Details

analyze207.0ms (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
12.5%	87.4%	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)

sample22.0ms (0.1%)

Algorithm

1×

intervals

Results

8.0ms	202×	body	128	valid
3.0ms	21×	body	1024	valid
2.0ms	21×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify198.0ms (1.1%)

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%)

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

14.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	22.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	14.5b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	14.5b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series19.0ms (0.1%)

Counts

2 → 48

Calls

2 calls:

10.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
8.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))

rewrite10.0ms (0.1%)

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)

simplify81.0ms (0.5%)

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

prune88.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	102	2	104

Error

0.0b

Counts

104 → 2

Alt Table

Status	Error	Program
	28.7b	(-.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))))
▶	22.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Status

Error

Program

28.7b

(-.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))))

▶

22.2b

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

Compiler

Compiled 1882 to 1289 computations (31.5% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 x) y)
✓	2.4b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	7.3b	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

series31.0ms (0.2%)

Counts

3 → 60

Calls

3 calls:

16.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
11.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
4.0ms	(*.f64 (-.f64 1 x) y)

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
30×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
20×	`times-frac_binary64`

Counts

3 → 113

Calls

3 calls:

8.0ms	(/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))
7.0ms	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
5.0ms	(*.f64 (-.f64 1 x) y)

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

395×	`fma-neg_binary64`
383×	`cancel-sign-sub-inv_binary64`
261×	`sub-neg_binary64`
216×	`distribute-rgt-neg-in_binary64`
160×	`exp-prod_binary64`

Counts

173 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	248	3950
1	690	3374
2	2734	2924
3	4540	2924
4	4860	2924

prune163.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	202	2	204

Error

0.0b

Counts

204 → 2

Alt Table

Status	Error	Program
▶	28.7b	(-.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))))
✓	22.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Status

Error

Program

▶

28.7b

(-.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))))

✓

22.2b

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

Compiler

Compiled 4898 to 3489 computations (28.8% saved)

localize58.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.2b	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
✓	5.7b	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
✓	7.5b	(/.f64 x (*.f64 y y))
✓	7.6b	(-.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))))

series165.0ms (0.9%)

Counts

4 → 96

Calls

4 calls:

65.0ms	(-.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))))
37.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
31.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
31.0ms	(/.f64 x (*.f64 y y))

rewrite137.0ms (0.8%)

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:

47.0ms	(-.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))))
30.0ms	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
13.0ms	(+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3)))
3.0ms	(/.f64 x (*.f64 y y))

simplify241.0ms (1.4%)

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

prune318.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	257	3	260

Error

Counts

260 → 3

Alt Table

Status	Error	Program
✓	28.7b	(-.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))))
✓	22.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
▶	28.8b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))))

Compiler

Compiled 16007 to 8277 computations (48.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.7b	(+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))
	7.5b	(/.f64 x (*.f64 y y))
✓	7.6b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))))
✓	14.8b	(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

series181.0ms (1%)

Counts

2 → 48

Calls

2 calls:

112.0ms

(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

68.0ms

(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))

rewrite1.5s (8.7%)

Algorithm

1×	rewrite-expression-head

Rules

2165×	`cbrt-div_binary64`
2162×	`frac-add_binary64`
1300×	`frac-times_binary64`
1296×	`flip-+_binary64`
1296×	`flip3-+_binary64`

Counts

2 → 913

Calls

2 calls:

64.0ms

(-.f64 (+.f64 (+.f64 x (/.f64 x (*.f64 y y))) (/.f64 1 (pow.f64 y 3))) (*.f64 (*.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))))

26.0ms

(cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (*.f64 y y)) (/.f64 (+.f64 x -1) y))))

simplify4.5s (25.8%)

Algorithm

1×	egg-herbie

Rules

869×	`fma-neg_binary64`
4×	`fma-udef_binary64`

Counts

961 → 937

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3852	430581
1	5597	430581

prune5.1s (29.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	1267	0	1267
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	1267	3	1270

Error

Counts

1270 → 3

Alt Table

Status	Error	Program
✓	28.7b	(-.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))))
✓	22.2b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))
✓	28.8b	(-.f64 (+.f64 (+.f64 x (/.f64 x (.f64 y y))) (/.f64 1 (pow.f64 y 3))) (.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y)))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))) (cbrt.f64 (+.f64 (/.f64 x (pow.f64 y 3)) (+.f64 (/.f64 1 (.f64 y y)) (/.f64 (+.f64 x -1) y))))))

Compiler

Compiled 318908 to 176660 computations (44.6% saved)

regimes2.6s (14.8%)

Accuracy

Total 0.0b remaining (27.2%)

Threshold costs 0.0b (27.2%)

Counts

201 → 3

Compiler

Compiled 33005 to 22677 computations (31.3% saved)

bsearch66.0ms (0.4%)

Steps

Iters	Range		Point
9	83.01073491701408	3581014701.3406816	11126.107645742042
5	-416460.5630576568	-113717.4146418128	-115615.37911247845

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

24×	`+-commutative_binary64`
16×	`sub-neg_binary64`
13×	`*-commutative_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	121
1	60	121
2	84	121
3	109	121
4	123	121
5	130	121
6	138	121
7	142	121
8	145	121
9	146	121
10	143	121

end2.0ms (0%)

Compiler: Compiled 84 to 50 computations (40.5% saved)

sample1.5s (8.4%)

Algorithm

1×

intervals

Results

479.0ms	6299×	body	128	valid
169.0ms	593×	body	1024	valid
154.0ms	674×	body	512	valid
68.0ms	428×	body	256	valid
2.0ms	6×	body	2048	valid

Compiler

Compiled 218 to 140 computations (35.8% saved)

Iter	Nodes	Cost
0	37	121
1	60	121
2	84	121
3	109	121
4	123	121
5	130	121
6	138	121
7	142	121
8	145	121
9	146	121
10	143	121

Iter	Nodes	Cost
0	37	121
1	60	121
2	84	121
3	109	121
4	123	121
5	130	121
6	138	121
7	142	121
8	145	121
9	146	121
10	143	121

Details

analyze207.0ms (1.2%)

sample22.0ms (0.1%)

simplify198.0ms (1.1%)

prune4.0ms (0%)

localize6.0ms (0%)

series19.0ms (0.1%)

rewrite10.0ms (0.1%)

simplify81.0ms (0.5%)

prune88.0ms (0.5%)

localize6.0ms (0%)

series31.0ms (0.2%)

rewrite28.0ms (0.2%)

simplify125.0ms (0.7%)

prune163.0ms (0.9%)

localize58.0ms (0.3%)

series165.0ms (0.9%)

rewrite137.0ms (0.8%)

simplify241.0ms (1.4%)

prune318.0ms (1.8%)

localize21.0ms (0.1%)

series181.0ms (1%)

rewrite1.5s (8.7%)

simplify4.5s (25.8%)

prune5.1s (29.7%)

regimes2.6s (14.8%)

bsearch66.0ms (0.4%)

simplify16.0ms (0.1%)

end2.0ms (0%)

sample1.5s (8.4%)

Profiling

Iter	Nodes	Cost
0	37	121
1	60	121
2	84	121
3	109	121
4	123	121
5	130	121
6	138	121
7	142	121
8	145	121
9	146	121
10	143	121