Details

Time bar (total: 18.5s)

sample37.0ms

Algorithm
intervals
Results
18.0ms256×body80valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11312
22012
32212
done2212

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) (* y y))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt add-log-exp
3×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
2×add-exp-log flip3-+ sqrt-div add-cbrt-cube flip-+
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 sum-log
Counts
2 → 26
Calls
2 calls:
15.0ms
(+ (* x x) (* y y))
62.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series183.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(+ (* x x) (* y y))
142.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.1s

Counts
32 → 32
Iterations

Useful iterations: 3 (330.0ms)

IterNodesCost
063471
1172417
2496387
31364377
44252377
done5001377

prune111.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.1b

localize25.0ms

Local error

Found 4 expressions with local error:

31.0b
(cbrt (+ (* x x) (* y y)))
31.0b
(cbrt (+ (* x x) (* y y)))
31.0b
(cbrt (+ (* x x) (* y y)))
35.1b
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×cbrt-div
5×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
5.0ms
(cbrt (+ (* x x) (* y y)))
7.0ms
(cbrt (+ (* x x) (* y y)))
5.0ms
(cbrt (+ (* x x) (* y y)))
170.0ms
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(cbrt (+ (* x x) (* y y)))
101.0ms
(cbrt (+ (* x x) (* y y)))
111.0ms
(cbrt (+ (* x x) (* y y)))
120.0ms
(sqrt (+ (* (* (cbrt (+ (* x x) (* y y))) (cbrt (+ (* x x) (* y y)))) (cbrt (+ (* x x) (* y y)))) (* z z)))

simplify3.2s

Counts
66 → 66
Iterations

Useful iterations: done (3.2s)

IterNodesCost
0831438
12041347
2480829
31257814
44436814
done5001793

prune310.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×add-cube-cbrt *-un-lft-identity
8×sqrt-div
7×pow1
6×cbrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 61
Calls
4 calls:
18.0ms
(cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))
30.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
53.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
31.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))
129.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
138.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
138.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))

simplify3.2s

Counts
73 → 73
Iterations

Useful iterations: 3 (359.0ms)

IterNodesCost
0771358
11701212
24641109
313501106
444691106
done50001106

prune387.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.1b

localize46.0ms

Local error

Found 4 expressions with local error:

4.4b
(exp (log (cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))
35.1b
(sqrt (+ (* z z) (+ (* y y) (* x x))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×sqrt-prod
11×add-cube-cbrt *-un-lft-identity
9×log-prod exp-sum
8×pow1 sqrt-div
6×cbrt-prod
5×exp-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×log-div cbrt-div exp-diff log-pow
1×pow1/3 rem-exp-log
Counts
4 → 69
Calls
4 calls:
38.0ms
(exp (log (cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))))
33.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
37.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
49.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))

series624.0ms

Counts
4 → 12
Calls
4 calls:
156.0ms
(exp (log (cbrt (sqrt (+ (* z z) (+ (* y y) (* x x)))))))
139.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
165.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))
162.0ms
(sqrt (+ (* z z) (+ (* y y) (* x x))))

simplify3.4s

Counts
81 → 81
Iterations

Useful iterations: 4 (1.7s)

IterNodesCost
01181561
12171349
25211184
314171181
445531169
done50011169

prune437.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.1b

regimes533.0ms

Accuracy

61.8% (7.5b remaining)

Error of 25.4b against oracle of 17.9b and baseline of 37.5b

bsearch62.0ms

Steps
ItersRangePoint
10
4.022397810881141e+88
1.565796980266273e+101
1.537188568549187e+101
1
-4.90105109200061e+89
-4.6551667645331244e+89
-4.839580010133739e+89

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01623
11823
done1823

end0.0ms

sample1.3s

Algorithm
intervals
Results
915.0ms8000×body80valid