Details

analyze51.0ms (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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	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)

sample1.2s (48%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify97.0ms (3.9%)

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

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)

localize8.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.6%)

Counts

1 → 24

Calls

1 calls:

16.0ms

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

rewrite18.0ms (0.7%)

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:

12.0ms

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

simplify120.0ms (4.7%)

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

prune44.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Error

Counts

58 → 3

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	36.2b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)

Compiler

Compiled 925 to 318 computations (65.6% saved)

localize15.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

series42.0ms (1.6%)

Counts

2 → 48

Calls

2 calls:

27.0ms	(exp.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
14.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))

rewrite39.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
52×	`exp-prod_binary64`
40×	`times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
27×	`log-pow_binary64`

Counts

2 → 76

Calls

2 calls:

16.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
11.0ms	(exp.f64 (/.f64 (+.f64 f n) (-.f64 n f)))

simplify138.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

454×	`times-frac_binary64`
368×	`cancel-sign-sub-inv_binary64`
313×	`associate-/l*_binary64`
290×	`fma-neg_binary64`
267×	`fma-def_binary64`

Counts

124 → 119

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2152
1	333	2044
2	939	1918
3	3637	1903
4	5016	1903

prune114.0ms (4.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	176	3	179

Error

Counts

179 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
	36.2b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)

Compiler

Compiled 3117 to 992 computations (68.2% saved)

localize7.0ms (0.3%)

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))
✓	0.6b	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))

series29.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

20.0ms	(expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f)))
9.0ms	(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))))

simplify84.0ms (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

prune63.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	117	3	120

Error

Counts

120 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
▶	36.2b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)

Compiler

Compiled 1930 to 795 computations (58.8% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 n f) 1)
✓	0.2b	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))

series18.0ms (0.7%)

Counts

2 → 48

Calls

2 calls:

14.0ms	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))
4.0ms	(+.f64 (/.f64 n f) 1)

rewrite19.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 66

Calls

2 calls:

10.0ms	(*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f))
5.0ms	(+.f64 (/.f64 n f) 1)

simplify94.0ms (3.7%)

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

114 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	99	1388
1	235	1221
2	779	1141
3	2612	1140
4	4070	1128
5	4976	1128

prune54.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	95	3	98

Error

Counts

98 → 3

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (exp.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 f n) (-.f64 n f))))
✓	36.2b	(fma.f64 (*.f64 (+.f64 (/.f64 n f) 1) (/.f64 n f)) -2 -1)

Compiler

Compiled 1830 to 891 computations (51.3% saved)

regimes172.0ms (6.8%)

Accuracy

Total 0.0b remaining (54.9%)

Threshold costs 0.0b (54.9%)

Counts

46 → 1

Compiler

Compiled 1530 to 1131 computations (26.1% 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	10	17
1	15	17
2	19	17
3	21	17
4	22	17
5	21	17

end52.0ms (2.1%)

Compiler: Compiled 62 to 41 computations (33.9% saved)

Details

analyze51.0ms (2%)

sample1.2s (48%)

simplify97.0ms (3.9%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

series16.0ms (0.6%)

rewrite18.0ms (0.7%)

simplify120.0ms (4.7%)

prune44.0ms (1.7%)

localize15.0ms (0.6%)

series42.0ms (1.6%)

rewrite39.0ms (1.5%)

simplify138.0ms (5.5%)

prune114.0ms (4.5%)

localize7.0ms (0.3%)

series29.0ms (1.2%)

rewrite1.0ms (0.1%)

simplify84.0ms (3.3%)

prune63.0ms (2.5%)

localize6.0ms (0.2%)

series18.0ms (0.7%)

rewrite19.0ms (0.8%)

simplify94.0ms (3.7%)

prune54.0ms (2.2%)

regimes172.0ms (6.8%)

simplify3.0ms (0.1%)

end52.0ms (2.1%)

Profiling