Details

Time bar (total: 16.0s)

sample27.0ms

Algorithm
intervals
Results
13.0ms472×body80valid

simplify33.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (10.0ms)

IterNodesCost
0715
11315
22313
3359
4439
5469
done469

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* y y))
0.1b
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
2×associate-+l+
Counts
3 → 38
Calls
3 calls:
9.0ms
(+ (* x x) (* y y))
38.0ms
(+ (+ (* x x) (* y y)) (* y y))
157.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series152.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (* x x) (* y y))
56.0ms
(+ (+ (* x x) (* y y)) (* y y))
57.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify2.1s

Counts
47 → 47
Iterations

Useful iterations: 3 (780.0ms)

IterNodesCost
070791
1211667
2725591
32852513
done5000513

prune180.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
0.3b
(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
6.8b
(sqrt (+ (pow x 2) (* 2 (pow y 2))))
6.8b
(sqrt (+ (pow x 2) (* 2 (pow y 2))))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
44.0ms
(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
103.0ms
(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
19.0ms
(sqrt (+ (pow x 2) (* 2 (pow y 2))))
14.0ms
(sqrt (+ (pow x 2) (* 2 (pow y 2))))

series231.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2))))) (* y y))
67.0ms
(* (sqrt (+ (pow x 2) (* 2 (pow y 2)))) (sqrt (+ (pow x 2) (* 2 (pow y 2)))))
56.0ms
(sqrt (+ (pow x 2) (* 2 (pow y 2))))
58.0ms
(sqrt (+ (pow x 2) (* 2 (pow y 2))))

simplify2.6s

Counts
110 → 110
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01082708
12471699
28221551
332411429
done50011401

prune317.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (pow x 2) (* y (* 3 y)))
0.2b
(* y (* 3 y))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l* pow-prod-down prod-exp cbrt-unprod
1×+-commutative flip3-+ associate-*r* sum-log *-commutative flip-+
Counts
2 → 29
Calls
2 calls:
19.0ms
(+ (pow x 2) (* y (* 3 y)))
17.0ms
(* y (* 3 y))

series67.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(+ (pow x 2) (* y (* 3 y)))
27.0ms
(* y (* 3 y))

simplify4.2s

Counts
35 → 35
Iterations

Useful iterations: 4 (2.2s)

IterNodesCost
056362
1155326
2477294
31323282
43717280
done5002280

prune145.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (pow y 2))
0.2b
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
6.8b
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
6.8b
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
24×sqrt-prod
21×pow1
17×add-cube-cbrt *-un-lft-identity
16×sqrt-div
14×associate-*r*
11×add-exp-log
10×sqrt-pow1 pow1/2
9×associate-*l*
8×flip3-+ swap-sqr add-cbrt-cube flip-+ unswap-sqr
5×pow-prod-up
4×frac-times unpow-prod-down prod-exp add-log-exp
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/ *-commutative cbrt-unprod unpow2 sqr-pow
1×pow2 pow-to-exp pow-plus sqrt-unprod pow-exp rem-square-sqrt
Counts
4 → 114
Calls
4 calls:
12.0ms
(* 3 (pow y 2))
92.0ms
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
24.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
27.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* 3 (pow y 2))
54.0ms
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
65.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
75.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

simplify2.6s

Counts
126 → 126
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01282444
12501633
26631498
321931415
done50001384

prune435.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes201.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
11015
done1015

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.3s14236×body80valid