Details

analyze59.0ms (1.6%)

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)

sample899.0ms (24.2%)

Results

785.0ms

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify71.0ms (1.9%)

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

prune2.0ms (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 (0.1%)

Local error

Found 1 expressions with local error:

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

series9.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite65.0ms (1.7%)

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:

62.0ms

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

simplify84.0ms (2.3%)

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

prune43.0ms (1.2%)

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
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (/.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (-.f64 n f))))
	29.8b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

Compiler

Compiled 1031 to 338 computations (67.2% saved)

localize5.0ms (0.1%)

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))

series20.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(/.f64 (-.f64 n f) (+.f64 f n))
10.0ms	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

rewrite81.0ms (2.2%)

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:

10.0ms	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))
7.0ms	(/.f64 (-.f64 n f) (+.f64 f n))

simplify170.0ms (4.6%)

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

prune173.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

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

Error

Counts

239 → 4

Alt Table

Status	Error	Program
	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (/.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (-.f64 n f))))
	29.8b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

Compiler

Compiled 4678 to 1445 computations (69.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series72.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

30.0ms

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

29.0ms

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

12.0ms

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

rewrite194.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

278×	`*-un-lft-identity_binary64`
214×	`cbrt-prod_binary64`
171×	`times-frac_binary64`
160×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`

Counts

3 → 247

Calls

3 calls:

113.0ms

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

28.0ms

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

5.0ms

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

simplify219.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

764×	`associate-/l*_binary64`
604×	`fma-def_binary64`
261×	`associate-l_binary64`
253×	`associate-r_binary64`
167×	`associate-/r/_binary64`

Counts

319 → 306

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	325	9494
1	689	9102
2	2309	8277
3	4906	8271
4	4962	8271

prune395.0ms (10.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	591	0	591
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	591	4	595

Error

Counts

595 → 4

Alt Table

Status	Error	Program
▶	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (/.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (-.f64 n f))))
	29.8b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

Compiler

Compiled 20591 to 3771 computations (81.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (+.f64 f n))
✓	0.5b	(cbrt.f64 (-.f64 n f))
✓	0.5b	(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))

series115.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

37.0ms	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
30.0ms	(cbrt.f64 (-.f64 n f))
26.0ms	(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))
21.0ms	(cbrt.f64 (+.f64 f n))

rewrite33.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`cbrt-prod_binary64`
54×	`*-un-lft-identity_binary64`
48×	`add-sqr-sqrt_binary64`
28×	`cbrt-div_binary64`
22×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

10.0ms	(*.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n)))
9.0ms	(*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))
2.0ms	(cbrt.f64 (-.f64 n f))
2.0ms	(cbrt.f64 (+.f64 f n))

simplify192.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

481×	`times-frac_binary64`
346×	`associate-r_binary64`
313×	`fma-neg_binary64`
310×	`fma-def_binary64`
302×	`unswap-sqr_binary64`

Counts

242 → 299

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	432	5935
1	1043	5703
2	3255	5371
3	5160	5371

prune466.0ms (12.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	521	0	521
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	521	4	525

Error

Counts

525 → 4

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (+.f64 f n))) (*.f64 (cbrt.f64 (-.f64 n f)) (cbrt.f64 (-.f64 n f)))) (/.f64 (cbrt.f64 (+.f64 f n)) (cbrt.f64 (-.f64 n f))))
	29.8b	(*.f64 (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (sqrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f)))) (cbrt.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(/.f64 1 (/.f64 (-.f64 n f) (+.f64 f n)))

Compiler

Compiled 23022 to 7375 computations (68% saved)

regimes264.0ms (7.1%)

Accuracy

Total 0.0b remaining (26.3%)

Threshold costs 0.0b (26.3%)

Counts

105 → 1

Compiler

Compiled 5454 to 3048 computations (44.1% 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

end54.0ms (1.5%)

Compiler: Compiled 119 to 49 computations (58.8% saved)

Details

analyze59.0ms (1.6%)

sample899.0ms (24.2%)

simplify71.0ms (1.9%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite65.0ms (1.7%)

simplify84.0ms (2.3%)

prune43.0ms (1.2%)

localize5.0ms (0.1%)

series20.0ms (0.5%)

rewrite81.0ms (2.2%)

simplify170.0ms (4.6%)

prune173.0ms (4.7%)

localize8.0ms (0.2%)

series72.0ms (1.9%)

rewrite194.0ms (5.2%)

simplify219.0ms (5.9%)

prune395.0ms (10.6%)

localize10.0ms (0.3%)

series115.0ms (3.1%)

rewrite33.0ms (0.9%)

simplify192.0ms (5.2%)

prune466.0ms (12.6%)

regimes264.0ms (7.1%)

simplify3.0ms (0.1%)

end54.0ms (1.5%)

Profiling