Details

Time bar (total: 13.6s)

sample150.0ms

Algorithm
intervals
Results
88.0ms98×body1280valid
38.0ms94×body640valid
8.0ms40×body320valid
4.0ms256×pre80true
2.0ms16×body160valid
0.0ms8×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.2b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.8b
(log (- 1.0 x))
5.9b
(log (+ 1.0 x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
17×add-sqr-sqrt
16×times-frac
15×pow1 add-cube-cbrt
12×log-pow
9×log-prod
7×add-exp-log
6×log-div
5×add-cbrt-cube
4×associate-/r* associate-/l*
3×add-log-exp
2×flip3-- div-sub rem-log-exp flip--
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 69
Calls
3 calls:
8.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms
(log (- 1.0 x))
3.0ms
(log (+ 1.0 x))

series219.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
48.0ms
(log (- 1.0 x))
42.0ms
(log (+ 1.0 x))

simplify578.0ms

Counts
78 → 78
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
01861203
14261150
213311064
done50001041

prune217.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 58.4b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.8b
(log (- 1.0 x))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
83×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
49×*-un-lft-identity
47×add-cube-cbrt
29×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×pow1 div-exp prod-exp add-cbrt-cube
6×pow-to-exp pow-exp
5×log-prod log-pow
4×log-div associate-/r/ associate-/l*
3×flip3-- associate-*r/ associate-*l* associate-/r* flip-- add-log-exp
2×cbrt-undiv div-sub frac-sub cbrt-unprod div-inv
1×frac-2neg flip3-+ rem-log-exp pow-prod-down clear-num *-commutative flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 163
Calls
3 calls:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
26.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
2.0ms
(log (- 1.0 x))

series230.0ms

Counts
3 → 9
Calls
3 calls:
49.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
139.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
42.0ms
(log (- 1.0 x))

simplify1.3s

Counts
172 → 172
Iterations

Useful iterations: 2 (689.0ms)

IterNodesCost
04093188
19962943
232042577
done50012577

prune511.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
158×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
94×*-un-lft-identity
82×add-cube-cbrt
51×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
15×add-cbrt-cube
12×pow-to-exp pow-exp
11×pow1
8×distribute-lft-out--
6×associate-*l* associate-/l*
4×associate-*r/ associate-/r/ log-pow cbrt-unprod difference-of-squares
3×cbrt-undiv associate-/r* div-inv add-log-exp
2×flip3-- pow-prod-down *-commutative frac-sub flip-- associate-/l/
1×frac-2neg flip3-+ div-sub clear-num flip-+
Counts
3 → 266
Calls
3 calls:
29.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
27.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
43.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series228.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
121.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.4s

Counts
275 → 275
Iterations

Useful iterations: 2 (573.0ms)

IterNodesCost
03345394
18554926
227574280
done50014280

prune782.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
0.0b
(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
0.0b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
170×times-frac
157×add-sqr-sqrt
139×*-un-lft-identity
108×unpow-prod-down
91×add-cube-cbrt
68×associate-*r*
58×cbrt-prod
52×cube-prod
32×add-exp-log distribute-lft-out--
26×sqr-pow
24×unpow2
23×pow1
20×associate-/r/
17×unswap-sqr
16×log-pow difference-of-squares
14×add-cbrt-cube
11×associate-*r/ div-exp
10×prod-exp frac-sub
8×pow-exp
7×pow-to-exp
6×flip3-- flip-- div-inv associate-/l*
5×flip3-+ flip-+
4×add-log-exp
3×cbrt-undiv pow-unpow associate-*l* associate-/r*
2×cube-div cube-mult unpow3 cbrt-unprod associate-/l/ rem-cube-cbrt
1×cbrt-div pow-pow frac-2neg pow1/3 div-sub pow-prod-down clear-num *-commutative rem-cbrt-cube
Counts
4 → 296
Calls
4 calls:
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
41.0ms
(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
38.0ms
(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
42.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
124.0ms
(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
173.0ms
(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)
128.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify1.7s

Counts
308 → 308
Iterations

Useful iterations: 2 (905.0ms)

IterNodesCost
045613083
1124512055
2421911052
done500111052

prune803.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01836
12236
done2236

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.9s3430×body1280valid
983.0ms2468×body640valid
249.0ms1275×body320valid
100.0ms8000×pre80true
68.0ms618×body160valid
10.0ms209×body80valid