Details

Time bar (total: 23.7s)

sample236.0ms

Algorithm
intervals
Results
148.0ms114×body1280valid
48.0ms77×body640valid
13.0ms42×body320valid
6.0ms256×pre80true
3.0ms18×body160valid
1.0ms5×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1119
done119

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 62.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.6b
(log (+ 1.0 x))
5.6b
(log (- 1.0 x))

rewrite86.0ms

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:
61.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
10.0ms
(log (+ 1.0 x))
11.0ms
(log (- 1.0 x))

series312.0ms

Counts
3 → 9
Calls
3 calls:
187.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
55.0ms
(log (+ 1.0 x))
70.0ms
(log (- 1.0 x))

simplify3.2s

Counts
78 → 78
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01861203
115441142
done50001022

prune303.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 59.8b

localize20.0ms

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)))))
5.6b
(log (- 1.0 x))

rewrite167.0ms

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:
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
93.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
10.0ms
(log (- 1.0 x))

series355.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
217.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
65.0ms
(log (- 1.0 x))

simplify908.0ms

Counts
172 → 172
Iterations

Useful iterations: done (900.0ms)

IterNodesCost
04093188
done50002798

prune865.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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)))))

rewrite289.0ms

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:
65.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
51.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
143.0ms
(/ (- (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)))))

series371.0ms

Counts
3 → 9
Calls
3 calls:
92.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
97.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
181.0ms
(/ (- (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)))))

simplify966.0ms

Counts
275 → 275
Iterations

Useful iterations: done (949.0ms)

IterNodesCost
03345394
done50004646

prune1.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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)))))
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)))))
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))))) (/ (- (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))))))
0.0b
(cbrt (* (* (/ (- (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))))) (/ (- (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)))))) (/ (- (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)))))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
186×*-un-lft-identity
148×times-frac
130×add-sqr-sqrt
78×add-cube-cbrt
64×distribute-lft-out--
44×swap-sqr
43×pow1
32×log-pow
26×associate-*r* associate-*l*
24×associate-/r/
20×add-exp-log add-cbrt-cube difference-of-squares
16×associate-*r/
12×frac-sub associate-/l*
8×flip3-- flip--
7×cbrt-div
6×cbrt-undiv frac-times flip3-+ div-exp associate-*l/ associate-/r* flip-+ div-inv
4×prod-exp cbrt-unprod associate-/l/ add-log-exp unswap-sqr
2×frac-2neg div-sub clear-num
1×cbrt-prod pow2 pow-plus pow1/3 pow3 pow-prod-down pow-sqr *-commutative pow-prod-up rem-cbrt-cube
Counts
4 → 233
Calls
4 calls:
136.0ms
(/ (- (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)))))
141.0ms
(/ (- (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)))))
506.0ms
(* (/ (- (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))))) (/ (- (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))))))
556.0ms
(cbrt (* (* (/ (- (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))))) (/ (- (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)))))) (/ (- (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)))))))

series841.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (- (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)))))
182.0ms
(/ (- (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)))))
275.0ms
(* (/ (- (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))))) (/ (- (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))))))
206.0ms
(cbrt (* (* (/ (- (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))))) (/ (- (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)))))) (/ (- (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)))))))

simplify2.3s

Counts
245 → 245
Iterations

Useful iterations: done (2.3s)

IterNodesCost
025518266
done500017623

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes45.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
018102
123102
done23102

end0.0ms

sample7.8s

Algorithm
intervals
Results
5.1s3393×body1280valid
1.6s2463×body640valid
455.0ms1297×body320valid
166.0ms630×body160valid
158.0ms8000×pre80true
17.0ms217×body80valid