Details

Time bar (total: 11.0s)

sample66.0ms

Algorithm
intervals
Results
34.0ms77×body1280valid
13.0ms54×body640valid
6.0ms21×body2560valid
3.0ms78×body80valid
2.0ms16×body320valid
1.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
079
199
done99

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.7b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.5b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series265.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
170.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms
(sqrt (+ (* x x) 1.0))

simplify1.7s

Counts
51 → 51
Iterations

Useful iterations: 3 (376.0ms)

IterNodesCost
0133761
1310695
2943618
34473602
done5000602

prune148.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
119.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
76.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series285.0ms

Counts
2 → 6
Calls
2 calls:
155.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
130.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify2.3s

Counts
292 → 292
Iterations

Useful iterations: 2 (438.0ms)

IterNodesCost
03364436
18743460
243862955
done50002955

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.5 x) x)
0.2b
(/ 0.125 (pow x 3))
10.2b
(log (+ x (- (+ (/ 0.5 x) x) (/ 0.125 (pow x 3)))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
6×log-prod
5×add-cbrt-cube distribute-lft-out add-log-exp
4×pow1 cube-mult unpow3 sqr-pow
3×div-exp associate-/l*
2×log-div flip3-+ flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative pow-to-exp frac-2neg rem-log-exp pow-exp clear-num sum-log log-pow div-inv
Counts
3 → 94
Calls
3 calls:
9.0ms
(+ (/ 0.5 x) x)
4.0ms
(/ 0.125 (pow x 3))
129.0ms
(log (+ x (- (+ (/ 0.5 x) x) (/ 0.125 (pow x 3)))))

series228.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(+ (/ 0.5 x) x)
39.0ms
(/ 0.125 (pow x 3))
149.0ms
(log (+ x (- (+ (/ 0.5 x) x) (/ 0.125 (pow x 3)))))

simplify687.0ms

Counts
103 → 103
Iterations

Useful iterations: 2 (148.0ms)

IterNodesCost
01841344
14031178
217391096
done50011096

prune185.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (pow x 3))
12.2b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite203.0ms

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×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+ div-inv
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
3.0ms
(/ 0.0625 (pow x 5))
6.0ms
(/ 0.125 (pow x 3))
86.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
101.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ 0.0625 (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
362.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
51.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.2s

Counts
172 → 172
Iterations

Useful iterations: done (1.2s)

IterNodesCost
03182936
17022663
230102511
done50012507

prune373.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.2b

bsearch84.0ms

Steps
ItersRangePoint
11
0.08347146558812443
3.320253512051989e+22
0.9004884393655546
9
-5.7596417613087905
-6.7357437175194845e-09
-1.03811431304858

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13957
done3957

end0.0ms

sample1.9s

Algorithm
intervals
Results
949.0ms2308×body1280valid
376.0ms1563×body640valid
218.0ms786×body2560valid
107.0ms767×body320valid
72.0ms2171×body80valid
33.0ms405×body160valid