Details

analyze307.0ms (9.4%)

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)

sample21.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 30 to 22 computations (26.7% saved)

simplify288.0ms (8.8%)

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

prune2.0ms (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)

localize10.0ms (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	(sqrt.f64 (-.f64 1 (*.f64 x x)))

rewrite420.0ms (12.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
43×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
16×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

223.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
22.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2373 to 1498 computations (36.9% saved)

series67.0ms (2%)

Error

0.0b

Counts

4 → 20

Calls

4 calls:

13.0ms	(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))
12.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
10.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 626 to 516 computations (17.6% saved)

simplify174.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

478×	`associate-/l/_binary64`
276×	`distribute-rgt-neg-in_binary64`
264×	`distribute-rgt-in_binary64`
218×	`distribute-lft-neg-in_binary64`
214×	`sub-neg_binary64` `associate-r_binary64`

Counts

137 → 64

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	2773
1	374	2641
2	897	2622
3	2420	2594
4	4792	2594
5	5000	2594
6	4860	2594

prune50.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	63	2	65

Error

Counts

65 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
▶	0.2b	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))

Status

Error

Program

✓

0.0b

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

▶

0.2b

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

Compiler

Compiled 1025 to 668 computations (34.8% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
0.2b	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))

rewrite343.0ms (10.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

148×	`*-un-lft-identity_binary64`
134×	`times-frac_binary64`
127×	`sqrt-prod_binary64`
111×	`add-sqr-sqrt_binary64`
70×	`add-cube-cbrt_binary64`

Counts

4 → 212

Calls

4 calls:

64.0ms	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
56.0ms	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 5005 to 2493 computations (50.2% saved)

series42.0ms (1.3%)

Error

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))
9.0ms	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))
8.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x))
7.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 444 to 346 computations (22.1% saved)

simplify223.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

448×	`unsub-neg_binary64`
353×	`distribute-rgt-in_binary64`
302×	`distribute-lft-in_binary64`
261×	`associate-+l+_binary64`
216×	`times-frac_binary64`

Counts

224 → 154

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	233	5062
1	491	4688
2	1342	4561
3	4374	4531
4	4976	4531
5	4942	4531

prune96.0ms (3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	154	2	156

Error

Counts

156 → 2

Alt Table

Status	Error	Program
	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	0.2b	(+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))

Status

Error

Program

0.0b

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

0.2b

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

Compiler

Compiled 2416 to 1226 computations (49.3% saved)

regimes470.0ms (14.4%)

Accuracy

Total 0.0b remaining (95.5%)

Threshold costs 0.0b (95.5%)

Compiler

Compiled 6106 to 4396 computations (28% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64` `*-commutative_binary64`
2×	`neg-mul-1_binary64` `neg-sub0_binary64`
1×	`1-exp_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	48
1	22	48
2	28	48
3	32	48
4	34	48
5	33	48

end1.0ms (0%)

Compiler: Compiled 31 to 21 computations (32.3% saved)

sample722.0ms (22.2%)

Algorithm

1×

intervals

Results

436.0ms	8000×	body	128	valid
0.0ms	4×	body	128	nan

Compiler

Compiled 82 to 57 computations (30.5% saved)

Details

analyze307.0ms (9.4%)

sample21.0ms (0.6%)

simplify288.0ms (8.8%)

prune2.0ms (0.1%)

localize10.0ms (0.3%)

rewrite420.0ms (12.9%)

series67.0ms (2%)

simplify174.0ms (5.3%)

prune50.0ms (1.5%)

localize15.0ms (0.5%)

rewrite343.0ms (10.5%)

series42.0ms (1.3%)

simplify223.0ms (6.8%)

prune96.0ms (3%)

regimes470.0ms (14.4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample722.0ms (22.2%)

Profiling