Details

analyze1.4s (8.7%)

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
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample2.1s (13.4%)

Results

742.0ms	6010×	body	128	valid
437.0ms	1090×	body	1024	valid
197.0ms	528×	body	1024	invalid
191.0ms	657×	body	512	valid
170.0ms	1621×	body	128	invalid
88.0ms	421×	body	256	valid
85.0ms	313×	body	512	invalid
40.0ms	78×	body	2048	valid
39.0ms	197×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify206.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

2748×	`fma-def_binary64`
1264×	`fma-neg_binary64`
934×	`associate--r-_binary64`
475×	`cancel-sign-sub-inv_binary64`
423×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	17
2	40	17
3	86	15
4	163	15
5	344	15
6	666	15
7	1217	15
8	1463	15
9	1608	15
10	1787	15
11	2322	15
12	2926	15
13	2987	15
14	3089	15
15	3133	15
16	3142	15
17	3142	15
18	3225	15
19	3233	15
20	3237	15
21	4979	15

prune3.0ms (0%)

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

16.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	1.4b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series152.0ms (0.9%)

Counts

3 → 72

Calls

3 calls:

82.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
59.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
10.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64`
44×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`

Counts

3 → 97

Calls

3 calls:

6.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
3.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
0.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-+l+_binary64`
242×	`associate--r+_binary64`
240×	`associate-/r*_binary64`
221×	`fma-def_binary64`
201×	`+-commutative_binary64`

Counts

169 → 262

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	510	6989
1	1448	6687
2	5068	6687

prune245.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	258	4	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	258	5	263

Error

0.1b

Counts

263 → 5

Alt Table

Status	Error	Program
▶	16.2b	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
✓	16.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
	51.1b	(-.f64 (+.f64 1 (fma.f64 1/2 (/.f64 (.f64 x x) (.f64 (.f64 y y) (pow.f64 (-.f64 1 x) 2))) (+.f64 (/.f64 x (.f64 y (-.f64 1 x))) (/.f64 1/2 (.f64 (.f64 y y) (pow.f64 (-.f64 1 x) 2)))))) (+.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (+.f64 (/.f64 x (.f64 (.f64 y y) (pow.f64 (-.f64 1 x) 2))) (+.f64 (log1p.f64 (neg.f64 x)) (+.f64 (/.f64 1 (.f64 y y)) (log.f64 (/.f64 -1 y)))))))
	40.6b	(-.f64 (+.f64 1 (log.f64 (/.f64 -1 x))) (log.f64 (/.f64 -1 (-.f64 y 1))))
	57.1b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))

Compiler

Compiled 9951 to 6721 computations (32.5% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 y 1))
✓	0.2b	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
✓	1.4b	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))

series900.0ms (5.6%)

Counts

4 → 96

Calls

4 calls:

769.0ms	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
110.0ms	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
13.0ms	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))
8.0ms	(/.f64 (-.f64 x y) (-.f64 y 1))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

86×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
59×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
20×	`difference-of-squares_binary64`

Counts

4 → 152

Calls

4 calls:

14.0ms	(/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1))))
12.0ms	(log.f64 (/.f64 (E.f64) (+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))))
11.0ms	(+.f64 1 (/.f64 (-.f64 x y) (-.f64 y 1)))
7.0ms	(/.f64 (-.f64 x y) (-.f64 y 1))

simplify258.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

475×	`+-commutative_binary64`
413×	`associate-+r+_binary64`
279×	`*-commutative_binary64`
271×	`fma-def_binary64`
221×	`sub-neg_binary64`

Counts

248 → 292

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1303	18604
1	4583	17764
2	4983	17764

prune459.0ms (2.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	291	1	292
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	295	2	297

Error

0.0b

Counts

297 → 2

Alt Table

Status	Error	Program
✓	16.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))

Compiler

Compiled 22087 to 15826 computations (28.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
✓	0.1b	(/.f64 (E.f64) (-.f64 1 x))
✓	0.6b	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))

series73.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

43.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
14.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
12.0ms	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
3.0ms	(/.f64 (E.f64) (-.f64 1 x))

rewrite853.0ms (5.3%)

Algorithm

1×	rewrite-expression-head

Rules

4494×	`times-frac_binary64`
3545×	`add-sqr-sqrt_binary64`
3537×	`*-un-lft-identity_binary64`
2132×	`add-cube-cbrt_binary64`
1704×	`prod-diff_binary64`

Counts

4 → 2012

Calls

4 calls:

103.0ms	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y))))
88.0ms	(-.f64 (/.f64 (E.f64) (-.f64 1 x)) (/.f64 (E.f64) (/.f64 (-.f64 1 x) y)))
7.0ms	(/.f64 (E.f64) (/.f64 (-.f64 1 x) y))
4.0ms	(/.f64 (E.f64) (-.f64 1 x))

simplify3.5s (21.8%)

Algorithm

1×	egg-herbie

Rules

882×	`fma-udef_binary64`
796×	`unsub-neg_binary64`
350×	`times-frac_binary64`
191×	`neg-mul-1_binary64`
190×	`neg-sub0_binary64`

Counts

2096 → 2513

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1703	210616
1	4138	205233
2	5447	205233

prune3.5s (22.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	2512	1	2513
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	2513	2	2515

Error

Counts

2515 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))))
✓	16.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 173412 to 97297 computations (43.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))))
	0.1b	(/.f64 (E.f64) (-.f64 1 x))
✓	0.2b	(*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))
✓	0.5b	(/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y))

series84.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

54.0ms

(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))))

18.0ms

(/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y))

12.0ms

(*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))

rewrite112.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

510×	`times-frac_binary64`
376×	`add-sqr-sqrt_binary64`
344×	`*-un-lft-identity_binary64`
227×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 365

Calls

3 calls:

33.0ms

(*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))

8.0ms

(/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y))

8.0ms

(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))))

simplify306.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

451×	`associate-/l*_binary64`
368×	`times-frac_binary64`
302×	`associate-*l/_binary64`
280×	`associate-/r/_binary64`
267×	`associate-/r*_binary64`

Counts

437 → 519

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	598	12249
1	1620	11851
2	4989	11851
3	4978	11851

prune448.0ms (2.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	580	0	580
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	580	2	582

Error

Counts

582 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (-.f64 (/.f64 (E.f64) (-.f64 1 x)) (*.f64 (sqrt.f64 (E.f64)) (/.f64 (sqrt.f64 (E.f64)) (/.f64 (-.f64 1 x) y)))))
✓	16.2b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 17981 to 9723 computations (45.9% saved)

regimes1.1s (6.7%)

Accuracy

Total 0.0b remaining (67.2%)

Threshold costs 0.0b (67.2%)

Counts

192 → 1

Compiler

Compiled 20234 to 15598 computations (22.9% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	31
1	24	31
2	36	31
3	45	31
4	50	31
5	51	31
6	50	31

end58.0ms (0.4%)

Compiler: Compiled 72 to 51 computations (29.2% saved)

Details

analyze1.4s (8.7%)

sample2.1s (13.4%)

simplify206.0ms (1.3%)

prune3.0ms (0%)

localize7.0ms (0%)

series152.0ms (0.9%)

rewrite16.0ms (0.1%)

simplify113.0ms (0.7%)

prune245.0ms (1.5%)

localize8.0ms (0%)

series900.0ms (5.6%)

rewrite56.0ms (0.3%)

simplify258.0ms (1.6%)

prune459.0ms (2.9%)

localize8.0ms (0.1%)

series73.0ms (0.5%)

rewrite853.0ms (5.3%)

simplify3.5s (21.8%)

prune3.5s (22.1%)

localize10.0ms (0.1%)

series84.0ms (0.5%)

rewrite112.0ms (0.7%)

simplify306.0ms (1.9%)

prune448.0ms (2.8%)

regimes1.1s (6.7%)

simplify5.0ms (0%)

end58.0ms (0.4%)

Profiling