Details

Time bar (total: 19.9s)

sample222.0ms

Algorithm
intervals
Results
118.0ms95×body1280valid
63.0ms92×body640valid
14.0ms44×body320valid
5.0ms256×pre80true
4.0ms18×body160valid
1.0ms7×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.5b
(log (- 1.0 x))
5.7b
(log (+ 1.0 x))

rewrite37.0ms

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 clear-num frac-2neg flip3-+ div-exp flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 69
Calls
3 calls:
27.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms
(log (- 1.0 x))
4.0ms
(log (+ 1.0 x))

series289.0ms

Counts
3 → 9
Calls
3 calls:
173.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
62.0ms
(log (- 1.0 x))
54.0ms
(log (+ 1.0 x))

simplify809.0ms

Counts
78 → 78
Iterations

Useful iterations: done (804.0ms)

IterNodesCost
01851203
14321148
217581068
done50001042

prune469.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.3b

localize24.0ms

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)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.5b
(log (- 1.0 x))

rewrite133.0ms

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 add-cbrt-cube div-exp prod-exp
6×pow-to-exp pow-exp
5×log-prod log-pow
4×log-div associate-/r/ associate-/l*
3×associate-/r* flip3-- associate-*l* associate-*r/ flip-- add-log-exp
2×cbrt-undiv div-sub frac-sub cbrt-unprod div-inv
1×clear-num frac-2neg flip3-+ rem-log-exp pow-prod-down *-commutative flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 163
Calls
3 calls:
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
81.0ms
(/ (log (- 1.0 x)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
8.0ms
(log (- 1.0 x))

series306.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
159.0ms
(/ (log (- 1.0 x)) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
60.0ms
(log (- 1.0 x))

simplify619.0ms

Counts
172 → 172
Iterations

Useful iterations: done (612.0ms)

IterNodesCost
04083188
110892941
done50002575

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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

rewrite218.0ms

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×clear-num frac-2neg flip3-+ div-sub flip-+
Counts
3 → 266
Calls
3 calls:
61.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
56.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
81.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series325.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
102.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
160.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify2.4s

Counts
275 → 275
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03345394
19434932
245014280
done50004278

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

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

rewrite346.0ms

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×div-exp associate-*r/
10×prod-exp frac-sub
8×pow-exp
7×pow-to-exp
6×flip3-- div-inv flip-- associate-/l*
5×flip3-+ flip-+
4×add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-*l*
2×cube-div cube-mult unpow3 cbrt-unprod rem-cube-cbrt associate-/l/
1×cbrt-div clear-num pow-pow frac-2neg pow1/3 div-sub pow-prod-down *-commutative rem-cbrt-cube
Counts
4 → 296
Calls
4 calls:
47.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
89.0ms
(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
116.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
75.0ms
(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)

series686.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
217.0ms
(cbrt (pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3))
143.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
239.0ms
(pow (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (log 1.0) (* 1.0 x)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) 3)

simplify758.0ms

Counts
308 → 308
Iterations

Useful iterations: done (730.0ms)

IterNodesCost
045613083
1149912105
done500011210

prune1.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes53.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01836
12236
done2236

end0.0ms

sample7.6s

Algorithm
intervals
Results
5.0s3451×body1280valid
1.6s2454×body640valid
513.0ms1269×body320valid
145.0ms8000×pre80true
109.0ms615×body160valid
16.0ms211×body80valid