Details

analyze45.0ms (1.7%)

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)

sample1.0s (38%)

Results

892.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify72.0ms (2.7%)

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))

series9.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite9.0ms (0.3%)

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))

simplify75.0ms (2.8%)

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

prune34.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Error

Counts

58 → 4

Alt Table

Status	Error	Program
	28.5b	(fma.f64 -2 (+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))) -1)
▶	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
	35.9b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (sqrt.f64 (-.f64 n f))) (/.f64 (cbrt.f64 (+.f64 f n)) (sqrt.f64 (-.f64 n f))))
	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 991 to 346 computations (65.1% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series18.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

9.0ms	(/.f64 (-.f64 n f) (+.f64 f n))
9.0ms	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

rewrite34.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

178×	`times-frac_binary64`
174×	`*-un-lft-identity_binary64`
122×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`
30×	`associate-/r*_binary64`

Counts

2 → 178

Calls

2 calls:

9.0ms	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
6.0ms	(/.f64 (-.f64 n f) (+.f64 f n))

simplify163.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

407×	`fma-def_binary64`
316×	`times-frac_binary64`
308×	`fma-neg_binary64`
296×	`distribute-rgt-in_binary64`
253×	`distribute-lft-in_binary64`

Counts

226 → 235

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	177	4611
1	439	4248
2	1327	4101
3	4264	4083
4	4979	4083
5	4959	4083

prune125.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	234	1	235
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	235	4	239

Error

Counts

239 → 4

Alt Table

Status	Error	Program
	28.5b	(fma.f64 -2 (+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))) -1)
	35.5b	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (sqrt.f64 (-.f64 n f)) (+.f64 f n)))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
▶	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 4620 to 1451 computations (68.6% saved)

localize6.0ms (0.2%)

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	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)
	0.0b	(/.f64 (+.f64 f n) (-.f64 n f))

series32.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
15.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

rewrite31.0ms (1.2%)

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:

8.0ms	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))
7.0ms	(pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3)

simplify120.0ms (4.5%)

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

prune113.0ms (4.2%)

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
▶	28.5b	(fma.f64 -2 (+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))) -1)
	35.5b	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (sqrt.f64 (-.f64 n f)) (+.f64 f n)))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 3819 to 1506 computations (60.6% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))
✓	0.2b	(pow.f64 (/.f64 n f) 3)
✓	9.0b	(+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)))

series59.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

26.0ms	(+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)))
17.0ms	(pow.f64 (/.f64 n f) 3)
16.0ms	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))

rewrite42.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64`
46×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64`
32×	`fma-def_binary64`

Counts

3 → 138

Calls

3 calls:

17.0ms	(+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)))
10.0ms	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))
7.0ms	(pow.f64 (/.f64 n f) 3)

simplify142.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

548×	`fma-neg_binary64`
280×	`log-prod_binary64`
273×	`associate-r_binary64`
258×	`associate-l_binary64`
225×	`cancel-sign-sub-inv_binary64`

Counts

210 → 170

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	185	2963
1	550	2639
2	2534	2606
3	4175	2578
4	5006	2578

prune121.0ms (4.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	170	4	174

Error

Counts

174 → 4

Alt Table

Status	Error	Program
✓	28.5b	(fma.f64 -2 (+.f64 (pow.f64 (/.f64 n f) 3) (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))) -1)
	35.5b	(/.f64 (/.f64 1 (sqrt.f64 (-.f64 n f))) (/.f64 (sqrt.f64 (-.f64 n f)) (+.f64 f n)))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
✓	0.0b	(cbrt.f64 (pow.f64 (/.f64 (+.f64 f n) (-.f64 n f)) 3))

Compiler

Compiled 4589 to 2345 computations (48.9% saved)

regimes217.0ms (8.1%)

Accuracy

Total 0.0b remaining (64.9%)

Threshold costs 0.0b (64.9%)

Counts

60 → 1

Compiler

Compiled 2206 to 1492 computations (32.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	14	19
2	20	19
3	24	19
4	27	19
5	28	19
6	27	19

end157.0ms (5.9%)

Compiler: Compiled 90 to 52 computations (42.2% saved)

Details

analyze45.0ms (1.7%)

sample1.0s (38%)

simplify72.0ms (2.7%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series9.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify75.0ms (2.8%)

prune34.0ms (1.3%)

localize8.0ms (0.3%)

series18.0ms (0.7%)

rewrite34.0ms (1.3%)

simplify163.0ms (6.1%)

prune125.0ms (4.7%)

localize6.0ms (0.2%)

series32.0ms (1.2%)

rewrite31.0ms (1.2%)

simplify120.0ms (4.5%)

prune113.0ms (4.2%)

localize8.0ms (0.3%)

series59.0ms (2.2%)

rewrite42.0ms (1.6%)

simplify142.0ms (5.3%)

prune121.0ms (4.6%)

regimes217.0ms (8.1%)

simplify3.0ms (0.1%)

end157.0ms (5.9%)

Profiling