Details

Time bar (total: 5.4s)

sample37.0ms

Algorithm
intervals
Results
12.0ms276×body80valid
4.0ms89×body80overflowed
3.0ms9×body640valid
2.0ms9×body320valid
1.0ms2×body1280valid
0.0ms3×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
1129
2199
done199

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.0b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.0b
(+ 1.0 (exp x))
1.0b
(log (+ 1.0 (exp x)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×log-prod
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt
4×pow1 add-exp-log log-div associate--l+
3×flip3-+ add-cbrt-cube flip-+ distribute-lft-out
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log log-pow flip--
Counts
3 → 45
Calls
3 calls:
11.0ms
(- (log (+ 1.0 (exp x))) (* x y))
4.0ms
(+ 1.0 (exp x))
4.0ms
(log (+ 1.0 (exp x)))

series25.0ms

Counts
3 → 9
Calls
3 calls:
10.0ms
(- (log (+ 1.0 (exp x))) (* x y))
2.0ms
(+ 1.0 (exp x))
12.0ms
(log (+ 1.0 (exp x)))

simplify908.0ms

Counts
54 → 54
Iterations

Useful iterations: 4 (410.0ms)

IterNodesCost
092575
1210544
2531514
31352508
42869506
done5000506

prune87.0ms

Filtered
40 candidates to 54 candidates (-35.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New51354
Fresh000
Picked101
Done000
Total52355

Merged error: 0.4b

Counts
55 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ 1.0 (exp x)))
0.2b
(sqrt (+ 1.0 (exp x)))
1.5b
(log (sqrt (+ 1.0 (exp x))))
1.5b
(log (sqrt (+ 1.0 (exp x))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
16×sqrt-prod
14×log-prod
12×add-sqr-sqrt
10×pow1 add-cube-cbrt
8×sqrt-div
6×add-exp-log log-pow
4×log-div sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ distribute-lft-out add-log-exp
2×rem-sqrt-square rem-log-exp
Counts
4 → 72
Calls
4 calls:
6.0ms
(sqrt (+ 1.0 (exp x)))
4.0ms
(sqrt (+ 1.0 (exp x)))
5.0ms
(log (sqrt (+ 1.0 (exp x))))
5.0ms
(log (sqrt (+ 1.0 (exp x))))

series40.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 (exp x)))
4.0ms
(sqrt (+ 1.0 (exp x)))
16.0ms
(log (sqrt (+ 1.0 (exp x))))
15.0ms
(log (sqrt (+ 1.0 (exp x))))

simplify1.0s

Counts
84 → 84
Iterations

Useful iterations: 3 (103.0ms)

IterNodesCost
086910
1163838
2409780
31143754
43914754
done5000754

prune164.0ms

Filtered
60 candidates to 84 candidates (-40.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh022
Picked011
Done000
Total84387

Merged error: 0.4b

Counts
87 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (pow x 2))
0.0b
(- (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) (* x y))
0.0b
(+ x (+ (* 1/2 (pow x 2)) 2.0))
6.3b
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt *-un-lft-identity
10×add-exp-log add-log-exp
9×add-cube-cbrt
8×log-prod associate-*r*
6×add-cbrt-cube
5×pow1
4×unpow-prod-down log-div associate--l+ unswap-sqr
3×flip3-+ associate-*l* prod-exp sum-log flip-+ distribute-lft-out
2×associate--l- unpow2 sqr-pow
1×+-commutative pow-to-exp sub-neg associate-+r+ flip3-- diff-log rem-log-exp pow-exp log-pow *-commutative flip-- cbrt-unprod
Counts
4 → 74
Calls
4 calls:
6.0ms
(* 1/2 (pow x 2))
9.0ms
(- (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) (* x y))
7.0ms
(+ x (+ (* 1/2 (pow x 2)) 2.0))
6.0ms
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

series22.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 1/2 (pow x 2))
11.0ms
(- (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) (* x y))
3.0ms
(+ x (+ (* 1/2 (pow x 2)) 2.0))
5.0ms
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

simplify961.0ms

Counts
86 → 86
Iterations

Useful iterations: done (958.0ms)

IterNodesCost
01541242
13731152
210891061
334861043
done50011041

prune159.0ms

Filtered
65 candidates to 86 candidates (-32.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh011
Picked101
Done011
Total85489

Merged error: 0.4b

Counts
89 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ (* 1/2 (pow x 2)) 2.0))
0.9b
(cbrt (pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3))
0.9b
(pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3)
6.3b
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
14×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt
10×pow1
9×add-log-exp
8×unpow-prod-down cube-prod
6×add-exp-log
5×log-pow add-cbrt-cube
4×log-prod
3×pow-unpow sum-log
2×cube-mult log-div flip3-+ unpow3 flip-+ distribute-lft-out sqr-pow
1×+-commutative pow-to-exp associate-+r+ pow-pow pow1/3 rem-log-exp pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 77
Calls
4 calls:
7.0ms
(+ x (+ (* 1/2 (pow x 2)) 2.0))
3.0ms
(cbrt (pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3))
3.0ms
(pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3)
7.0ms
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

series26.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(+ x (+ (* 1/2 (pow x 2)) 2.0))
5.0ms
(cbrt (pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3))
13.0ms
(pow (log (+ x (+ (* 1/2 (pow x 2)) 2.0))) 3)
5.0ms
(log (+ x (+ (* 1/2 (pow x 2)) 2.0)))

simplify508.0ms

Counts
89 → 89
Iterations

Useful iterations: done (505.0ms)

IterNodesCost
02021930
15411749
219651542
done50011531

prune173.0ms

Filtered
57 candidates to 89 candidates (-56.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New88189
Fresh112
Picked101
Done011
Total90393

Merged error: 0.4b

Counts
93 → 3

regimes83.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01017
11217
done1217

end0.0ms

sample1.0s

Algorithm
intervals
Results
376.0ms8416×body80valid
104.0ms2517×body80overflowed
71.0ms249×body640valid
63.0ms125×body1280valid
40.0ms231×body320valid
12.0ms115×body160valid

Profiling

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