Details

analyze56.0ms (1.8%)

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
59.3%	40.6%	0.1%	6
76.5%	23.4%	0.1%	7
82%	18%	0.1%	8
87.8%	12.1%	0.1%	9
90.7%	9.2%	0.1%	10
93.8%	6.1%	0.1%	11
95.3%	4.6%	0.1%	12
96.8%	3.1%	0.1%	13
97.6%	2.3%	0.1%	14

Compiler

Compiled 10 to 6 computations (40% saved)

sample826.0ms (25.9%)

Results

716.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 17 computations (41.4% saved)

simplify76.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

801×	`fma-def_binary64`
511×	`fma-neg_binary64`
365×	`times-frac_binary64`
331×	`div-sub_binary64`
156×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	12	10
2	19	10
3	30	10
4	52	10
5	81	10
6	124	10
7	191	10
8	300	10
9	641	10
10	822	10
11	1299	10
12	1328	10
13	1343	10
14	1357	10
15	1377	10
16	1377	10
17	1276	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

Compiler

Compiled 27 to 15 computations (44.4% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 x y))

series8.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

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 → 48

Calls

1 calls:

6.0ms

(/.f64 (-.f64 x y) (+.f64 x y))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

610×	`div-sub_binary64`
586×	`fma-neg_binary64`
530×	`cancel-sign-sub-inv_binary64`
194×	`distribute-neg-frac_binary64`
184×	`fma-def_binary64`

Counts

72 → 59

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	106	1287
1	283	1239
2	748	1195
3	2488	1183
4	4383	1183
5	5485	1183

prune41.0ms (1.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	3	60

Error

Counts

60 → 3

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
	29.0b	(fma.f64 2 (-.f64 (+.f64 (/.f64 x y) (pow.f64 (/.f64 x y) 3)) (*.f64 (/.f64 x y) (/.f64 x y))) -1)

Compiler

Compiled 976 to 311 computations (68.1% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.0b	(/.f64 y (+.f64 x y))

series28.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

10.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
10.0ms	(/.f64 x (+.f64 x y))
8.0ms	(/.f64 y (+.f64 x y))

rewrite621.0ms (19.5%)

Algorithm

1×	rewrite-expression-head

Rules

595×	`*-un-lft-identity_binary64`
496×	`times-frac_binary64`
339×	`add-sqr-sqrt_binary64`
327×	`add-cube-cbrt_binary64`
324×	`prod-diff_binary64`

Counts

3 → 459

Calls

3 calls:

291.0ms	(-.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 x y)))
3.0ms	(/.f64 x (+.f64 x y))
3.0ms	(/.f64 y (+.f64 x y))

simplify403.0ms (12.6%)

Algorithm

1×	egg-herbie

Rules

764×	`fma-neg_binary64`
542×	`times-frac_binary64`
251×	`unsub-neg_binary64`
239×	`sub-neg_binary64`
210×	`fma-udef_binary64`

Counts

531 → 507

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	463	25191
1	1077	16096
2	2498	11283
3	4634	11271
4	4896	11271

prune280.0ms (8.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	506	1	507
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	508	2	510

Error

Counts

510 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
▶	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 19777 to 3519 computations (82.2% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y))))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))
	0.0b	(/.f64 x (+.f64 x y))
	0.0b	(/.f64 y (+.f64 x y))

series20.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

11.0ms	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))
9.0ms	(expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y))))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
54×	`prod-diff_binary64`
53×	`add-cube-cbrt_binary64`
49×	`times-frac_binary64`

Counts

2 → 103

Calls

2 calls:

12.0ms	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y))))

simplify113.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-neg_binary64`
512×	`fma-def_binary64`
373×	`associate-l_binary64`
312×	`associate-r_binary64`
217×	`associate-/l*_binary64`

Counts

151 → 156

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	4762
1	369	3543
2	1124	2647
3	4237	2626
4	4927	2626

prune143.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	291	0	291
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	291	2	293

Error

Counts

293 → 2

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 8215 to 1498 computations (81.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (+.f64 x y))
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))

series19.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
8.0ms	(/.f64 1 (+.f64 x y))

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
18×	`associate-r_binary64`

Counts

2 → 88

Calls

2 calls:

10.0ms	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
4.0ms	(/.f64 1 (+.f64 x y))

simplify142.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

550×	`fma-neg_binary64`
262×	`associate-l_binary64`
254×	`fma-def_binary64`
245×	`times-frac_binary64`
244×	`associate-/l*_binary64`

Counts

136 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	137	2203
1	347	2083
2	1108	1813
3	3679	1801
4	4957	1801

prune65.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	135	2	137

Error

Counts

137 → 2

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 (-.f64 x y) (/.f64 1 (+.f64 x y)))
✓	0.0b	(-.f64 (/.f64 x (+.f64 x y)) (expm1.f64 (log1p.f64 (/.f64 y (+.f64 x y)))))

Compiler

Compiled 2213 to 901 computations (59.3% saved)

regimes156.0ms (4.9%)

Accuracy

Total 0.0b remaining (25.7%)

Threshold costs 0.0b (25.7%)

Counts

66 → 1

Compiler

Compiled 2860 to 1677 computations (41.4% 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	7	16
1	10	16
2	17	16
3	21	16
4	24	16
5	25	16
6	25	16

end40.0ms (1.3%)

Compiler: Compiled 52 to 27 computations (48.1% saved)

Details

analyze56.0ms (1.8%)

sample826.0ms (25.9%)

simplify76.0ms (2.4%)

prune1.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.3%)

rewrite9.0ms (0.3%)

simplify77.0ms (2.4%)

prune41.0ms (1.3%)

localize5.0ms (0.2%)

series28.0ms (0.9%)

rewrite621.0ms (19.5%)

simplify403.0ms (12.6%)

prune280.0ms (8.8%)

localize9.0ms (0.3%)

series20.0ms (0.6%)

rewrite25.0ms (0.8%)

simplify113.0ms (3.5%)

prune143.0ms (4.5%)

localize5.0ms (0.2%)

series19.0ms (0.6%)

rewrite19.0ms (0.6%)

simplify142.0ms (4.4%)

prune65.0ms (2%)

regimes156.0ms (4.9%)

simplify3.0ms (0.1%)

end40.0ms (1.3%)

Profiling