Details

analyze101.0ms (2.3%)

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
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
67.1%	32.8%	0.1%	7
71%	28.9%	0.1%	8
82.3%	17.6%	0.1%	9
84.9%	15%	0.1%	10
90.8%	9.1%	0.1%	11
92.2%	7.7%	0.1%	12
95.3%	4.6%	0.1%	13
96%	3.9%	0.1%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample1.2s (27.9%)

Results

669.0ms	6437×	body	128	valid
201.0ms	656×	body	1024	valid
164.0ms	690×	body	512	valid
75.0ms	469×	body	256	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify200.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

1996×	`fma-def_binary64`
1626×	`fma-neg_binary64`
1098×	`div-sub_binary64`
733×	`sub-neg_binary64`
664×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	19	16
2	43	16
3	102	14
4	274	14
5	652	14
6	1272	14
7	1697	14
8	2416	14
9	2933	14
10	3278	14
11	3461	14
12	1980	14
13	1996	14
14	2659	14
15	2539	14
16	2497	14
17	2531	14
18	2531	14
19	4723	14
20	4903	14
21	5942	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

15.7b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.4b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	15.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	16.0b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series25.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
11×	`distribute-lft-out_binary64`

Counts

2 → 57

Calls

2 calls:

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

simplify78.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

780×	`fma-neg_binary64`
491×	`associate--l+_binary64`
425×	`associate--r+_binary64`
390×	`associate-+l+_binary64`
315×	`fma-def_binary64`

Counts

105 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2086
1	416	1897
2	1275	1850
3	4701	1850
4	5402	1850

prune82.0ms (1.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	4	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Error

0.0b

Counts

104 → 4

Alt Table

Status	Error	Program
▶	15.9b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	16.5b	(fma.f64 y (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 1 y))) (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 1 y)))) (cbrt.f64 (/.f64 (+.f64 x -1) (+.f64 1 y)))) 1)
	28.9b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	29.9b	(exp.f64 (log1p.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))))

Compiler

Compiled 1970 to 1357 computations (31.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
✓	0.0b	(/.f64 y (+.f64 1 y))
✓	2.7b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

series24.0ms (0.5%)

Counts

3 → 60

Calls

3 calls:

12.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
9.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
2.0ms	(/.f64 y (+.f64 1 y))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`add-cube-cbrt_binary64`
18×	`associate-l_binary64`

Counts

3 → 98

Calls

3 calls:

10.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
9.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
3.0ms	(/.f64 y (+.f64 1 y))

simplify115.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-neg_binary64`
621×	`distribute-rgt-in_binary64`
465×	`times-frac_binary64`
290×	`cancel-sign-sub-inv_binary64`
257×	`sub-neg_binary64`

Counts

158 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2569
1	702	2474
2	2288	2452
3	4520	2452
4	4961	2452

prune130.0ms (2.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	191	4	195

Error

0.0b

Counts

195 → 4

Alt Table

Status	Error	Program
✓	15.9b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
▶	15.9b	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)
	28.9b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	29.9b	(exp.f64 (log1p.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))))

Compiler

Compiled 3659 to 2541 computations (30.6% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1))
✓	0.0b	(/.f64 (+.f64 1 y) y)
✓	0.1b	(/.f64 1 (/.f64 (+.f64 1 y) y))
✓	2.7b	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)

series27.0ms (0.6%)

Counts

4 → 72

Calls

4 calls:

13.0ms	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)
9.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1))
2.0ms	(/.f64 1 (/.f64 (+.f64 1 y) y))
2.0ms	(/.f64 (+.f64 1 y) y)

rewrite56.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`times-frac_binary64`
158×	`*-un-lft-identity_binary64`
119×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
53×	`associate-l_binary64`

Counts

4 → 232

Calls

4 calls:

16.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1))
13.0ms	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)
6.0ms	(/.f64 1 (/.f64 (+.f64 1 y) y))
4.0ms	(/.f64 (+.f64 1 y) y)

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

789×	`times-frac_binary64`
499×	`fma-neg_binary64`
326×	`cancel-sign-sub-inv_binary64`
257×	`sub-neg_binary64`
172×	`associate-l_binary64`

Counts

304 → 366

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5200
1	788	4585
2	2562	4542
3	4662	4542
4	4991	4542

prune280.0ms (6.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	366	0	366
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	366	4	370

Error

0.0b

Counts

370 → 4

Alt Table

Status	Error	Program
✓	15.9b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
✓	15.9b	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)
▶	28.9b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	29.9b	(exp.f64 (log1p.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))))

Compiler

Compiled 8028 to 5922 computations (26.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.2b	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	6.7b	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
✓	7.2b	(/.f64 x (*.f64 y y))
✓	8.3b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))

series168.0ms (3.8%)

Counts

4 → 96

Calls

4 calls:

62.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
44.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
33.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
29.0ms	(/.f64 x (*.f64 y y))

rewrite147.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`*-un-lft-identity_binary64`
158×	`distribute-lft-out_binary64`
57×	`times-frac_binary64`
51×	`div-inv_binary64`
50×	`add-log-exp_binary64`

Counts

4 → 237

Calls

4 calls:

49.0ms	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
29.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
19.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
3.0ms	(/.f64 x (*.f64 y y))

simplify210.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

487×	`distribute-rgt-in_binary64`
478×	`associate-l_binary64`
467×	`distribute-lft-in_binary64`
224×	`fma-def_binary64`
103×	`sub-neg_binary64`

Counts

333 → 258

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	338	18732
1	1193	13212
2	5025	13212

prune288.0ms (6.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	257	5	262

Error

0.0b

Counts

262 → 5

Alt Table

Status	Error	Program
✓	15.9b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
✓	15.9b	(+.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 1 y) y)) (+.f64 x -1)) 1)
✓	28.9b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))
	55.0b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (/.f64 (fma.f64 (pow.f64 y 3) (-.f64 (/.f64 (/.f64 1 (pow.f64 y 3)) y) (.f64 (/.f64 (+.f64 x -1) y) (/.f64 (+.f64 x -1) y))) (.f64 x (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (.f64 (pow.f64 y 3) (-.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))))
	29.9b	(exp.f64 (log1p.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))))

Compiler

Compiled 15959 to 8251 computations (48.3% saved)

regimes896.0ms (20.2%)

Accuracy

Total 0.0b remaining (60.4%)

Threshold costs 0.0b (60.4%)

Counts

102 → 3

Compiler

Compiled 10767 to 7563 computations (29.8% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

22×	`+-commutative_binary64`
15×	`*-commutative_binary64`
14×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	118
1	54	118
2	69	118
3	87	118
4	99	118
5	110	118
6	123	118
7	131	118
8	137	118
9	139	118
10	136	118

end127.0ms (2.9%)

Compiler: Compiled 304 to 209 computations (31.3% saved)

Iter	Nodes	Cost
0	37	118
1	54	118
2	69	118
3	87	118
4	99	118
5	110	118
6	123	118
7	131	118
8	137	118
9	139	118
10	136	118

Iter	Nodes	Cost
0	37	118
1	54	118
2	69	118
3	87	118
4	99	118
5	110	118
6	123	118
7	131	118
8	137	118
9	139	118
10	136	118

Details

analyze101.0ms (2.3%)

sample1.2s (27.9%)

simplify200.0ms (4.5%)

prune4.0ms (0.1%)

localize7.0ms (0.1%)

series25.0ms (0.6%)

rewrite9.0ms (0.2%)

simplify78.0ms (1.7%)

prune82.0ms (1.9%)

localize6.0ms (0.1%)

series24.0ms (0.5%)

rewrite27.0ms (0.6%)

simplify115.0ms (2.6%)

prune130.0ms (2.9%)

localize7.0ms (0.2%)

series27.0ms (0.6%)

rewrite56.0ms (1.3%)

simplify156.0ms (3.5%)

prune280.0ms (6.3%)

localize16.0ms (0.4%)

series168.0ms (3.8%)

rewrite147.0ms (3.3%)

simplify210.0ms (4.7%)

prune288.0ms (6.5%)

regimes896.0ms (20.2%)

bsearch4.0ms (0.1%)

simplify8.0ms (0.2%)

end127.0ms (2.9%)

Profiling

Iter	Nodes	Cost
0	37	118
1	54	118
2	69	118
3	87	118
4	99	118
5	110	118
6	123	118
7	131	118
8	137	118
9	139	118
10	136	118