Details

analyze1.8s (1.2%)

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
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)

sample3.7s (2.5%)

Results

1.3s	6038×	body	128	valid
797.0ms	1057×	body	1024	valid
374.0ms	661×	body	512	valid
342.0ms	528×	body	1024	invalid
265.0ms	1494×	body	128	invalid
170.0ms	351×	body	512	invalid
156.0ms	420×	body	256	valid
77.0ms	80×	body	2048	valid
59.0ms	178×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify223.0ms (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

prune5.0ms (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

20.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize13.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x y) (+.f64 y -1))
✓	3.4b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series125.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

108.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
17.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite169.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
716×	`fma-udef_binary64`
231×	`fma-neg_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`

Counts

2 → 88

Calls

2 calls:

165.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
165.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	22
1	181	22
2	2546	22
3	4714	22
4	4517	22
5	5006	22
0	0	0
1	0	0

simplify132.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

475×	`associate-+r+_binary64`
373×	`sub-neg_binary64`
335×	`+-commutative_binary64`
305×	`cancel-sign-sub-inv_binary64`
303×	`associate-+l+_binary64`

Counts

136 → 155

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	279	2659
1	918	2609
2	4007	2577
3	5150	2577

prune263.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	151	5	156

Error

0.1b

Counts

156 → 5

Alt Table

Status	Error	Program
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
	44.9b	(-.f64 1 (-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))))))))
	47.6b	(-.f64 1 (+.f64 (+.f64 (/.f64 y (.f64 (-.f64 y 1) x)) (log.f64 (/.f64 -1 (-.f64 y 1)))) (-.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y (-.f64 y 1)) (/.f64 y x)) (+.f64 (/.f64 1 x) (log.f64 (/.f64 -1 x)))))))
	58.3b	(-.f64 1 (-.f64 (log.f64 x) (log.f64 (-.f64 y 1))))
▶	40.4b	(-.f64 1 (+.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))

Compiler

Compiled 5723 to 3985 computations (30.4% saved)

localize26.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 1 x))
✓	0.2b	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
✓	0.7b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	5.9b	(/.f64 x (*.f64 y (-.f64 1 x)))

series464.0ms (0.3%)

Counts

4 → 96

Calls

4 calls:

417.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
21.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
18.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
7.0ms	(*.f64 y (-.f64 1 x))

rewrite125.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

735×	`prod-diff_binary64`
143×	`add-sqr-sqrt_binary64`
139×	`egg-rr`
134×	`expm1-log1p-u_binary64`
133×	`log1p-expm1-u_binary64`

Counts

4 → 139

Calls

4 calls:

116.0ms	(*.f64 y (-.f64 1 x))
116.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
116.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
115.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40
1	295	38
2	3545	38
3	4922	38
0	0	0
1	0	0

simplify151.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

891×	`sub-neg_binary64`
416×	`cancel-sign-sub-inv_binary64`
378×	`distribute-neg-in_binary64`
334×	`fma-neg_binary64`
321×	`neg-mul-1_binary64`

Counts

235 → 202

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	108	1379
1	299	1309
2	862	1309
3	2748	1275
4	4350	1275
5	4713	1247
6	5005	1247

prune450.0ms (0.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	234	2	236
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	235	6	241

Error

0.1b

Counts

241 → 6

Alt Table

Status	Error	Program
	55.5b	(-.f64 1 (+.f64 (+.f64 (/.f64 -1 x) (-.f64 (log.f64 (/.f64 -1 y)) (log.f64 (/.f64 -1 x)))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
	58.3b	(-.f64 1 (-.f64 (log.f64 x) (log.f64 (-.f64 y 1))))
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	44.9b	(-.f64 1 (-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))))))))
	47.6b	(-.f64 1 (+.f64 (+.f64 (/.f64 y (.f64 (-.f64 y 1) x)) (log.f64 (/.f64 -1 (-.f64 y 1)))) (-.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y (-.f64 y 1)) (/.f64 y x)) (+.f64 (/.f64 1 x) (log.f64 (/.f64 -1 x)))))))
	48.8b	(-.f64 1 (+.f64 (.f64 (-.f64 (pow.f64 (log1p.f64 x) 2) (pow.f64 (log.f64 (/.f64 -1 y)) 2)) (/.f64 1 (-.f64 (log1p.f64 x) (log.f64 (/.f64 -1 y))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (*.f64 y (-.f64 1 x))))))

Compiler

Compiled 7783 to 5238 computations (32.7% saved)

localize64.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.9b	(/.f64 x (*.f64 (-.f64 1 x) y))
✓	7.0b	(/.f64 x (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))
✓	7.2b	(-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))))))
✓	22.5b	(/.f64 (pow.f64 x 2) (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))

series301.0ms (0.2%)

Counts

4 → 58

Calls

4 calls:

127.0ms	(-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))))))
74.0ms	(/.f64 x (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))
74.0ms	(/.f64 (pow.f64 x 2) (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))
26.0ms	(/.f64 x (*.f64 (-.f64 1 x) y))

rewrite141.0ms (0.1%)

Algorithm

2×	batch-egg-rewrite

Rules

357×	`log1p-expm1-u_binary64`
357×	`expm1-log1p-u_binary64`
339×	`add-log-exp_binary64`
338×	`add-exp-log_binary64`
327×	`pow1_binary64`

Counts

4 → 82

Calls

4 calls:

135.0ms	(/.f64 x (*.f64 (-.f64 1 x) y))
135.0ms	(/.f64 x (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))
135.0ms	(-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))))))
134.0ms	(/.f64 (pow.f64 x 2) (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	132
1	747	127
2	4977	127
3	5066	127
0	0	0
1	0	0

simplify163.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

373×	`fma-def_binary64`
327×	`associate-/r*_binary64`
291×	`sub-neg_binary64`
234×	`cancel-sign-sub-inv_binary64`
194×	`times-frac_binary64`

Counts

140 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2086
1	550	2034
2	1890	2016
3	4728	2016
4	4997	2016
5	4957	2016

prune548.0ms (0.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	163	2	165
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Error

0.1b

Counts

171 → 7

Alt Table

Status	Error	Program
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	44.9b	(-.f64 1 (-.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (/.f64 x (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))) (+.f64 (log.f64 (/.f64 -1 y)) (+.f64 (/.f64 1 (pow.f64 y 2)) (log.f64 (-.f64 1 x)))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2)))) (+.f64 (/.f64 x (.f64 (-.f64 1 x) y)) (.f64 1/2 (/.f64 1 (*.f64 (pow.f64 (-.f64 1 x) 2) (pow.f64 y 2))))))))
	47.6b	(-.f64 1 (+.f64 (+.f64 (/.f64 y (.f64 (-.f64 y 1) x)) (log.f64 (/.f64 -1 (-.f64 y 1)))) (-.f64 (/.f64 y x) (+.f64 (.f64 (/.f64 y (-.f64 y 1)) (/.f64 y x)) (+.f64 (/.f64 1 x) (log.f64 (/.f64 -1 x)))))))
	58.3b	(-.f64 1 (-.f64 (log.f64 x) (log.f64 (-.f64 y 1))))
	55.5b	(-.f64 1 (+.f64 (-.f64 (+.f64 (/.f64 1 y) (+.f64 (log.f64 (/.f64 -1 y)) (/.f64 1/2 (*.f64 y y)))) (log.f64 (/.f64 -1 x))) (/.f64 -1 x)))
▶	45.1b	(-.f64 1 (/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) 3) (pow.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (.f64 (-.f64 1 x) y)))) 3)) (+.f64 (pow.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (.f64 (-.f64 1 x) y)))) 2) (.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (*.f64 (-.f64 1 x) y)))))))))
	48.8b	(-.f64 1 (+.f64 (.f64 (-.f64 (pow.f64 (log1p.f64 x) 2) (pow.f64 (log.f64 (/.f64 -1 y)) 2)) (/.f64 1 (-.f64 (log1p.f64 x) (log.f64 (/.f64 -1 y))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (*.f64 y (-.f64 1 x))))))

Compiler

Compiled 12972 to 9613 computations (25.9% saved)

localize72.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.9b	(/.f64 x (*.f64 (-.f64 1 x) y))
✓	12.2b	(-.f64 (pow.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) 3) (pow.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (.f64 (-.f64 1 x) y)))) 3))
✓	13.2b	(/.f64 (-.f64 (pow.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) 3) (pow.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (.f64 (-.f64 1 x) y)))) 3)) (+.f64 (pow.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) 2) (+.f64 (pow.f64 (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (.f64 (-.f64 1 x) y)))) 2) (.f64 (+.f64 (/.f64 1 (.f64 (-.f64 1 x) y)) (+.f64 (fma.f64 x (pow.f64 (.f64 (-.f64 1 x) y) -2) (log.f64 (/.f64 -1 y))) (+.f64 (pow.f64 y -2) (log1p.f64 (neg.f64 x))))) (fma.f64 (/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2)) 1/2 (fma.f64 1/2 (pow.f64 (.f64 (-.f64 1 x) y) -2) (/.f64 x (*.f64 (-.f64 1 x) y))))))))
✓	22.5b	(/.f64 (.f64 x x) (pow.f64 (.f64 (-.f64 1 x) y) 2))

series2.4min (94%)

Calls

1 calls:

84.0ms

(/.f64 (*.f64 x x) (pow.f64 (*.f64 (-.f64 1 x) y) 2))

Details

analyze1.8s (1.2%)

sample3.7s (2.5%)

simplify223.0ms (0.1%)

prune5.0ms (0%)

localize13.0ms (0%)

series125.0ms (0.1%)

rewrite169.0ms (0.1%)

simplify132.0ms (0.1%)

prune263.0ms (0.2%)

localize26.0ms (0%)

series464.0ms (0.3%)

rewrite125.0ms (0.1%)

simplify151.0ms (0.1%)

prune450.0ms (0.3%)

localize64.0ms (0%)

series301.0ms (0.2%)

rewrite141.0ms (0.1%)

simplify163.0ms (0.1%)

prune548.0ms (0.4%)

localize72.0ms (0%)

series2.4min (94%)

Profiling