Details

Time bar (total: 6.2s)

sample71.0ms

Algorithm
intervals
Results
37.0ms83×body1280valid
11.0ms47×body640valid
9.0ms33×body2560valid
2.0ms15×body320valid
2.0ms69×body80valid
1.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
095
195
done95

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.4b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.5b
(sqrt (+ (* x x) 1.0))

rewrite43.0ms

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:
16.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series263.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(+ x (sqrt (+ (* x x) 1.0)))
164.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify144.0ms

Counts
51 → 51
Iterations

Useful iterations: 3 (139.0ms)

IterNodesCost
0309393
11027364
24764348
35002347
done5002347

prune155.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite264.0ms

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:
157.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
87.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series291.0ms

Counts
2 → 6
Calls
2 calls:
156.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
135.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify112.0ms

Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542089
146421654
250011654
done50011654

prune432.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.125 (pow x 3)) (* 2 x))
0.0b
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
0.2b
(/ 0.125 (pow x 3))
13.4b
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
34×*-un-lft-identity
30×add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
11×add-log-exp
10×add-exp-log
6×log-prod add-cbrt-cube
5×pow1 flip3-- flip--
4×cube-mult log-div diff-log unpow3 frac-sub difference-of-squares sqr-pow
3×sub-neg div-exp associate-/l*
2×associate--r+ distribute-lft-out--
1×cbrt-undiv pow-to-exp frac-2neg rem-log-exp pow-exp clear-num log-pow div-inv associate--r-
Counts
4 → 117
Calls
4 calls:
43.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
80.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
8.0ms
(/ 0.125 (pow x 3))
80.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(- (/ 0.125 (pow x 3)) (* 2 x))
43.0ms
(- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x)))
44.0ms
(/ 0.125 (pow x 3))
153.0ms
(log (- (/ 0.5 x) (- (/ 0.125 (pow x 3)) (* 2 x))))

simplify72.0ms

Counts
129 → 129
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
0484980
12212929
25002929
done5002929

prune266.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
14.3b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
21.3b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite458.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
10.0ms
(/ (- 0.0625) (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
204.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
227.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (- 0.0625) (pow x 5))
43.0ms
(/ 0.125 (pow x 3))
187.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
59.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify96.0ms

Counts
235 → 235
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
08371970
138171891
250021883
done50021883

prune578.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes86.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch76.0ms

Steps
ItersRangePoint
8
0.02319676823116778
7.055123656280252
0.8861387644120478
10
-1.8070707071506563e+17
-0.15939393977811658
-0.9993980925116871

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04127
14127
done4127

end0.0ms

sample1.9s

Algorithm
intervals
Results
928.0ms2311×body1280valid
371.0ms1559×body640valid
217.0ms829×body2560valid
108.0ms799×body320valid
63.0ms2129×body80valid
31.0ms373×body160valid