Details

analyze192.0ms (7.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.5%	62.4%	0.1%	5
62.4%	37.5%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
93.7%	6.2%	0.1%	9
93.7%	6.2%	0.1%	10
96.8%	3.1%	0.1%	11
96.8%	3.1%	0.1%	12
98.3%	1.6%	0.1%	13
98.3%	1.6%	0.1%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample31.0ms (1.3%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify80.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-def_binary64`
621×	`fma-neg_binary64`
457×	`times-frac_binary64`
316×	`div-sub_binary64`
141×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	12
2	38	12
3	71	12
4	152	12
5	207	12
6	597	10
7	937	10
8	1314	10
9	1337	10
10	1342	10
11	1369	10
12	1379	10
13	1379	10
14	1274	10

prune5.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 35 to 18 computations (48.6% saved)

localize9.0ms (0.4%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

series16.0ms (0.7%)

Counts

1 → 24

Calls

1 calls:

16.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

rewrite54.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
20×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64`

Counts

1 → 47

Calls

1 calls:

47.0ms

(/.f64 (+.f64 f n) (-.f64 n f))

simplify119.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

360×	`cancel-sign-sub-inv_binary64`
305×	`neg-mul-1_binary64`
284×	`div-sub_binary64`
252×	`fma-def_binary64`
243×	`fma-neg_binary64`

Counts

71 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1291
1	274	1214
2	795	1163
3	2594	1145
4	4436	1145
5	5107	1145

prune57.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	33.4b	(/.f64 (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))) (sqrt.f64 (-.f64 n f)))
▶	30.1b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)
	33.4b	(fma.f64 2 (/.f64 f n) 1)
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 936 to 321 computations (65.7% saved)

localize12.0ms (0.5%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))

series27.0ms (1.1%)

Counts

1 → 24

Calls

1 calls:

27.0ms

(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))

rewrite98.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 39

Calls

1 calls:

93.0ms

(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))

simplify133.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

332×	`associate-l_binary64`
268×	`associate-r_binary64`
245×	`associate-*l/_binary64`
242×	`associate-*r/_binary64`
228×	`distribute-rgt-in_binary64`

Counts

63 → 63

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	91	1078
1	227	929
2	773	850
3	2605	849
4	4059	838
5	4960	838

prune65.0ms (2.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	63	0	63
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	63	4	67

Error

Counts

67 → 4

Alt Table

Status	Error	Program
	33.4b	(/.f64 (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))) (sqrt.f64 (-.f64 n f)))
✓	30.1b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)
▶	33.4b	(fma.f64 2 (/.f64 f n) 1)
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 1287 to 634 computations (50.7% saved)

localize8.0ms (0.3%)

prune4.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Error

Counts

4 → 4

Alt Table

Status	Error	Program
▶	33.4b	(/.f64 (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))) (sqrt.f64 (-.f64 n f)))
✓	30.1b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)
✓	33.4b	(fma.f64 2 (/.f64 f n) 1)
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 61 to 34 computations (44.3% saved)

localize13.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 n f))
✓	0.2b	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))

series116.0ms (4.7%)

Counts

2 → 16

Calls

2 calls:

77.0ms	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))
39.0ms	(sqrt.f64 (-.f64 n f))

rewrite56.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
22×	`add-cube-cbrt_binary64`

Counts

2 → 81

Calls

2 calls:

36.0ms	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))
7.0ms	(sqrt.f64 (-.f64 n f))

simplify150.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

758×	`times-frac_binary64`
486×	`fma-def_binary64`
460×	`associate-/l*_binary64`
378×	`associate-/r*_binary64`
147×	`fma-neg_binary64`

Counts

97 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	2126
1	477	2065
2	1480	2042
3	4937	2042
4	4969	2042

prune123.0ms (5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	158	4	162

Error

Counts

162 → 4

Alt Table

Status	Error	Program
✓	33.4b	(/.f64 (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))) (sqrt.f64 (-.f64 n f)))
✓	30.1b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)
✓	33.4b	(fma.f64 2 (/.f64 f n) 1)
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

Compiler

Compiled 3949 to 1220 computations (69.1% saved)

regimes79.0ms (3.2%)

Accuracy

Total 0.0b remaining (67.8%)

Threshold costs 0.0b (67.8%)

Counts

14 → 1

Compiler

Compiled 458 to 296 computations (35.4% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	18	12
2	29	12
3	37	12
4	40	12
5	40	12

end1.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

sample1.0s (40.8%)

Algorithm

1×

intervals

Results

477.0ms

8000×

body

128

valid

Compiler

Compiled 69 to 42 computations (39.1% saved)

Details

analyze192.0ms (7.8%)

sample31.0ms (1.3%)

simplify80.0ms (3.2%)

prune5.0ms (0.2%)

localize9.0ms (0.4%)

series16.0ms (0.7%)

rewrite54.0ms (2.2%)

simplify119.0ms (4.8%)

prune57.0ms (2.3%)

localize12.0ms (0.5%)

series27.0ms (1.1%)

rewrite98.0ms (4%)

simplify133.0ms (5.4%)

prune65.0ms (2.7%)

localize8.0ms (0.3%)

prune4.0ms (0.2%)

localize13.0ms (0.5%)

series116.0ms (4.7%)

rewrite56.0ms (2.3%)

simplify150.0ms (6.1%)

prune123.0ms (5%)

regimes79.0ms (3.2%)

simplify6.0ms (0.2%)

end1.0ms (0%)

sample1.0s (40.8%)

Profiling