Details

analyze105.0ms (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 (34.2%)

Results

639.0ms	6522×	body	128	valid
194.0ms	614×	body	1024	valid
142.0ms	653×	body	512	valid
71.0ms	458×	body	256	valid
3.0ms	9×	body	2048	valid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify199.0ms (5.7%)

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

15.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	15.8b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)
	24.0b	(-.f64 1 (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)))

Compiler

Compiled 73 to 55 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 x -1) (+.f64 1 y))
✓	15.9b	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

series19.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

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

rewrite8.0ms (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:

5.0ms	(/.f64 (+.f64 x -1) (+.f64 1 y))
0.0ms	(fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)

simplify80.0ms (2.3%)

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

prune102.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	101	3	104

Error

0.0b

Counts

104 → 3

Alt Table

Status	Error	Program
▶	15.8b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	32.4b	(-.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))))
	36.8b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 1910 to 1311 computations (31.4% saved)

localize6.0ms (0.2%)

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))
✓	2.6b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)

series23.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

10.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
9.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
5.0ms	(/.f64 y (+.f64 1 y))

rewrite33.0ms (0.9%)

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:

14.0ms	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
8.0ms	(*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1))
4.0ms	(/.f64 y (+.f64 1 y))

simplify101.0ms (2.9%)

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

prune124.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	190	4	194

Error

0.0b

Counts

194 → 4

Alt Table

Status	Error	Program
✓	15.8b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	32.4b	(-.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))))
▶	27.3b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)))
	36.8b	(log.f64 (exp.f64 (fma.f64 y (/.f64 (+.f64 x -1) (+.f64 1 y)) 1)))

Compiler

Compiled 3681 to 2557 computations (30.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (+.f64 1 y))
✓	0.0b	(sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1))
✓	0.1b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)))
✓	2.6b	(fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)

series48.0ms (1.4%)

Counts

3 → 64

Calls

3 calls:

31.0ms

(sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1))

9.0ms

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

8.0ms

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

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

5.0ms

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

1.0ms

(sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1))

0.0ms

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

simplify105.0ms (3%)

Algorithm

1×	egg-herbie

Rules

514×	`times-frac_binary64`
320×	`associate-/l*_binary64`
313×	`cancel-sign-sub-inv_binary64`
297×	`associate-/r*_binary64`
284×	`fma-neg_binary64`

Counts

142 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	3692
1	557	3307
2	1997	3200
3	4981	3198
4	5113	3198

prune263.0ms (7.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	286	3	289

Error

0.0b

Counts

289 → 3

Alt Table

Status	Error	Program
✓	15.8b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	32.4b	(-.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))))
▶	27.2b	(.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 (.f64 y (/.f64 1 (+.f64 1 y))) (-.f64 x 1) 1)))

Compiler

Compiled 9692 to 7076 computations (27% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 y (/.f64 1 (+.f64 1 y)))
✓	0.1b	(.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 (.f64 y (/.f64 1 (+.f64 1 y))) (-.f64 x 1) 1)))
	2.6b	(fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)
✓	4.8b	(fma.f64 (*.f64 y (/.f64 1 (+.f64 1 y))) (-.f64 x 1) 1)

series23.0ms (0.7%)

Counts

3 → 60

Calls

3 calls:

13.0ms

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

8.0ms

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

2.0ms

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

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
24×	`associate-r_binary64`
23×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`

Counts

3 → 86

Calls

3 calls:

11.0ms

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

5.0ms

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

0.0ms

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

simplify143.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
408×	`sub-neg_binary64`
335×	`fma-def_binary64`
240×	`associate--l+_binary64`
235×	`associate-l_binary64`

Counts

146 → 149

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	2664
1	360	2494
2	1050	2211
3	3290	2202
4	4650	2202
5	4980	2202
6	4956	2202

prune170.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	179	4	183

Error

0.0b

Counts

183 → 4

Alt Table

Status	Error	Program
✓	15.8b	(+.f64 (*.f64 (/.f64 y (+.f64 1 y)) (+.f64 x -1)) 1)
	32.4b	(-.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))))
	27.6b	(*.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 x 1) (+.f64 1 y)) 1)))
✓	27.2b	(.f64 (sqrt.f64 (fma.f64 (/.f64 y (+.f64 1 y)) (-.f64 x 1) 1)) (sqrt.f64 (fma.f64 (.f64 y (/.f64 1 (+.f64 1 y))) (-.f64 x 1) 1)))

Compiler

Compiled 5744 to 4287 computations (25.4% saved)

regimes547.0ms (15.8%)

Accuracy

Total 0.0b remaining (44.4%)

Threshold costs 0.0b (44.4%)

Counts

63 → 3

Compiler

Compiled 5353 to 3976 computations (25.7% saved)

bsearch2.0ms (0.1%)

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

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	126
1	51	126
2	66	126
3	85	126
4	104	126
5	114	126
6	122	126
7	128	126
8	132	126
9	135	126
10	136	126
11	133	126

end109.0ms (3.2%)

Compiler: Compiled 272 to 189 computations (30.5% saved)

Iter	Nodes	Cost
0	35	126
1	51	126
2	66	126
3	85	126
4	104	126
5	114	126
6	122	126
7	128	126
8	132	126
9	135	126
10	136	126
11	133	126

Iter	Nodes	Cost
0	35	126
1	51	126
2	66	126
3	85	126
4	104	126
5	114	126
6	122	126
7	128	126
8	132	126
9	135	126
10	136	126
11	133	126

Details

analyze105.0ms (3%)

sample1.2s (34.2%)

simplify199.0ms (5.7%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

series19.0ms (0.6%)

rewrite8.0ms (0.2%)

simplify80.0ms (2.3%)

prune102.0ms (2.9%)

localize6.0ms (0.2%)

series23.0ms (0.7%)

rewrite33.0ms (0.9%)

simplify101.0ms (2.9%)

prune124.0ms (3.6%)

localize8.0ms (0.2%)

series48.0ms (1.4%)

rewrite13.0ms (0.4%)

simplify105.0ms (3%)

prune263.0ms (7.6%)

localize12.0ms (0.4%)

series23.0ms (0.7%)

rewrite22.0ms (0.6%)

simplify143.0ms (4.1%)

prune170.0ms (4.9%)

regimes547.0ms (15.8%)

bsearch2.0ms (0.1%)

simplify8.0ms (0.2%)

end109.0ms (3.2%)

Profiling

Iter	Nodes	Cost
0	35	126
1	51	126
2	66	126
3	85	126
4	104	126
5	114	126
6	122	126
7	128	126
8	132	126
9	135	126
10	136	126
11	133	126