Details

Time bar (total: 11.0s)

sample20.0ms

Algorithm
intervals
Results
10.0ms343×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
1147
2207
3227
done227

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1.0 (* y y))
4.8b
(* x (+ 1.0 (* y y)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×flip3-+ associate-*r/ flip-+
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
2 → 33
Calls
2 calls:
5.0ms
(+ 1.0 (* y y))
16.0ms
(* x (+ 1.0 (* y y)))

series95.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(+ 1.0 (* y y))
61.0ms
(* x (+ 1.0 (* y y)))

simplify2.1s

Counts
39 → 39
Iterations

Useful iterations: 3 (457.0ms)

IterNodesCost
059371
1165359
2499309
31609307
done5000307

prune95.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (sqrt (+ 1.0 (* y y))))
0.1b
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-div
17×add-sqr-sqrt
13×pow1 sqrt-prod
12×associate-*r*
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ *-commutative unswap-sqr
Counts
4 → 83
Calls
4 calls:
22.0ms
(* x (sqrt (+ 1.0 (* y y))))
51.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
11.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(* x (sqrt (+ 1.0 (* y y))))
70.0ms
(* (* x (sqrt (+ 1.0 (* y y)))) (sqrt (+ 1.0 (* y y))))
70.0ms
(sqrt (+ 1.0 (* y y)))
63.0ms
(sqrt (+ 1.0 (* y y)))

simplify1.9s

Counts
95 → 95
Iterations

Useful iterations: 3 (915.0ms)

IterNodesCost
01221468
13031152
28351012
327461002
done50021002

prune302.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
30×sqrt-div
18×sqrt-prod
13×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log flip3-+ associate-*r* add-cbrt-cube flip-+
8×associate-*r/
4×frac-times add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×associate-*l/
1×associate-*l* *-commutative
Counts
4 → 77
Calls
4 calls:
65.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
7.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))
10.0ms
(sqrt (+ 1.0 (* y y)))

series233.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (* x (sqrt (sqrt (+ 1.0 (* y y))))) (sqrt (sqrt (+ 1.0 (* y y)))))
54.0ms
(sqrt (+ 1.0 (* y y)))
53.0ms
(sqrt (+ 1.0 (* y y)))
46.0ms
(sqrt (+ 1.0 (* y y)))

simplify2.2s

Counts
89 → 89
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01201511
12951169
28111027
320581015
done50011002

prune276.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 4.9b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (+ 1.0 (* y y)))
4.9b
(cbrt (+ 1.0 (* y y)))
4.9b
(cbrt (+ 1.0 (* y y)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log cbrt-div flip3-+ sqrt-div add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 56
Calls
4 calls:
7.0ms
(sqrt (+ 1.0 (* y y)))
5.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))
3.0ms
(cbrt (+ 1.0 (* y y)))

series522.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (+ 1.0 (* y y)))
52.0ms
(sqrt (+ 1.0 (* y y)))
197.0ms
(cbrt (+ 1.0 (* y y)))
213.0ms
(cbrt (+ 1.0 (* y y)))

simplify1.5s

Counts
68 → 68
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0105920
1237834
2650776
32159754
done5000748

prune364.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 4.9b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 5.8b against oracle of 5.6b and baseline of 5.8b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
done87

end0.0ms

sample731.0ms

Algorithm
intervals
Results
434.0ms10573×body80valid