Details

Time bar (total: 15.7s)

sample90.0ms

Algorithm
intervals
Results
34.0ms65×body1280valid
22.0ms66×body640valid
9.0ms24×body2560valid
6.0ms31×body320valid
3.0ms58×body80valid
1.0ms12×body160valid

simplify4.0ms

Counts
1 → 1
Iterations
IterNodes
done9
19
07

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 55.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.9b
(sqrt (+ (* x x) 1.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log
3×flip3-+ add-cbrt-cube sqrt-prod flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 42
Calls
3 calls:
15.0ms
(+ x (sqrt (+ (* x x) 1.0)))
33.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
13.0ms
(sqrt (+ (* x x) 1.0))

series396.0ms

Counts
3 → 9
Calls
3 calls:
101.0ms
(+ x (sqrt (+ (* x x) 1.0)))
250.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify679.0ms

Counts
51 → 51
Iterations
IterNodes
done5001
21377
1320
0134

prune285.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
0.1b
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
106×times-frac
76×associate-*l*
52×*-un-lft-identity add-cube-cbrt
44×sqrt-prod
26×add-exp-log
22×unpow-prod-down cube-prod
18×unswap-sqr
14×add-cbrt-cube
13×associate-*r*
10×div-exp sqr-pow
8×prod-exp
6×cube-mult unpow3 frac-sub add-log-exp
4×pow1 cbrt-undiv cbrt-unprod
3×frac-times flip3-+ associate-*l/ associate-*r/ flip-+
2×pow-to-exp diff-log pow-exp div-inv
1×sum-log sub-neg flip3-- pow-prod-down associate--l+ *-commutative flip--
Counts
2 → 151
Calls
2 calls:
256.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
64.0ms
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

series306.0ms

Counts
2 → 6
Calls
2 calls:
169.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0)))
137.0ms
(* (/ (pow x 3) (sqrt 1.0)) (/ 1/6 1.0))

simplify1.7s

Counts
157 → 157
Iterations
IterNodes
done5000
23791
1733
0236

prune737.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.5b
(/ 0.0625 (pow x 5))
12.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.3b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite423.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×pow-to-exp cbrt-undiv clear-num frac-2neg flip3-+ flip3-- diff-log frac-add pow-exp flip-+ div-inv flip--
1×sum-log sub-neg rem-log-exp log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
13.0ms
(/ 0.125 (pow x 3))
11.0ms
(/ 0.0625 (pow x 5))
187.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
201.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series535.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ 0.125 (pow x 3))
95.0ms
(/ 0.0625 (pow x 5))
302.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
87.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.9s

Counts
172 → 172
Iterations
IterNodes
done5002
23344
1726
0316

prune892.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
0.0b
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
0.1b
(/ 0.125 (pow x 3))
10.7b
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

rewrite560.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
18×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log
9×distribute-lft-out
6×log-prod add-cbrt-cube distribute-lft-out--
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult diff-log unpow3
3×associate-+r+ flip3-+ div-exp flip-+ associate-/l*
2×log-div sub-neg associate--l+ frac-sub
1×pow-to-exp cbrt-undiv +-commutative clear-num associate-+r- frac-2neg flip3-- rem-log-exp pow-exp log-pow div-inv flip--
Counts
4 → 125
Calls
4 calls:
236.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
148.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
7.0ms
(/ 0.125 (pow x 3))
160.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

series420.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3))))
71.0ms
(- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))
49.0ms
(/ 0.125 (pow x 3))
241.0ms
(log (+ x (- (+ x (/ 0.5 x)) (/ 0.125 (pow x 3)))))

simplify1.5s

Counts
137 → 137
Iterations
IterNodes
done5001
22654
1539
0227

prune615.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes78.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 32.1b

bsearch126.0ms

Steps
ItersRangePoint
9
0.030359728269424062
9645967.64350026
0.8817659968088067
11
-14746478108.679678
-8.433739504313006e-14
-1.021540982075884

simplify4.0ms

Iterations
IterNodes
done39
139
034

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.0s2320×body1280valid
790.0ms1556×body640valid
472.0ms793×body2560valid
196.0ms812×body320valid
172.0ms2100×body80valid
59.0ms419×body160valid