Details

Time bar (total: 17.3s)

sample86.0ms

Algorithm
intervals
Results
43.0ms78×body1280valid
12.0ms40×body640valid
11.0ms31×body2560valid
4.0ms26×body320valid
3.0ms72×body80valid
1.0ms9×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07232
19232
done9232

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize27.0ms

Local error

Found 3 expressions with local error:

0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.1b
(log (+ x (sqrt (+ (* x x) 1.0))))
16.8b
(sqrt (+ (* x x) 1.0))

rewrite92.0ms

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:
30.0ms
(+ x (sqrt (+ (* x x) 1.0)))
45.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms
(sqrt (+ (* x x) 1.0))

series440.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(+ x (sqrt (+ (* x x) 1.0)))
271.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
74.0ms
(sqrt (+ (* x x) 1.0))

simplify2.5s

Counts
51 → 51
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
013418845
131214789
293714143
3347413983
done501513983

prune391.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.1b
(* x (* x x))
0.1b
(* 1/6 (* x (* x x)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
16×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
6×associate-*l*
5×add-sqr-sqrt pow-prod-up
4×*-un-lft-identity add-cube-cbrt
2×associate-*r* *-commutative add-log-exp
1×pow2 pow-plus cube-unmult pow-sqr unswap-sqr
Counts
2 → 45
Calls
2 calls:
30.0ms
(* x (* x x))
72.0ms
(* 1/6 (* x (* x x)))

series143.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(* x (* x x))
73.0ms
(* 1/6 (* x (* x x)))

simplify2.5s

Counts
51 → 51
Iterations

Useful iterations: 2 (149.0ms)

IterNodesCost
0598200
11436462
24596025
318656025
done50076025

prune179.0ms

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
(+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)
0.1b
(* x (* x x))
0.1b
(/ 0.125 (* x (* x x)))
11.2b
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)))

rewrite681.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
19×pow1 add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt add-log-exp
8×add-cube-cbrt
7×distribute-lft-out
6×log-prod prod-exp cbrt-unprod
5×pow-prod-up
3×cbrt-undiv times-frac div-exp associate-*l* pow-prod-down associate-/l*
2×log-div associate-+l+ sum-log flip3-+ flip-+ distribute-lft-out--
1×pow2 +-commutative clear-num associate-/r* sub-neg frac-2neg pow-plus diff-log cube-unmult rem-log-exp associate-*r* pow-sqr log-pow *-commutative associate-+l- div-inv unswap-sqr
Counts
4 → 81
Calls
4 calls:
227.0ms
(+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)
28.0ms
(* x (* x x))
20.0ms
(/ 0.125 (* x (* x x)))
401.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)
59.0ms
(* x (* x x))
51.0ms
(/ 0.125 (* x (* x x)))
255.0ms
(log (+ x (+ (- (/ 0.5 x) (/ 0.125 (* x (* x x)))) x)))

simplify1.9s

Counts
93 → 93
Iterations

Useful iterations: done (1.9s)

IterNodesCost
016627556
137823198
2128121916
done500321797

prune329.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (* x (* x x)))
0.2b
(/ 0.0625 (pow x 5))
13.4b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.5b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
27×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
19×add-exp-log
15×add-cbrt-cube
12×unpow-prod-down
9×add-log-exp
8×associate-/r*
6×log-prod div-exp frac-sub associate-/l*
5×pow1 log-div
4×cbrt-undiv distribute-lft-out-- sqr-pow
3×prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ div-inv flip-- distribute-lft-out difference-of-squares
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+
Counts
4 → 108
Calls
4 calls:
16.0ms
(/ 0.125 (* x (* x x)))
11.0ms
(/ 0.0625 (pow x 5))
158.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
161.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series435.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 0.125 (* x (* x x)))
60.0ms
(/ 0.0625 (pow x 5))
243.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
86.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify2.4s

Counts
120 → 120
Iterations

Useful iterations: done (2.4s)

IterNodesCost
026865965
163559752
2251546386
done500546347

prune567.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.3b

bsearch135.0ms

Steps
ItersRangePoint
9
0.1909160003853501
166131308.15705827
0.8807071635272687
10
-27652538170.40468
-0.18371106458419734
-1.0266836572228921

simplify12.0ms

Iterations

Useful iterations: 0 (5.0ms)

IterNodesCost
0341369
1401369
done401369

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s2272×body1280valid
611.0ms1555×body640valid
348.0ms832×body2560valid
164.0ms795×body320valid
105.0ms2154×body80valid
89.0ms392×body160valid