Details

analyze601.0ms (0.4%)

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%	68.7%	9.5%	7
23.4%	65.6%	11%	8
32%	53.9%	14.1%	9
33.2%	51.9%	14.9%	10
37.7%	45.9%	16.5%	11
38.3%	44.8%	16.9%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample1.9s (1.2%)

Infinites

0% of outputs are infinite.

Results

598.0ms	6057×	body	128	valid
340.0ms	1049×	body	1024	valid
285.0ms	1087×	body	1024	invalid
158.0ms	682×	body	512	valid
138.0ms	671×	body	512	invalid
70.0ms	405×	body	256	valid
51.0ms	380×	body	256	invalid
42.0ms	539×	body	128	invalid
29.0ms	63×	body	2048	valid
1.0ms	3×	body	2048	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify209.0ms (0.1%)

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

2 alts after pruning (2 fresh and 0 done)

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

Error

19.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.6b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))

Compiler

Compiled 52 to 39 computations (25% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
✓	0.0b	(/.f64 (-.f64 x y) (-.f64 1 y))
✓	3.7b	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
✓	3.7b	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))

series151.0ms (0.1%)

Counts

4 → 96

Calls

4 calls:

76.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
57.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
10.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
8.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

rewrite91.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`add-sqr-sqrt_binary64`
308×	`*-un-lft-identity_binary64`
186×	`times-frac_binary64`
125×	`add-cube-cbrt_binary64`
120×	`prod-diff_binary64`

Counts

4 → 330

Calls

4 calls:

16.0ms	(-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))
16.0ms	(log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y))))
14.0ms	(-.f64 1 (log.f64 (-.f64 1 (/.f64 (-.f64 x y) (-.f64 1 y)))))
7.0ms	(/.f64 (-.f64 x y) (-.f64 1 y))

simplify327.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

336×	`fma-def_binary64`
264×	`sub-neg_binary64`
259×	`associate-/r*_binary64`
224×	`+-commutative_binary64`
215×	`associate-/l*_binary64`

Counts

426 → 482

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	720	18151
1	2204	14737
2	4965	14737
3	4971	14737

prune469.0ms (0.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	478	4	482
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	479	4	483

Error

Counts

483 → 4

Alt Table

Status	Error	Program
	37.5b	(-.f64 1 (log.f64 (-.f64 (+.f64 (/.f64 x y) (+.f64 (/.f64 x (pow.f64 y 3)) (/.f64 x (pow.f64 y 2)))) (+.f64 (/.f64 1 y) (+.f64 (/.f64 1 (pow.f64 y 3)) (/.f64 1 (pow.f64 y 2)))))))
	19.7b	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
	20.3b	(/.f64 (-.f64 1 (pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)) (fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1))
▶	11.6b	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))

Compiler

Compiled 19624 to 12408 computations (36.8% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))
✓	0.0b	(/.f64 x (-.f64 1 y))
✓	3.6b	(+.f64 1 (/.f64 y (-.f64 1 y)))
✓	8.0b	(log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y))))

series145.0ms (0.1%)

Counts

4 → 72

Calls

4 calls:

75.0ms	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))
57.0ms	(log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y))))
8.0ms	(/.f64 x (-.f64 1 y))
4.0ms	(+.f64 1 (/.f64 y (-.f64 1 y)))

rewrite58.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`
14×	`difference-of-squares_binary64`

Counts

4 → 130

Calls

4 calls:

20.0ms	(log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y))))
19.0ms	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))
7.0ms	(+.f64 1 (/.f64 y (-.f64 1 y)))
4.0ms	(/.f64 x (-.f64 1 y))

simplify127.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

506×	`associate-+l+_binary64`
248×	`fma-def_binary64`
238×	`associate-/r*_binary64`
215×	`+-commutative_binary64`
207×	`associate--r+_binary64`

Counts

202 → 283

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	562	8439
1	1639	7714
2	5401	7714

prune359.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	282	1	283
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	283	4	287

Error

Counts

287 → 4

Alt Table

Status	Error	Program
	20.3b	(/.f64 (-.f64 1 (pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)) (fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1))
▶	19.7b	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
	35.9b	(-.f64 1 (log.f64 (-.f64 (-.f64 (/.f64 -1 y) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 1 (pow.f64 y 3)))) (/.f64 x (-.f64 1 y)))))
✓	11.6b	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))

Compiler

Compiled 12097 to 8764 computations (27.6% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))
✓	0.2b	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
✓	0.2b	(pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3)
✓	3.6b	(log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))

series2.1s (1.4%)

Counts

4 → 96

Calls

4 calls:

2.0s	(pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3)
76.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
59.0ms	(log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))
11.0ms	(/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`*-un-lft-identity_binary64`
131×	`add-sqr-sqrt_binary64`
84×	`times-frac_binary64`
52×	`difference-of-squares_binary64`
46×	`add-cube-cbrt_binary64`

Counts

4 → 199

Calls

4 calls:

8.0ms	(/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))
3.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
3.0ms	(pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3)
0.0ms	(log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))

simplify349.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-def_binary64`
404×	`associate-/l*_binary64`
360×	`associate-/r*_binary64`
303×	`times-frac_binary64`
76×	`sub-neg_binary64`

Counts

295 → 339

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2621	30855
1	5521	30855

prune833.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	339	0	339
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	339	4	343

Error

Counts

343 → 4

Alt Table

Status	Error	Program
▶	20.3b	(/.f64 (-.f64 1 (pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)) (fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1))
✓	19.7b	(cbrt.f64 (pow.f64 (-.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 3))
	35.9b	(-.f64 1 (log.f64 (-.f64 (-.f64 (/.f64 -1 y) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 1 (pow.f64 y 3)))) (/.f64 x (-.f64 1 y)))))
✓	11.6b	(-.f64 1 (log.f64 (-.f64 (+.f64 1 (/.f64 y (-.f64 1 y))) (/.f64 x (-.f64 1 y)))))

Compiler

Compiled 40419 to 29634 computations (26.7% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (-.f64 1 (pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)) (fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1))
✓	0.2b	(fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1)
✓	0.3b	(pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)
	3.6b	(log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))

series2.4min (94.8%)

Calls

2 calls:

1.7s	(pow.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) 3)
540.0ms	(fma.f64 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y))) (+.f64 1 (log1p.f64 (/.f64 (neg.f64 (-.f64 x y)) (-.f64 1 y)))) 1)

Details

analyze601.0ms (0.4%)

sample1.9s (1.2%)

simplify209.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0%)

series151.0ms (0.1%)

rewrite91.0ms (0.1%)

simplify327.0ms (0.2%)

prune469.0ms (0.3%)

localize9.0ms (0%)

series145.0ms (0.1%)

rewrite58.0ms (0%)

simplify127.0ms (0.1%)

prune359.0ms (0.2%)

localize9.0ms (0%)

series2.1s (1.4%)

rewrite32.0ms (0%)

simplify349.0ms (0.2%)

prune833.0ms (0.6%)

localize14.0ms (0%)

series2.4min (94.8%)

Profiling