Details

Time bar (total: 8.6s)

sample70.0ms

Algorithm
intervals
Results
36.0ms88×body1280valid
13.0ms53×body640valid
7.0ms26×body2560valid
3.0ms21×body320valid
2.0ms58×body80valid
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: 54.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
3.0ms
(+ (* x x) 1.0)
8.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series312.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* x x) 1.0)
55.0ms
(+ x (sqrt (+ (* x x) 1.0)))
176.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify1.4s

Counts
65 → 65
Iterations

Useful iterations: 3 (613.0ms)

IterNodesCost
0141885
1332804
2941719
33538703
done5000703

prune168.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
70.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series137.0ms

Counts
1 → 3
Calls
1 calls:
137.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify978.0ms

Counts
273 → 273
Iterations

Useful iterations: 2 (611.0ms)

IterNodesCost
02933830
17292926
223212545
done50002545

prune343.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.8b
(/ 0.125 (pow x 3))
14.6b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
20.3b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite195.0ms

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))
4.0ms
(/ 0.125 (pow x 3))
83.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
98.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series309.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ 0.0625 (pow x 5))
34.0ms
(/ 0.125 (pow x 3))
176.0ms
(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))))

simplify745.0ms

Counts
172 → 172
Iterations

Useful iterations: 2 (346.0ms)

IterNodesCost
03182936
16892663
221202507
done50002507

prune378.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(- x (/ 0.125 (pow x 3)))
0.0b
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
0.8b
(/ 0.125 (pow x 3))
11.9b
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

rewrite333.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
43×add-sqr-sqrt
40×times-frac
30×add-cube-cbrt
15×add-log-exp
13×unpow-prod-down cube-prod
12×associate-/r*
10×add-exp-log distribute-lft-out
6×log-prod add-cbrt-cube
5×pow1 sum-log difference-of-squares sqr-pow
4×cube-mult unpow3
3×div-exp associate-/l* distribute-lft-out--
2×associate-+r- log-div flip3-+ diff-log flip-+
1×cbrt-undiv +-commutative pow-to-exp sub-neg associate-+r+ flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 118
Calls
4 calls:
14.0ms
(- x (/ 0.125 (pow x 3)))
155.0ms
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
6.0ms
(/ 0.125 (pow x 3))
152.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

series305.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(- x (/ 0.125 (pow x 3)))
44.0ms
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
37.0ms
(/ 0.125 (pow x 3))
144.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

simplify508.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (208.0ms)

IterNodesCost
02081888
14491686
213141568
done50011568

prune226.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes28.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 31.8b

bsearch82.0ms

Steps
ItersRangePoint
10
5.968040026638966e-05
117627206.70733242
0.9001758350297782
10
-64880754058.88788
-2.651420353119469e-05
-0.9989549344709008

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03457
13957
done3957

end0.0ms

sample1.9s

Algorithm
intervals
Results
995.0ms2398×body1280valid
372.0ms1535×body640valid
222.0ms806×body2560valid
109.0ms761×body320valid
66.0ms2126×body80valid
32.0ms374×body160valid