Details

analyze50.0ms (2%)

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)

sample948.0ms (39%)

Results

837.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify75.0ms (3.1%)

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

prune3.0ms (0.1%)

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)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series10.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

10.0ms

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

rewrite10.0ms (0.4%)

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:

7.0ms

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

simplify75.0ms (3.1%)

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

prune85.0ms (3.5%)

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
	33.0b	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 938 to 321 computations (65.8% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.0b	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

series45.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

30.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
15.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

rewrite101.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
76×	`add-sqr-sqrt_binary64`
58×	`cbrt-prod_binary64`
52×	`cube-prod_binary64`

Counts

2 → 144

Calls

2 calls:

78.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
7.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

simplify125.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

413×	`fma-def_binary64`
329×	`unswap-sqr_binary64`
283×	`distribute-rgt-in_binary64`
228×	`log-prod_binary64`
219×	`distribute-lft-in_binary64`

Counts

192 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	227	4212
1	630	3868
2	2080	3747
3	4590	3741
4	4974	3741

prune120.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	201	4	205

Error

Counts

205 → 4

Alt Table

Status	Error	Program
	33.0b	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 3795 to 1490 computations (60.7% saved)

localize14.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.5b	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))

series29.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

19.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
10.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
0.0ms	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))

simplify80.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

472×	`fma-neg_binary64`
450×	`cancel-sign-sub-inv_binary64`
423×	`times-frac_binary64`
309×	`associate-/l*_binary64`
256×	`fma-def_binary64`

Counts

70 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	100	1424
1	262	1306
2	852	1222
3	3573	1207
4	4953	1207
5	4966	1207

prune64.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	117	4	121

Error

Counts

121 → 4

Alt Table

Status	Error	Program
▶	33.0b	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 1942 to 797 computations (59% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (+.f64 f n))
✓	0.1b	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f))

series64.0ms (2.6%)

Counts

3 → 40

Calls

3 calls:

34.0ms	(/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f))
21.0ms	(sqrt.f64 (+.f64 f n))
10.0ms	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))

rewrite130.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
74×	`times-frac_binary64`
57×	`sqrt-prod_binary64`
44×	`add-cube-cbrt_binary64`

Counts

3 → 158

Calls

3 calls:

16.0ms	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
6.0ms	(/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f))
3.0ms	(sqrt.f64 (+.f64 f n))

simplify121.0ms (5%)

Algorithm

1×	egg-herbie

Rules

551×	`fma-def_binary64`
538×	`associate-/l*_binary64`
424×	`times-frac_binary64`
244×	`associate-/l/_binary64`
162×	`fma-neg_binary64`

Counts

198 → 244

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	4005
1	627	3864
2	1957	3741
3	4685	3735
4	5080	3735

prune105.0ms (4.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	285	0	285
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	285	4	289

Error

Counts

289 → 4

Alt Table

Status	Error	Program
✓	33.0b	(*.f64 (sqrt.f64 (+.f64 f n)) (/.f64 (sqrt.f64 (+.f64 f n)) (-.f64 n f)))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 6495 to 1671 computations (74.3% saved)

regimes101.0ms (4.1%)

Accuracy

Total 0.0b remaining (56.5%)

Threshold costs 0.0b (56.5%)

Counts

38 → 1

Compiler

Compiled 1349 to 980 computations (27.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	12	15
2	17	15
3	19	15
4	20	15
5	20	15

end56.0ms (2.3%)

Compiler: Compiled 71 to 43 computations (39.4% saved)

Details

analyze50.0ms (2%)

sample948.0ms (39%)

simplify75.0ms (3.1%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite10.0ms (0.4%)

simplify75.0ms (3.1%)

prune85.0ms (3.5%)

localize6.0ms (0.3%)

series45.0ms (1.8%)

rewrite101.0ms (4.2%)

simplify125.0ms (5.1%)

prune120.0ms (4.9%)

localize14.0ms (0.6%)

series29.0ms (1.2%)

rewrite1.0ms (0.1%)

simplify80.0ms (3.3%)

prune64.0ms (2.6%)

localize6.0ms (0.2%)

series64.0ms (2.6%)

rewrite130.0ms (5.3%)

simplify121.0ms (5%)

prune105.0ms (4.3%)

regimes101.0ms (4.1%)

simplify4.0ms (0.1%)

end56.0ms (2.3%)

Profiling