Details

analyze7.0ms (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)

sample90.0ms (4.4%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 56 to 37 computations (33.9% saved)

simplify57.0ms (2.8%)

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 (0.2%)

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

0.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	44.2b	(/.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))

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

series5.0ms (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))

rewrite15.0ms (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:

7.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))

simplify120.0ms (5.9%)

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

prune104.0ms (5.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	2	116

Error

Counts

116 → 2

Alt Table

Status	Error	Program
	31.1b	(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)))))
▶	10.9b	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))

Compiler

Compiled 1853 to 1390 computations (25% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (pow.f64 i 6))
✓	0.3b	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
✓	19.3b	(cbrt.f64 (/.f64 1 (pow.f64 i 6)))

series9.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

3.0ms	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
3.0ms	(/.f64 1 (pow.f64 i 6))
2.0ms	(cbrt.f64 (/.f64 1 (pow.f64 i 6)))

rewrite31.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`add-sqr-sqrt_binary64`
102×	`times-frac_binary64`
70×	`*-un-lft-identity_binary64`
53×	`cbrt-prod_binary64`
50×	`add-cube-cbrt_binary64`

Counts

3 → 158

Calls

3 calls:

11.0ms	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))
3.0ms	(/.f64 1 (pow.f64 i 6))
3.0ms	(cbrt.f64 (/.f64 1 (pow.f64 i 6)))

simplify162.0ms (7.9%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-neg_binary64`
369×	`times-frac_binary64`
307×	`associate-l_binary64`
302×	`log-prod_binary64`
256×	`associate-r_binary64`

Counts

182 → 210

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	212	3352
1	374	3146
2	826	2980
3	2808	2978
4	4603	2954
5	4961	2954
6	4850	2954

prune167.0ms (8.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	210	2	212

Error

Counts

212 → 2

Alt Table

Status	Error	Program
▶	31.1b	(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)))))
✓	10.9b	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))

Compiler

Compiled 4175 to 3698 computations (11.4% saved)

localize11.0ms (0.5%)

Local error

Found 2 expressions with local error:

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

series9.0ms (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 (.f64 i i) (fma.f64 i i 1/4) (fma.f64 4 (pow.f64 i 6) (.f64 16 (pow.f64 i 8))))
0.0ms	(fma.f64 4 (pow.f64 i 6) (*.f64 16 (pow.f64 i 8)))

simplify38.0ms (1.8%)

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

prune33.0ms (1.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	43	2	45

Error

Counts

45 → 2

Alt Table

Status	Error	Program
✓	31.1b	(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)))))
✓	10.9b	(/.f64 1/4 (-.f64 4 (cbrt.f64 (/.f64 1 (pow.f64 i 6)))))

Compiler

Compiled 1023 to 714 computations (30.2% saved)

regimes207.0ms (10.2%)

Accuracy

Total 0.1b remaining (87.5%)

Threshold costs 0.1b (87.5%)

Counts

102 → 1

Compiler

Compiled 2944 to 2471 computations (16.1% 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	13	22
1	19	22
2	25	22
3	27	22
4	28	22
5	25	22

end2.0ms (0.1%)

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

sample955.0ms (46.8%)

Algorithm

1×

intervals

Results

563.0ms	8000×	body	128	valid
105.0ms	8000×	pre	128	true

Compiler

Compiled 77 to 58 computations (24.7% saved)

Details

analyze7.0ms (0.4%)

sample90.0ms (4.4%)

simplify57.0ms (2.8%)

prune4.0ms (0.2%)

localize5.0ms (0.2%)

series5.0ms (0.3%)

rewrite15.0ms (0.7%)

simplify120.0ms (5.9%)

prune104.0ms (5.1%)

localize7.0ms (0.3%)

series9.0ms (0.4%)

rewrite31.0ms (1.5%)

simplify162.0ms (7.9%)

prune167.0ms (8.2%)

localize11.0ms (0.5%)

series9.0ms (0.5%)

rewrite1.0ms (0.1%)

simplify38.0ms (1.8%)

prune33.0ms (1.6%)

regimes207.0ms (10.2%)

simplify3.0ms (0.1%)

end2.0ms (0.1%)

sample955.0ms (46.8%)

Profiling