Details

Time bar (total: 25.6s)

sample219.0ms

Algorithm
intervals
Results
66.0ms60×body1280valid
58.0ms73×body10240exit
37.0ms314×body80valid
20.0ms45×body640valid
7.0ms20×body320valid
2.0ms12×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
2.4b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
42×associate-*l/
38×associate-*r/
32×flip3-- flip--
28×flip3-+ flip-+
23×add-sqr-sqrt
19×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cbrt-cube add-cube-cbrt
9×associate-*r* add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 166
Calls
4 calls:
109.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
36.0ms
(* (- 1.0 eps) x)
33.0ms
(* (+ 1.0 eps) x)
51.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series481.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
56.0ms
(* (- 1.0 eps) x)
49.0ms
(* (+ 1.0 eps) x)
289.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.6s

Counts
178 → 178
Iterations
IterNodes
done5001
11272
0396

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* 0.6666666666666667 (* (* x x) x))
0.2b
(/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0)
4.0b
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1
20×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac pow-prod-down prod-exp cbrt-unprod add-log-exp
6×pow-plus pow-prod-up
4×associate-*r* associate-*l*
3×associate-/r* associate-/l*
2×pow2 flip3-- diff-log pow-sqr *-commutative flip-- associate-/l/
1×cbrt-undiv clear-num sum-log sub-neg frac-2neg div-sub div-exp pow3 associate--l+ div-inv unswap-sqr
Counts
4 → 93
Calls
4 calls:
16.0ms
(* (* x x) x)
42.0ms
(* 0.6666666666666667 (* (* x x) x))
79.0ms
(/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0)
59.0ms
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))

series274.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* x x) x)
52.0ms
(* 0.6666666666666667 (* (* x x) x))
90.0ms
(/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0)
71.0ms
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))

simplify2.4s

Counts
105 → 105
Iterations
IterNodes
done5001
22330
1385
0141

prune438.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize59.0ms

Local error

Found 4 expressions with local error:

4.0b
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×add-log-exp
4×pow1 add-cbrt-cube add-exp-log
3×cbrt-div pow1/3 div-inv
2×diff-log
1×sum-log sub-neg flip3-- associate--l+ flip--
Counts
4 → 80
Calls
4 calls:
38.0ms
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))
13.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
13.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
10.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

series837.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0))
262.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
277.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
253.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

simplify1.8s

Counts
92 → 92
Iterations
IterNodes
done5002
21507
1364
0153

prune855.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize170.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
7.6b
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-prod
36×times-frac
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 cbrt-div add-cbrt-cube pow1/3 add-exp-log div-inv add-log-exp
Counts
4 → 88
Calls
4 calls:
10.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
10.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
11.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
18.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
244.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
305.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
305.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))
300.0ms
(cbrt (/ (- (+ 2.0 (* 0.6666666666666667 (* (* x x) x))) (* (* x x) 1.0)) 2.0))

simplify2.2s

Counts
100 → 100
Iterations
IterNodes
done5001
21006
1276
0126

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

regimes145.0ms

Accuracy

96.2% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.0b

bsearch267.0ms

Steps
ItersRangePoint
9
6.220956769517991e-07
20.852008069825544
1.6169303695992086

simplify16.0ms

Iterations
IterNodes
done61
261
155
037

end0.0ms

sample8.0s

Algorithm
intervals
Results
3.1s2000×body10240exit
1.9s1723×body1280valid
1.4s10052×body80valid
663.0ms1285×body640valid
247.0ms669×body320valid
113.0ms347×body160valid