Details

Time bar (total: 20.6s)

sample283.0ms

Algorithm
intervals
Results
183.0ms118×body1280valid
55.0ms73×body640valid
13.0ms33×body320valid
7.0ms256×pre80true
5.0ms24×body160valid
1.0ms8×body80valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1109
2119
done119

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.9b
(log (+ 1.0 x))
6.9b
(log (- 1.0 x))

rewrite59.0ms

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:
44.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms
(log (+ 1.0 x))
7.0ms
(log (- 1.0 x))

series274.0ms

Counts
3 → 9
Calls
3 calls:
166.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
53.0ms
(log (+ 1.0 x))
55.0ms
(log (- 1.0 x))

simplify1.1s

Counts
78 → 78
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01861203
14321150
217501064
done50021043

prune303.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 58.8b

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)))))
6.9b
(log (- 1.0 x))

rewrite197.0ms

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:
68.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
110.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.0ms
(log (- 1.0 x))

series372.0ms

Counts
3 → 9
Calls
3 calls:
90.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
214.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
68.0ms
(log (- 1.0 x))

simplify644.0ms

Counts
172 → 172
Iterations

Useful iterations: done (638.0ms)

IterNodesCost
04093188
110902943
done50002587

prune825.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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)))))

rewrite300.0ms

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:
73.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
146.0ms
(/ (- (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)))))

series317.0ms

Counts
3 → 9
Calls
3 calls:
83.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
82.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
152.0ms
(/ (- (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)))))

simplify3.1s

Counts
275 → 275
Iterations

Useful iterations: done (3.1s)

IterNodesCost
03345394
19444934
245274280
done50014278

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
0.1b
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
0.1b
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
30.7b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
40×add-exp-log add-sqr-sqrt
36×times-frac
31×associate-*l*
26×add-cube-cbrt
23×add-cbrt-cube
21×prod-exp
19×flip3-- associate-*l/ flip--
15×pow1
14×associate-*r/ distribute-lft-out--
12×associate-/r/ frac-sub
9×cbrt-unprod
7×log-pow difference-of-squares
6×associate-/l* add-log-exp
5×div-exp
4×associate--l+
3×cbrt-undiv pow-to-exp sub-neg pow-exp associate-/r*
2×distribute-rgt-in frac-times distribute-lft-in associate-*r* pow-prod-down *-commutative div-inv associate-/l/
1×frac-2neg diff-log div-sub clear-num
Counts
4 → 144
Calls
4 calls:
147.0ms
(- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
92.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
684.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
279.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
182.0ms
(- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
375.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
324.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
261.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (pow 1.0 2) (- (* (* 1.0 x) (* 1.0 x)) (pow (log 1.0) 2))) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

simplify584.0ms

Counts
156 → 156
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
02939144
19668808
done50007879

prune865.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01533
11933
done1933

end0.0ms

sample7.7s

Algorithm
intervals
Results
4.7s3435×body1280valid
2.1s2516×body640valid
383.0ms1222×body320valid
150.0ms8000×pre80true
112.0ms618×body160valid
17.0ms209×body80valid