Details

Time bar (total: 7.9s)

sample68.0ms

Algorithm
intervals
Results
20.0ms46×body1280valid
13.0ms46×body640valid
8.0ms148×body80valid
6.0ms34×body320valid
4.0ms94×body80nan
1.0ms10×body160valid

simplify682.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (3.0ms)

IterNodesCost
0811
11511
2249
3519
41099
52709
66509
721829
done50009

prune13.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 11.6b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ x (+ x y))
6.1b
(pow (/ x (+ x y)) x)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity
24×times-frac
20×add-sqr-sqrt add-cube-cbrt
18×unpow-prod-down
add-exp-log distribute-lft-out
associate-/r* associate-/r/ add-cbrt-cube
pow1 pow-unpow associate-/l*
flip3-+ div-exp pow-exp flip-+ div-inv add-log-exp
cbrt-undiv pow-to-exp pow-pow frac-2neg clear-num sqr-pow
Counts
2 → 66
Calls
2 calls:
5.0ms
(/ x (+ x y))
7.0ms
(pow (/ x (+ x y)) x)

series26.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(/ x (+ x y))
21.0ms
(pow (/ x (+ x y)) x)

simplify419.0ms

Counts
72 → 72
Iterations

Useful iterations: done (417.0ms)

IterNodesCost
01751011
1459950
21461892
done5000861

prune110.0ms

Filtered
53 candidates to 72 candidates (-35.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New67572
Fresh000
Picked101
Done000
Total68573

Merged error: 2.0b

Counts
73 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
1.2b
(pow (/ (cbrt x) (cbrt (+ x y))) x)
1.9b
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
61×unpow-prod-down
51×cbrt-prod
48×*-un-lft-identity
43×times-frac
36×add-sqr-sqrt add-cube-cbrt
20×add-exp-log
14×cbrt-div
10×associate-/r/
flip3-+ pow-exp flip-+
pow1 pow-unpow distribute-lft-out
div-exp
frac-times prod-exp add-cbrt-cube add-log-exp
pow-to-exp pow-pow pow1/3 associate-*r/ associate-*l/ div-inv sqr-pow
Counts
4 → 116
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
12.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
17.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

series126.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cbrt x)
25.0ms
(cbrt x)
29.0ms
(pow (/ (cbrt x) (cbrt (+ x y))) x)
45.0ms
(pow (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x y)) (cbrt (+ x y)))) x)

simplify698.0ms

Counts
128 → 128
Iterations

Useful iterations: done (694.0ms)

IterNodesCost
03952771
19742629
228532349
done50002331

prune187.0ms

Filtered
93 candidates to 128 candidates (-37.6%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1271128
Fresh224
Picked011
Done000
Total1294133

Merged error: 0.9b

Counts
133 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (* (- (log x) (log (+ x y))) x))
0.1b
(* (- (log x) (log (+ x y))) x)
1.6b
(- (log x) (log (+ x y)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
13×pow1 add-sqr-sqrt
associate-*l* log-pow distribute-lft-out--
add-cube-cbrt log-prod
add-exp-log add-cbrt-cube add-log-exp
associate--r+
associate-*r* associate--l+
log-div flip3-- exp-to-pow diff-log associate-*l/ flip-- associate--r- difference-of-squares
sub-neg exp-prod flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ rem-exp-log distribute-lft-out unswap-sqr
Counts
3 → 62
Calls
3 calls:
3.0ms
(exp (* (- (log x) (log (+ x y))) x))
8.0ms
(* (- (log x) (log (+ x y))) x)
8.0ms
(- (log x) (log (+ x y)))

series67.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(exp (* (- (log x) (log (+ x y))) x))
23.0ms
(* (- (log x) (log (+ x y))) x)
13.0ms
(- (log x) (log (+ x y)))

simplify1.1s

Counts
71 → 71
Iterations

Useful iterations: 3 (333.0ms)

IterNodesCost
0134860
1306836
21019717
33902687
done5001687

prune91.0ms

Filtered
55 candidates to 71 candidates (-29.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New70171
Fresh202
Picked011
Done011
Total72375

Merged error: 0.0b

Counts
75 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(/ (exp (neg y)) x)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
associate-/r* add-cbrt-cube associate-/l*
add-exp-log associate-/l/
pow1 cbrt-undiv neg-sub0 exp-neg frac-2neg exp-diff div-exp clear-num div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
6.0ms
(/ (exp (neg y)) x)

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(/ (exp (neg y)) x)

simplify1.9s

Counts
32 → 32
Iterations

Useful iterations: 3 (96.0ms)

IterNodesCost
064299
1118289
2322271
31087267
44704267
done5000267

prune30.0ms

Filtered
24 candidates to 32 candidates (-33.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New30232
Fresh000
Picked101
Done022
Total31435

Merged error: 0b

Counts
35 → 4

regimes117.0ms

Accuracy

86.6% (0.8b remaining)

Error of 1.3b against oracle of 0.5b and baseline of 6.7b

bsearch64.0ms

Steps
ItersRangePoint
8
0.009971872296741319
483.8343007553032
2.105386851920235
8
-3.817206138481307e+76
-8.704679048448932e+71
-1.7314167029711811e+72

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02854
13454
done3454

end0.0ms

sample2.2s

Algorithm
intervals
Results
748.0ms1583×body1280valid
417.0ms1473×body640valid
257.0ms4833×body80valid
158.0ms816×body320valid
138.0ms3067×body80nan
56.0ms429×body160valid

Profiling

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