Details

Time bar (total: 9.3s)

sample151.0ms

Algorithm
intervals
Results
95.0ms111×body1280valid
31.0ms77×body640valid
7.0ms37×body320valid
3.0ms256×pre80true
2.0ms22×body160valid
0.0ms9×body80valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115
done115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.1b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.3b
(log (- 1.0 x))
6.5b
(log (+ 1.0 x))

rewrite31.0ms

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:
19.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms
(log (- 1.0 x))
5.0ms
(log (+ 1.0 x))

series214.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
47.0ms
(log (- 1.0 x))
44.0ms
(log (+ 1.0 x))

simplify43.0ms

Counts
78 → 78
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0425668
11561624
25001599
done5001599

prune196.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 59.1b

localize13.0ms

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)))))
6.3b
(log (- 1.0 x))

rewrite107.0ms

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:
38.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
57.0ms
(/ (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))

series235.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(* 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)))))
43.0ms
(log (- 1.0 x))

simplify104.0ms

Counts
172 → 172
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09951550
142131389
250011389
done50011389

prune471.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
178×times-frac
159×add-sqr-sqrt
136×associate-*r*
112×unpow-prod-down
95×*-un-lft-identity
83×add-cube-cbrt
52×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
20×prod-exp
19×div-exp
16×add-cbrt-cube
12×pow1 pow-to-exp pow-exp
8×distribute-lft-out--
6×associate-*l* associate-/l* add-log-exp
4×associate-*r/ associate-/r/ log-pow cbrt-unprod difference-of-squares
3×cbrt-undiv associate-/r* div-inv
2×flip3-- flip3-+ pow-prod-down *-commutative frac-sub flip-- flip-+ associate-/l/
1×+-commutative frac-2neg div-sub clear-num sum-log
Counts
4 → 277
Calls
4 calls:
8.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
36.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
89.0ms
(/ (- (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)))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
59.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
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)))))

simplify113.0ms

Counts
289 → 289
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
08962664
138602372
250012372
done50012372

prune791.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 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
(/ 1 (/ (- (+ (* 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)))))))
0.0b
(/ (- (+ (* 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))))))

rewrite284.0ms

Algorithm
rewrite-expression-head
Rules
322×times-frac
248×add-sqr-sqrt
196×*-un-lft-identity
148×add-cube-cbrt
136×associate-*r*
112×unpow-prod-down
63×add-exp-log
48×unpow2 sqr-pow
34×unswap-sqr
32×distribute-lft-out--
30×associate-/r*
26×div-exp
25×pow1
21×add-cbrt-cube
20×prod-exp
16×log-pow difference-of-squares
12×pow-to-exp pow-exp
11×associate-/r/
8×div-inv
6×cbrt-undiv flip3-- associate-*l* flip-- associate-/l*
4×associate-*r/ cbrt-unprod associate-/l/ add-log-exp
2×rec-exp frac-2neg 1-exp pow-prod-down clear-num *-commutative frac-sub
1×pow-flip flip3-+ div-sub flip-+ inv-pow
Counts
4 → 386
Calls
4 calls:
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
36.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
72.0ms
(/ 1 (/ (- (+ (* 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)))))))
118.0ms
(/ (- (+ (* 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))))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
55.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
133.0ms
(/ 1 (/ (- (+ (* 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)))))))
126.0ms
(/ (- (+ (* 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))))))

simplify83.0ms

Counts
398 → 398
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
011366212
150015693
done50015693

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02620
12620
done2620

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.8s3353×body1280valid
990.0ms2497×body640valid
259.0ms1328×body320valid
94.0ms8000×pre80true
70.0ms625×body160valid
9.0ms197×body80valid