Details

analyze7.0ms (0.2%)

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)

sample1.4s (49.9%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 84 to 55 computations (34.5% saved)

simplify57.0ms (2%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
	44.3b	(/.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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
✓	0.6b	(/.f64 1 (*.f64 i i))

series5.0ms (0.2%)

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 (0.5%)

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:

8.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
3.0ms	(/.f64 1 (*.f64 i i))

simplify121.0ms (4.2%)

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

prune127.0ms (4.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

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

Error

Counts

116 → 4

Alt Table

Status	Error	Program
	44.3b	(/.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))
	0.2b	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
▶	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 1911 to 1434 computations (25% saved)

localize8.0ms (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)))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite48.0ms (1.7%)

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))))
7.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
6.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

simplify125.0ms (4.4%)

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

prune263.0ms (9.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	241	1	242
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	242	4	246

Error

Counts

246 → 4

Alt Table

Status	Error	Program
	0.7b	(*.f64 (/.f64 (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	0.2b	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 5860 to 5064 computations (13.6% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
✓	0.6b	(/.f64 4 (*.f64 i i))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
3.0ms	(/.f64 4 (*.f64 i i))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
23×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`add-exp-log_binary64`

Counts

2 → 70

Calls

2 calls:

7.0ms	(/.f64 4 (*.f64 i i))
5.0ms	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))

simplify97.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

497×	`cancel-sign-sub-inv_binary64`
466×	`fma-neg_binary64`
420×	`associate-/l/_binary64`
255×	`div-sub_binary64`
225×	`neg-mul-1_binary64`

Counts

94 → 97

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	1381
1	264	1308
2	617	1298
3	1771	1298
4	4243	1298
5	4950	1298

prune72.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	97	4	101

Error

Counts

101 → 4

Alt Table

Status	Error	Program
	0.7b	(*.f64 (/.f64 (/.f64 1/2 (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (sqrt.f64 (+.f64 2 (/.f64 1 i)))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
✓	0.2b	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
▶	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

Compiler

Compiled 1646 to 1234 computations (25% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

series13.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

13.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`

Counts

1 → 47

Calls

1 calls:

5.0ms

(/.f64 1/4 (-.f64 4 (pow.f64 i -2)))

simplify92.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-neg_binary64`
422×	`cancel-sign-sub-inv_binary64`
390×	`times-frac_binary64`
288×	`associate-/l*_binary64`
224×	`div-sub_binary64`

Counts

59 → 74

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	1059
1	274	1013
2	620	989
3	1604	947
4	4381	947
5	4877	947
6	4896	947

prune64.0ms (2.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	75	3	78

Error

Counts

78 → 3

Alt Table

Status	Error	Program
	0.3b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (-.f64 4 (pow.f64 i -2))))
✓	0.2b	(/.f64 1 (-.f64 16 (/.f64 4 (*.f64 i i))))
✓	0.1b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))

Compiler

Compiled 1200 to 1039 computations (13.4% saved)

regimes191.0ms (6.7%)

Accuracy

Total 0.1b remaining (86.4%)

Threshold costs 0.1b (86.4%)

Counts

93 → 1

Compiler

Compiled 2678 to 2243 computations (16.2% 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

end69.0ms (2.4%)

Compiler: Compiled 73 to 64 computations (12.3% saved)

Details

analyze7.0ms (0.2%)

sample1.4s (49.9%)

simplify57.0ms (2%)

prune4.0ms (0.1%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite15.0ms (0.5%)

simplify121.0ms (4.2%)

prune127.0ms (4.4%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite48.0ms (1.7%)

simplify125.0ms (4.4%)

prune263.0ms (9.2%)

localize5.0ms (0.2%)

series6.0ms (0.2%)

rewrite16.0ms (0.5%)

simplify97.0ms (3.4%)

prune72.0ms (2.5%)

localize4.0ms (0.1%)

series13.0ms (0.5%)

rewrite8.0ms (0.3%)

simplify92.0ms (3.2%)

prune64.0ms (2.2%)

regimes191.0ms (6.7%)

simplify2.0ms (0.1%)

end69.0ms (2.4%)

Profiling