Details

analyze967.0ms (13.8%)

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
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)

sample2.3s (32.2%)

Results

802.0ms	6019×	body	128	valid
460.0ms	1093×	body	1024	valid
250.0ms	683×	body	512	valid
186.0ms	514×	body	1024	invalid
163.0ms	1470×	body	128	invalid
87.0ms	336×	body	512	invalid
81.0ms	373×	body	256	valid
46.0ms	88×	body	2048	valid
32.0ms	173×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify202.0ms (2.9%)

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

16.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.3b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 48 to 35 computations (27.1% saved)

localize6.0ms (0.1%)

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))
✓	1.7b	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

series133.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

69.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
56.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
8.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite16.0ms (0.2%)

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))
4.0ms	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
0.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify117.0ms (1.7%)

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

prune219.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	259	4	263

Error

0.1b

Counts

263 → 4

Alt Table

Status	Error	Program
	48.6b	(-.f64 1 (+.f64 (+.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))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (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))))))))
▶	44.3b	(-.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))))))
✓	16.3b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
	58.2b	(-.f64 1 (-.f64 (log.f64 (+.f64 x -1)) (log.f64 y)))

Compiler

Compiled 9949 to 6715 computations (32.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 1 x))
✓	0.1b	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
✓	0.2b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	6.6b	(/.f64 x (*.f64 y (-.f64 1 x)))

series267.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

244.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
10.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
9.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
4.0ms	(*.f64 y (-.f64 1 x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
32×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64`
18×	`prod-diff_binary64`

Counts

4 → 141

Calls

4 calls:

5.0ms	(*.f64 y (-.f64 1 x))
5.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
5.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
5.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))

simplify137.0ms (2%)

Algorithm

1×	egg-herbie

Rules

635×	`fma-def_binary64`
443×	`distribute-rgt-in_binary64`
225×	`sub-neg_binary64`
175×	`fma-neg_binary64`
169×	`times-frac_binary64`

Counts

237 → 255

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	302	3291
1	672	2984
2	2481	2899
3	4527	2899
4	4968	2887
5	4908	2887

prune242.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	325	1	326
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	327	3	330

Error

0.0b

Counts

330 → 3

Alt Table

Status	Error	Program
▶	38.2b	(-.f64 1 (+.f64 (log.f64 (/.f64 (+.f64 x -1) y)) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
	48.6b	(-.f64 1 (+.f64 (+.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))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (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))))))))
✓	16.3b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 11263 to 6905 computations (38.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 1 x))
	0.2b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	2.2b	(log.f64 (/.f64 (+.f64 x -1) y))
	6.6b	(/.f64 x (*.f64 y (-.f64 1 x)))

series244.0ms (3.5%)

Counts

1 → 24

Calls

1 calls:

244.0ms

(log.f64 (/.f64 (+.f64 x -1) y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`log-prod_binary64`
16×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 32

Calls

1 calls:

3.0ms

(log.f64 (/.f64 (+.f64 x -1) y))

simplify77.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
584×	`fma-neg_binary64`
467×	`sub-neg_binary64`
360×	`cancel-sign-sub-inv_binary64`
326×	`distribute-rgt-in_binary64`

Counts

56 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	131	954
1	272	908
2	713	876
3	2154	869
4	4496	869
5	5004	869

prune228.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	330	0	330
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	330	3	333

Error

0.0b

Counts

333 → 3

Alt Table

Status	Error	Program
✓	38.2b	(-.f64 1 (+.f64 (log.f64 (/.f64 (+.f64 x -1) y)) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
▶	48.6b	(-.f64 1 (+.f64 (+.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))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (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))))))))
✓	16.3b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 10746 to 6952 computations (35.3% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.4b	(+.f64 (+.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))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (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)))))))
	6.6b	(/.f64 x (*.f64 y (-.f64 1 x)))
✓	9.2b	(/.f64 x (.f64 (.f64 y y) (pow.f64 (-.f64 1 x) 2)))
✓	24.3b	(/.f64 (.f64 x x) (.f64 (*.f64 y y) (pow.f64 (-.f64 1 x) 2)))

series154.0ms (2.2%)

Counts

3 → 72

Calls

3 calls:

70.0ms

(+.f64 (+.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))))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (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)))))))

44.0ms

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

39.0ms

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

rewrite95.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`*-un-lft-identity_binary64`
81×	`distribute-lft-out_binary64`
73×	`add-exp-log_binary64`
47×	`add-log-exp_binary64`
34×	`sum-log_binary64`

Counts

3 → 160

Calls

3 calls:

33.0ms

(+.f64 (+.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))))) (-.f64 (/.f64 1 (*.f64 y (-.f64 1 x))) (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)))))))

8.0ms

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

7.0ms

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

simplify297.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

358×	`distribute-rgt-in_binary64`
350×	`distribute-lft-in_binary64`
337×	`times-frac_binary64`
253×	`fma-def_binary64`
213×	`associate-/r*_binary64`

Counts

232 → 241

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	452	16795
1	1360	15871
2	4744	15871
3	4954	15871

prune542.0ms (7.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	295	0	295
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	295	3	298

Error

0.0b

Counts

298 → 3

Alt Table

Status	Error	Program
✓	38.2b	(-.f64 1 (+.f64 (log.f64 (/.f64 (+.f64 x -1) y)) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
✓	48.6b	(-.f64 1 (+.f64 (+.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))))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (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))))))))
✓	16.3b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 32793 to 20115 computations (38.7% saved)

regimes609.0ms (8.7%)

Accuracy

Total 0.2b remaining (93.2%)

Threshold costs 0.2b (93.2%)

Counts

61 → 2

Compiler

Compiled 9596 to 7120 computations (25.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
17×	`sub-neg_binary64`
14×	`neg-sub0_binary64`
14×	`neg-mul-1_binary64`
12×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66
1	43	66
2	64	66
3	84	66
4	109	66
5	122	66
6	131	66
7	137	66
8	143	66
9	148	66
10	150	66
11	146	66

end89.0ms (1.3%)

Compiler: Compiled 203 to 141 computations (30.5% saved)

Iter	Nodes	Cost
0	26	66
1	43	66
2	64	66
3	84	66
4	109	66
5	122	66
6	131	66
7	137	66
8	143	66
9	148	66
10	150	66
11	146	66

Iter	Nodes	Cost
0	26	66
1	43	66
2	64	66
3	84	66
4	109	66
5	122	66
6	131	66
7	137	66
8	143	66
9	148	66
10	150	66
11	146	66

Details

analyze967.0ms (13.8%)

sample2.3s (32.2%)

simplify202.0ms (2.9%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series133.0ms (1.9%)

rewrite16.0ms (0.2%)

simplify117.0ms (1.7%)

prune219.0ms (3.1%)

localize15.0ms (0.2%)

series267.0ms (3.8%)

rewrite27.0ms (0.4%)

simplify137.0ms (2%)

prune242.0ms (3.5%)

localize13.0ms (0.2%)

series244.0ms (3.5%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.1%)

prune228.0ms (3.3%)

localize29.0ms (0.4%)

series154.0ms (2.2%)

rewrite95.0ms (1.4%)

simplify297.0ms (4.3%)

prune542.0ms (7.7%)

regimes609.0ms (8.7%)

bsearch2.0ms (0%)

simplify6.0ms (0.1%)

end89.0ms (1.3%)

Profiling

Iter	Nodes	Cost
0	26	66
1	43	66
2	64	66
3	84	66
4	109	66
5	122	66
6	131	66
7	137	66
8	143	66
9	148	66
10	150	66
11	146	66