved)

Details

analyze8.0ms (0.4%)

sample95.0ms (5.3%)

simplify56.0ms (3.1%)

prune4.0ms (0.2%)

localize6.0ms (0.3%)

series6.0ms (0.3%)

rewrite19.0ms (1%)

simplify123.0ms (6.9%)

prune83.0ms (4.6%)

localize7.0ms (0.4%)

series6.0ms (0.3%)

rewrite19.0ms (1.1%)

simplify98.0ms (5.5%)

prune136.0ms (7.6%)

localize12.0ms (0.7%)

series10.0ms (0.5%)

rewrite1.0ms (0.1%)

simplify37.0ms (2.1%)

prune40.0ms (2.2%)

regimes77.0ms (4.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample943.0ms (52.7%)

Profiling