Details

Time bar (total: 27.2s)

sample167.0ms

Algorithm
intervals
Results
75.0ms107×body1280valid
30.0ms74×body640valid
18.0ms50×body320valid
13.0ms283×body80nan
2.0ms18×body160valid
0.0ms7×body80valid

simplify18.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
1158
2208
3238
done238

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- 1.0 eps) (+ 1.0 eps))
5.1b
(log (/ (- 1.0 eps) (+ 1.0 eps)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
41×add-sqr-sqrt
40×times-frac
26×log-prod
23×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
7×add-exp-log
5×associate-/l*
4×associate-/r* associate-/r/ add-cbrt-cube
3×pow1
2×flip3-+ div-exp rem-log-exp flip-+ div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div flip3-- frac-2neg div-sub clear-num log-pow flip--
Counts
2 → 83
Calls
2 calls:
60.0ms
(/ (- 1.0 eps) (+ 1.0 eps))
18.0ms
(log (/ (- 1.0 eps) (+ 1.0 eps)))

series283.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (- 1.0 eps) (+ 1.0 eps))
224.0ms
(log (/ (- 1.0 eps) (+ 1.0 eps)))

simplify988.0ms

Counts
89 → 89
Iterations

Useful iterations: done (981.0ms)

IterNodesCost
01431284
13491221
213251156
done50021154

prune478.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 2.0 (pow eps 2))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×associate-*r*
6×add-exp-log
4×add-cube-cbrt unpow-prod-down *-un-lft-identity unswap-sqr
3×associate-*l* prod-exp add-cbrt-cube
2×unpow2 sqr-pow
1×pow1 pow-to-exp pow-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 27
Calls
1 calls:
24.0ms
(* 2.0 (pow eps 2))

series51.0ms

Counts
1 → 3
Calls
1 calls:
51.0ms
(* 2.0 (pow eps 2))

simplify4.2s

Counts
30 → 30
Iterations

Useful iterations: done (4.2s)

IterNodesCost
051232
1115209
2431178
32950176
done5002173

prune194.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (log (sqrt (+ 1.0 eps)))) (log (/ (- 1.0 eps) (sqrt (+ 1.0 eps)))))
0.0b
(/ (- 1.0 eps) (sqrt (+ 1.0 eps)))
5.1b
(log (/ (- 1.0 eps) (sqrt (+ 1.0 eps))))
5.2b
(log (sqrt (+ 1.0 eps)))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
151×*-un-lft-identity
108×add-sqr-sqrt
105×times-frac
96×log-prod
72×sqrt-prod
64×add-cube-cbrt
41×associate-+r+
24×distribute-lft-out
22×distribute-lft-out-- difference-of-squares
12×pow1
10×add-exp-log
9×log-pow
8×sqrt-div
7×associate-+l+ distribute-neg-in associate-/r*
6×associate-/r/ add-cbrt-cube
5×flip3-+ flip-+ associate-/l* add-log-exp
4×log-div distribute-rgt-neg-in
3×rem-log-exp div-inv
2×div-exp sum-log associate-/l/
1×cbrt-undiv +-commutative neg-sub0 associate-+l- associate-+r- flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub neg-log clear-num flip--
Counts
4 → 204
Calls
4 calls:
77.0ms
(+ (- (log (sqrt (+ 1.0 eps)))) (log (/ (- 1.0 eps) (sqrt (+ 1.0 eps)))))
56.0ms
(/ (- 1.0 eps) (sqrt (+ 1.0 eps)))
23.0ms
(log (/ (- 1.0 eps) (sqrt (+ 1.0 eps))))
11.0ms
(log (sqrt (+ 1.0 eps)))

series1.3s

Counts
4 → 12
Calls
4 calls:
620.0ms
(+ (- (log (sqrt (+ 1.0 eps)))) (log (/ (- 1.0 eps) (sqrt (+ 1.0 eps)))))
169.0ms
(/ (- 1.0 eps) (sqrt (+ 1.0 eps)))
394.0ms
(log (/ (- 1.0 eps) (sqrt (+ 1.0 eps))))
165.0ms
(log (sqrt (+ 1.0 eps)))

simplify2.0s

Counts
216 → 216
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03013844
17243534
230093266
done50013259

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize128.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps))
0.0b
(+ (+ (* 1/2 (/ (pow eps 2) (pow 1.0 2))) (log (sqrt 1.0))) (+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3)))))
0.0b
(+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3))))
0.1b
(+ (/ (/ (* 0.125 (* eps eps)) 1.0) 1.0) (* (/ (* eps eps) 1.0) 1.0))

rewrite5.1s

Algorithm
rewrite-expression-head
Rules
48×add-log-exp
34×sum-log
15×frac-add
13×flip3-+ flip-+
11×*-un-lft-identity
4×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt add-cbrt-cube distribute-lft-out
3×associate-+l+
1×associate-+r+ associate-*l/
Counts
4 → 72
Calls
4 calls:
307.0ms
(+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps))
3.4s
(+ (+ (* 1/2 (/ (pow eps 2) (pow 1.0 2))) (log (sqrt 1.0))) (+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3)))))
1.3s
(+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3))))
62.0ms
(+ (/ (/ (* 0.125 (* eps eps)) 1.0) 1.0) (* (/ (* eps eps) 1.0) 1.0))

series652.0ms

Counts
4 → 12
Calls
4 calls:
243.0ms
(+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps))
134.0ms
(+ (+ (* 1/2 (/ (pow eps 2) (pow 1.0 2))) (log (sqrt 1.0))) (+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3)))))
217.0ms
(+ (+ (+ (/ (* 0.5 (* eps eps)) (pow 1.0 3)) (* (/ eps 1.0) 1.0)) (* 1.0 eps)) (/ (* 0.125 (* eps eps)) (* 1.0 (pow 1.0 3))))
57.0ms
(+ (/ (/ (* 0.125 (* eps eps)) 1.0) 1.0) (* (/ (* eps eps) 1.0) 1.0))

simplify3.1s

Counts
84 → 84
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01945149
16774831
239884353
done50024344

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes162.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01320
11720
done1720

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.8s3404×body1280valid
1.2s2555×body640valid
489.0ms168×body80valid
374.0ms8118×body80nan
357.0ms1266×body320valid
88.0ms607×body160valid