Details

analyze50.0ms (2.1%)

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)

sample114.0ms (4.8%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

128

valid

Compiler

Compiled 23 to 15 computations (34.8% saved)

simplify77.0ms (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

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)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.4%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite9.0ms (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:

6.0ms

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

simplify78.0ms (3.3%)

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

prune79.0ms (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Error

Counts

58 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
	31.6b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
	32.6b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
	31.4b	(fma.f64 (/.f64 n f) -2 -1)

Compiler

Compiled 974 to 337 computations (65.4% saved)

localize7.0ms (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))
✓	0.1b	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

series73.0ms (3%)

Counts

2 → 48

Calls

2 calls:

56.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
17.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

rewrite35.0ms (1.5%)

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:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
9.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

simplify210.0ms (8.7%)

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 (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	201	5	206

Error

Counts

206 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
	31.6b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
	32.6b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
▶	31.4b	(fma.f64 (/.f64 n f) -2 -1)

Compiler

Compiled 3831 to 1506 computations (60.7% saved)

localize4.0ms (0.2%)

prune3.0ms (0.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	2	2
Total	5	5

Error

Counts

5 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
▶	31.6b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
	32.6b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
✓	31.4b	(fma.f64 (/.f64 n f) -2 -1)

Compiler

Compiled 101 to 51 computations (49.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (-.f64 n f))
✓	0.1b	(/.f64 1 (sqrt.f64 (-.f64 n f)))
✓	0.1b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
✓	0.3b	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))

series113.0ms (4.7%)

Counts

4 → 44

Calls

4 calls:

39.0ms	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))
35.0ms	(/.f64 1 (sqrt.f64 (-.f64 n f)))
20.0ms	(sqrt.f64 (-.f64 n f))
19.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))

rewrite71.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`add-sqr-sqrt_binary64`
147×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
96×	`sqrt-prod_binary64`
73×	`add-cube-cbrt_binary64`

Counts

4 → 247

Calls

4 calls:

27.0ms	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
7.0ms	(/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f)))
5.0ms	(/.f64 1 (sqrt.f64 (-.f64 n f)))
5.0ms	(sqrt.f64 (-.f64 n f))

simplify301.0ms (12.6%)

Algorithm

1×	egg-herbie

Rules

493×	`distribute-rgt-in_binary64`
225×	`associate-r_binary64`
201×	`cancel-sign-sub-inv_binary64`
193×	`associate-/l*_binary64`
178×	`fma-def_binary64`

Counts

291 → 342

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	344	6758
1	929	5972
2	3352	5898
3	5194	5898

prune180.0ms (7.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	375	0	375
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	375	5	380

Error

Counts

380 → 5

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))
✓	31.6b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (+.f64 f n) (sqrt.f64 (-.f64 n f))))
	32.6b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
✓	31.4b	(fma.f64 (/.f64 n f) -2 -1)

Compiler

Compiled 9738 to 3160 computations (67.5% saved)

regimes186.0ms (7.8%)

Accuracy

Total 0.0b remaining (57.3%)

Threshold costs 0.0b (57.3%)

Counts

49 → 1

Compiler

Compiled 1944 to 1260 computations (35.2% saved)

simplify3.0ms (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	6	10
1	9	10
2	14	10
3	16	10
4	17	10
5	17	10

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample659.0ms (27.5%)

Algorithm

1×

intervals

Results

375.0ms

8000×

body

128

valid

Compiler

Compiled 87 to 49 computations (43.7% saved)

Details

analyze50.0ms (2.1%)

sample114.0ms (4.8%)

simplify77.0ms (3.2%)

prune3.0ms (0.1%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite9.0ms (0.4%)

simplify78.0ms (3.3%)

prune79.0ms (3.3%)

localize7.0ms (0.3%)

series73.0ms (3%)

rewrite35.0ms (1.5%)

simplify210.0ms (8.7%)

prune120.0ms (5%)

localize4.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series113.0ms (4.7%)

rewrite71.0ms (2.9%)

simplify301.0ms (12.6%)

prune180.0ms (7.5%)

regimes186.0ms (7.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample659.0ms (27.5%)

Profiling