Details

Time bar (total: 45.8s)

sample44.0ms

Algorithm
intervals
Results
21.0ms398×body80valid
7.0ms146×body80nan

simplify2.8s

Counts
1 → 1
Iterations
IterNodes
done5001
62300
5639
4204
387
247
126
012

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (+ k 10) k) 1)
0.0b
(* (+ k 10) k)
1.8b
(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
159×times-frac
89×add-sqr-sqrt *-un-lft-identity
87×add-cube-cbrt
36×unpow-prod-down
25×associate-/r*
15×add-exp-log
12×sqr-pow
10×add-cbrt-cube
7×div-exp
5×pow1 div-inv add-log-exp
4×associate-*l*
3×cbrt-undiv associate-*r* insert-posit16 associate-/l*
2×flip3-+ associate-*l/ flip-+
1×pow-to-exp +-commutative clear-num sum-log frac-2neg pow-prod-down pow-exp prod-exp associate-/r/ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 155
Calls
3 calls:
23.0ms
(+ (* (+ k 10) k) 1)
52.0ms
(* (+ k 10) k)
27.0ms
(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

series243.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(+ (* (+ k 10) k) 1)
58.0ms
(* (+ k 10) k)
166.0ms
(/ a (/ (+ (* (+ k 10) k) 1) (pow k m)))

simplify3.3s

Counts
164 → 164
Iterations
IterNodes
done5016
23495
1904
0344

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m))
0.0b
(/ (/ a (/ (sqrt (+ (* (+ k 10) k) 1)) 1)) (/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m)))
14.9b
(sqrt (+ (* (+ k 10) k) 1))
14.9b
(sqrt (+ (* (+ k 10) k) 1))

rewrite798.0ms

Algorithm
rewrite-expression-head
Rules
11972×times-frac
4896×add-sqr-sqrt
4894×*-un-lft-identity add-cube-cbrt
2811×sqrt-prod
1317×unpow-prod-down
439×sqr-pow
262×div-inv
77×associate-/l*
65×add-exp-log
53×associate-/r*
51×div-exp
48×associate-/r/
27×add-cbrt-cube
16×cbrt-undiv
6×pow1 sqrt-div
5×pow-to-exp pow-exp
4×1-exp insert-posit16 add-log-exp
3×flip3-+ flip-+ associate-/l/
2×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2
Counts
4 → 3522
Calls
4 calls:
55.0ms
(/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m))
180.0ms
(/ (/ a (/ (sqrt (+ (* (+ k 10) k) 1)) 1)) (/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m)))
24.0ms
(sqrt (+ (* (+ k 10) k) 1))
37.0ms
(sqrt (+ (* (+ k 10) k) 1))

series386.0ms

Counts
4 → 12
Calls
4 calls:
142.0ms
(/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m))
167.0ms
(/ (/ a (/ (sqrt (+ (* (+ k 10) k) 1)) 1)) (/ (sqrt (+ (* (+ k 10) k) 1)) (pow k m)))
33.0ms
(sqrt (+ (* (+ k 10) k) 1))
43.0ms
(sqrt (+ (* (+ k 10) k) 1))

simplify6.1s

Counts
3534 → 3534
Iterations
IterNodes
done5001
04172

prune19.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt a)
14.9b
(sqrt (+ (* (+ k 10) k) 1))
14.9b
(sqrt (+ (* (+ k 10) k) 1))
14.9b
(sqrt (+ (* (+ k 10) k) 1))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×sqrt-div
4×add-cbrt-cube add-exp-log insert-posit16 add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow1/3
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt a)
21.0ms
(sqrt (+ (* (+ k 10) k) 1))
25.0ms
(sqrt (+ (* (+ k 10) k) 1))
23.0ms
(sqrt (+ (* (+ k 10) k) 1))

series403.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(cbrt a)
52.0ms
(sqrt (+ (* (+ k 10) k) 1))
57.0ms
(sqrt (+ (* (+ k 10) k) 1))
42.0ms
(sqrt (+ (* (+ k 10) k) 1))

simplify1.8s

Counts
72 → 72
Iterations
IterNodes
done5009
42220
3797
2356
1152
073

prune601.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

5.0b
(/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k)))
6.8b
(/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))
7.7b
(- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k)))
9.8b
(+ (* 99 (* (/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k))) a)) (- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))))

rewrite733.0ms

Algorithm
rewrite-expression-head
Rules
58×add-cbrt-cube
47×add-exp-log
26×prod-exp cbrt-unprod
14×cbrt-undiv div-exp
12×log-prod distribute-neg-in exp-sum
11×times-frac add-log-exp
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt associate-/l*
9×associate-*r/
7×associate-*l/
6×distribute-rgt-in exp-neg distribute-lft-in frac-sub associate-/l/
5×frac-add
4×pow1 insert-posit16
3×distribute-lft-neg-out distribute-rgt-neg-out
2×frac-times associate-+r+ clear-num associate-/r* sum-log sub-neg frac-2neg flip3-- diff-log un-div-inv div-inv flip--
1×+-commutative associate-+r- flip3-+ distribute-rgt-out-- flip-+
Counts
4 → 116
Calls
4 calls:
77.0ms
(/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k)))
81.0ms
(/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))
46.0ms
(- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k)))
521.0ms
(+ (* 99 (* (/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k))) a)) (- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))))

series609.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k)))
98.0ms
(/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))
206.0ms
(- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k)))
240.0ms
(+ (* 99 (* (/ (exp (* (- m) (- (log k)))) (* (* k k) (* k k))) a)) (- (* (/ a k) (/ (exp (* (- m) (- (log k)))) k)) (/ (* (* 10 a) (exp (* (- m) (- (log k))))) (* (* k k) k))))

simplify2.5s

Counts
128 → 128
Iterations
IterNodes
done5005
24365
1991
0324

prune828.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

98.4% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch98.0ms

Steps
ItersRangePoint
7
2.802632506075539e+90
1.0101875118888572e+92
3.765086051784335e+91

simplify1.4s

Iterations
IterNodes
done5001
2474985
2464967
2454945
2444927
2434905
2424887
2414865
2404847
2394825
2384807
2374785
2364767
2354745
2344727
2334705
2324687
2314665
2304647
2294625
2284607
2274585
2264567
2254545
2244527
2234505
2224487
2214465
2204447
2194425
2184407
2174385
2164367
2154345
2144327
2134305
2124287
2114265
2104247
2094225
2084207
2074185
2064167
2054145
2044127
2034105
2024087
2014065
2004047
1994025
1984007
1973985
1963967
1953945
1943927
1933905
1923887
1913865
1903847
1893825
1883807
1873785
1863767
1853745
1843727
1833705
1823687
1813665
1803647
1793625
1783607
1773585
1763567
1753545
1743527
1733505
1723487
1713465
1703447
1693425
1683407
1673385
1663367
1653345
1643327
1633305
1623287
1613265
1603247
1593225
1583207
1573185
1563167
1553145
1543127
1533105
1523087
1513065
1503047
1493025
1483007
1472985
1462967
1452945
1442927
1432905
1422887
1412865
1402847
1392825
1382807
1372785
1362767
1352745
1342727
1332705
1322687
1312665
1302647
1292625
1282607
1272585
1262567
1252545
1242527
1232505
1222487
1212465
1202447
1192425
1182407
1172385
1162367
1152345
1142327
1132305
1122287
1112265
1102247
1092225
1082207
1072185
1062167
1052145
1042127
1032105
1022087
1012065
1002047
992025
982007
971985
961967
951945
941927
931905
921887
911865
901847
891825
881807
871785
861767
851745
841727
831705
821687
811665
801647
791625
781607
771585
761567
751545
741527
731505
721487
711465
701447
691425
681407
671385
661367
651345
641327
631305
621287
611265
601247
591225
581207
571185
561167
551145
541127
531105
521087
511065
501047
491025
481007
47985
46967
45945
44927
43905
42887
41865
40847
39825
38807
37785
36767
35745
34727
33705
32687
31665
30647
29625
28607
27585
26567
25545
24527
23505
22487
21465
20447
19425
18407
17385
16367
15345
14327
13305
12287
11265
10247
9225
8207
7185
6167
5149
4109
385
261
151
034

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.6s11942×body80valid
272.0ms4150×body80nan