Details

analyze278.0ms (9.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify272.0ms (9.7%)

Algorithm

1×	egg-herbie

Rules

2074×	`distribute-lft-out--_binary64`
788×	`distribute-rgt-out--_binary64`
756×	`unsub-neg_binary64`
614×	`sub-neg_binary64`
581×	`distribute-rgt-out_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	24	20
3	31	20
4	45	20
5	60	20
6	96	20
7	213	20
8	364	20
9	486	20
10	1099	20
11	1877	20
12	1931	20
13	2167	20
14	2315	20
15	2313	20
16	2390	20
17	2649	20
18	3212	20
19	4204	20
20	4738	20
21	4780	20
22	4791	20
23	4788	20
24	4573	20
25	4366	20
26	4503	20
27	4563	20
28	4606	20
29	7544	20

prune1.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(-.f64 1 (*.f64 x x))

rewrite112.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

65×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
41×	`add-sqr-sqrt_binary64`
30×	`add-cube-cbrt_binary64`
26×	`sqrt-prod_binary64`

Counts

4 → 114

Calls

4 calls:

18.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
15.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
2.0ms	(-.f64 1 (*.f64 x x))

Compiler

Compiled 2319 to 1460 computations (37% saved)

series44.0ms (1.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

9.0ms	(-.f64 1 (*.f64 x x))
8.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
6.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Compiler

Compiled 653 to 536 computations (17.9% saved)

simplify154.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

330×	`distribute-rgt-neg-in_binary64`
269×	`distribute-lft-neg-in_binary64`
263×	`sub-neg_binary64`
248×	`associate-l_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

138 → 72

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	198	2979
1	401	2761
2	1014	2727
3	2890	2597
4	4629	2597
5	4972	2597
6	4859	2597

prune33.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	2	73

Error

0.0b

Counts

73 → 2

Alt Table

Status	Error	Program
▶	62.9b	(log.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 1040 to 685 computations (34.1% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(log.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
0.0b	(-.f64 1 (*.f64 x x))
2.9b	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite166.0ms (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

217×	`times-frac_binary64`
207×	`add-sqr-sqrt_binary64`
159×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
77×	`log-prod_binary64`

Counts

4 → 217

Calls

4 calls:

23.0ms	(log.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
17.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
5.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(-.f64 1 (*.f64 x x))

Compiler

Compiled 5004 to 3369 computations (32.7% saved)

series45.0ms (1.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

9.0ms	(log.f64 (/.f64 1 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
9.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
7.0ms	(-.f64 1 (*.f64 x x))

Compiler

Compiled 740 to 623 computations (15.8% saved)

simplify231.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

621×	`times-frac_binary64`
427×	`associate-/l*_binary64`
231×	`cancel-sign-sub-inv_binary64`
172×	`associate-/r/_binary64`
170×	`associate-/l/_binary64`

Counts

241 → 172

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	6465
1	679	6304
2	1872	6137
3	4392	6029
4	4971	6029
5	4910	6029

prune36.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	172	2	174

Error

Counts

174 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	62.9b	(.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))

Status

Error

Program

✓

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

▶

62.9b

(*.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))

Compiler

Compiled 1620 to 1109 computations (31.5% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (*.f64 x x))
0.0b	(.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))
2.9b	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
2.9b	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite205.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

141×	`add-sqr-sqrt_binary64`
112×	`sqrt-prod_binary64`
111×	`*-un-lft-identity_binary64`
98×	`times-frac_binary64`
58×	`add-cube-cbrt_binary64`

Counts

4 → 222

Calls

4 calls:

20.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
18.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
12.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))
3.0ms	(-.f64 1 (*.f64 x x))

Compiler

Compiled 7649 to 5185 computations (32.2% saved)

series66.0ms (2.3%)

Error

Counts

4 → 24

Calls

4 calls:

21.0ms	(.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))
12.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
9.0ms	(-.f64 1 (*.f64 x x))
9.0ms	(-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

Compiler

Compiled 1373 to 1096 computations (20.2% saved)

simplify193.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

369×	`associate-/l*_binary64`
264×	`associate-*l/_binary64`
254×	`times-frac_binary64`
231×	`div-sub_binary64`
220×	`associate-*r/_binary64`

Counts

246 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	272	6694
1	630	6269
2	1812	6110
3	4238	5866
4	4975	5866

prune56.0ms (2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	192	0	192
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	192	2	194

Error

Counts

194 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	62.9b	(.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))

Status

Error

Program

0.0b

(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

62.9b

(*.f64 (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (sqrt.f64 (neg.f64 (log.f64 (-.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))

Compiler

Compiled 2907 to 2001 computations (31.2% saved)

regimes102.0ms (3.6%)

Accuracy

Total 0.0b remaining (1%)

Threshold costs 0.0b (1%)

Compiler

Compiled 1495 to 1165 computations (22.1% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	18	23
2	22	23
3	24	23
4	25	23
5	24	23

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample761.0ms (27%)

Algorithm

1×

intervals

Results

526.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 78 to 57 computations (26.9% saved)

Details

analyze278.0ms (9.9%)

sample23.0ms (0.8%)

simplify272.0ms (9.7%)

prune1.0ms (0.1%)

localize9.0ms (0.3%)

rewrite112.0ms (4%)

series44.0ms (1.5%)

simplify154.0ms (5.5%)

prune33.0ms (1.2%)

localize10.0ms (0.4%)

rewrite166.0ms (5.9%)

series45.0ms (1.6%)

simplify231.0ms (8.2%)

prune36.0ms (1.3%)

localize12.0ms (0.4%)

rewrite205.0ms (7.3%)

series66.0ms (2.3%)

simplify193.0ms (6.9%)

prune56.0ms (2%)

regimes102.0ms (3.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample761.0ms (27%)

Profiling