Details

analyze1.4s (9.6%)

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)

sample3.8s (26.5%)

Results

1.3s	6038×	body	128	valid
792.0ms	1057×	body	1024	valid
370.0ms	528×	body	1024	invalid
365.0ms	661×	body	512	valid
298.0ms	1494×	body	128	invalid
170.0ms	351×	body	512	invalid
155.0ms	420×	body	256	valid
79.0ms	80×	body	2048	valid
59.0ms	178×	body	256	invalid

Compiler

Compiled 44 to 35 computations (20.5% saved)

simplify231.0ms (1.6%)

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)

localize12.0ms (0.1%)

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)))

series75.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

60.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))
15.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
32×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out--_binary64`

Counts

2 → 65

Calls

2 calls:

14.0ms	(/.f64 (-.f64 x y) (+.f64 y -1))
1.0ms	(log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1)))

simplify175.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-+r+_binary64`
403×	`sub-neg_binary64`
349×	`+-commutative_binary64`
306×	`associate-+l+_binary64`
240×	`associate-/r*_binary64`

Counts

113 → 166

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	377	3806
1	1121	3687
2	4545	3655
3	5244	3655

prune251.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	4	166
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	162	5	167

Error

0.1b

Counts

167 → 5

Alt Table

Status	Error	Program
	58.3b	(-.f64 1 (-.f64 (log.f64 x) (log.f64 (-.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))))))))
▶	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))))))
	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)))))))
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))

Compiler

Compiled 5566 to 3687 computations (33.8% saved)

localize28.0ms (0.2%)

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)))

series388.0ms (2.7%)

Counts

4 → 96

Calls

4 calls:

342.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))
19.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
17.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
10.0ms	(*.f64 y (-.f64 1 x))

rewrite53.0ms (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:

11.0ms	(*.f64 y (-.f64 1 x))
8.0ms	(/.f64 x (*.f64 y (-.f64 1 x)))
8.0ms	(/.f64 1 (*.f64 y (-.f64 1 x)))
8.0ms	(+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))

simplify231.0ms (1.6%)

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

prune522.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	323	3	326
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	326	5	331

Error

Counts

331 → 5

Alt Table

Status	Error	Program
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
▶	34.7b	(-.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))))))
	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))))))))
	40.5b	(-.f64 1 (+.f64 (+.f64 (fma.f64 2 (log.f64 (cbrt.f64 (/.f64 -1 y))) (log1p.f64 (neg.f64 x))) (log.f64 (cbrt.f64 (/.f64 -1 y)))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (.f64 y (-.f64 1 x))))))
	40.8b	(-.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y)))) (cbrt.f64 (+.f64 (log1p.f64 (neg.f64 x)) (log.f64 (/.f64 -1 y))))) (cbrt.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 11441 to 7053 computations (38.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 1 x))
	0.7b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	1.9b	(log.f64 (/.f64 (+.f64 x -1) y))
	5.9b	(/.f64 x (*.f64 y (-.f64 1 x)))

series296.0ms (2.1%)

Counts

1 → 24

Calls

1 calls:

296.0ms

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

rewrite13.0ms (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:

9.0ms

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

simplify110.0ms (0.8%)

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

prune543.0ms (3.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	329	1	330
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	331	4	335

Error

Counts

335 → 4

Alt Table

Status	Error	Program
▶	34.8b	(-.f64 1 (+.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (*.f64 y (-.f64 1 x))))))
	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))))))))
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	34.7b	(-.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))))))

Compiler

Compiled 10828 to 7032 computations (35.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y))))
	0.7b	(/.f64 1 (*.f64 y (-.f64 1 x)))
✓	5.3b	(cbrt.f64 (/.f64 (+.f64 -1 x) y))
	5.9b	(/.f64 x (*.f64 y (-.f64 1 x)))

series1.6s (10.9%)

Counts

2 → 48

Calls

2 calls:

1.2s	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y))))
345.0ms	(cbrt.f64 (/.f64 (+.f64 -1 x) y))

rewrite60.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`cbrt-prod_binary64`
62×	`*-un-lft-identity_binary64`
57×	`log-prod_binary64`
48×	`times-frac_binary64`
38×	`associate-+l+_binary64`

Counts

2 → 102

Calls

2 calls:

27.0ms	(+.f64 (*.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y))))
7.0ms	(cbrt.f64 (/.f64 (+.f64 -1 x) y))

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

643×	`fma-def_binary64`
365×	`fma-neg_binary64`
297×	`associate-r_binary64`
281×	`associate-l_binary64`
203×	`distribute-rgt-in_binary64`

Counts

150 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	273	3719
1	612	3560
2	1634	3286
3	4427	3094
4	4945	3094
5	4910	3094

prune788.0ms (5.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	380	4	384

Error

Counts

384 → 4

Alt Table

Status	Error	Program
✓	34.8b	(-.f64 1 (+.f64 (+.f64 (.f64 2 (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (log.f64 (cbrt.f64 (/.f64 (+.f64 -1 x) y)))) (-.f64 (/.f64 1 (.f64 y (-.f64 1 x))) (/.f64 x (*.f64 y (-.f64 1 x))))))
	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))))))))
✓	20.0b	(-.f64 1 (log1p.f64 (/.f64 (-.f64 x y) (+.f64 y -1))))
✓	34.7b	(-.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))))))

Compiler

Compiled 16907 to 12519 computations (26% saved)

regimes3.1s (22.1%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Counts

149 → 2

Compiler

Compiled 27530 to 20488 computations (25.6% saved)

bsearch13.0ms (0.1%)

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

simplify12.0ms (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	60
1	43	60
2	64	60
3	84	60
4	109	60
5	122	60
6	131	60
7	137	60
8	143	60
9	148	60
10	150	60
11	146	60

end249.0ms (1.8%)

Compiler: Compiled 236 to 175 computations (25.8% saved)

Iter	Nodes	Cost
0	26	60
1	43	60
2	64	60
3	84	60
4	109	60
5	122	60
6	131	60
7	137	60
8	143	60
9	148	60
10	150	60
11	146	60

Iter	Nodes	Cost
0	26	60
1	43	60
2	64	60
3	84	60
4	109	60
5	122	60
6	131	60
7	137	60
8	143	60
9	148	60
10	150	60
11	146	60

Details

analyze1.4s (9.6%)

sample3.8s (26.5%)

simplify231.0ms (1.6%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series75.0ms (0.5%)

rewrite21.0ms (0.1%)

simplify175.0ms (1.2%)

prune251.0ms (1.8%)

localize28.0ms (0.2%)

series388.0ms (2.7%)

rewrite53.0ms (0.4%)

simplify231.0ms (1.6%)

prune522.0ms (3.7%)

localize23.0ms (0.2%)

series296.0ms (2.1%)

rewrite13.0ms (0.1%)

simplify110.0ms (0.8%)

prune543.0ms (3.8%)

localize34.0ms (0.2%)

series1.6s (10.9%)

rewrite60.0ms (0.4%)

simplify244.0ms (1.7%)

prune788.0ms (5.6%)

regimes3.1s (22.1%)

bsearch13.0ms (0.1%)

simplify12.0ms (0.1%)

end249.0ms (1.8%)

Profiling

Iter	Nodes	Cost
0	26	60
1	43	60
2	64	60
3	84	60
4	109	60
5	122	60
6	131	60
7	137	60
8	143	60
9	148	60
10	150	60
11	146	60