Details

Time bar (total: 14.8s)

sample117.0ms

Algorithm
intervals
Results
43.0ms62×body1280valid
35.0ms60×body640valid
12.0ms24×body2560valid
5.0ms25×body320valid
4.0ms72×body80valid
2.0ms13×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.3b
(+ x (sqrt (+ (* x x) 1.0)))
3.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
12.8b
(sqrt (+ (* x x) 1.0))

rewrite84.0ms

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:
8.0ms
(+ (* x x) 1.0)
32.0ms
(+ x (sqrt (+ (* x x) 1.0)))
23.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
20.0ms
(sqrt (+ (* x x) 1.0))

series456.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(+ (* x x) 1.0)
97.0ms
(+ x (sqrt (+ (* x x) 1.0)))
249.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
65.0ms
(sqrt (+ (* x x) 1.0))

simplify2.0s

Counts
65 → 65
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0141885
1331804
2935719
33071703
done5000701

prune266.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)))

rewrite468.0ms

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:
300.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
128.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series397.0ms

Counts
2 → 6
Calls
2 calls:
171.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
226.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify1.4s

Counts
292 → 292
Iterations

Useful iterations: 2 (509.0ms)

IterNodesCost
03364436
17273364
225942955
done50002955

prune596.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.0b
(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
0.1b
(/ 0.125 (pow x 3))
11.2b
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

rewrite739.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt
51×times-frac
36×*-un-lft-identity
30×add-cube-cbrt
14×unpow-prod-down cube-prod
12×associate-/r*
11×add-log-exp
10×add-exp-log difference-of-squares
6×add-cbrt-cube sqr-pow
5×pow1
4×cube-mult unpow3
3×log-prod div-exp associate-/l*
2×sub-neg log-div associate-+l+ flip3-+ diff-log sum-log flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative pow-to-exp associate-+l- flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow frac-sub flip-- div-inv
Counts
4 → 119
Calls
4 calls:
67.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
389.0ms
(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
9.0ms
(/ 0.125 (pow x 3))
271.0ms
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
63.0ms
(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
51.0ms
(/ 0.125 (pow x 3))
254.0ms
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

simplify1.1s

Counts
131 → 131
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02202024
14691818
213401704
done50011686

prune301.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.1b
(/ 0.125 (pow x 3))
12.9b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
18.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite347.0ms

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:
9.0ms
(/ 0.0625 (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
133.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
182.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series432.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 0.0625 (pow x 5))
53.0ms
(/ 0.125 (pow x 3))
237.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
64.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.4s

Counts
172 → 172
Iterations

Useful iterations: 2 (500.0ms)

IterNodesCost
03182936
16782663
220832515
done50012515

prune596.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes35.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.0b

bsearch123.0ms

Steps
ItersRangePoint
10
1.5244367550608482e-07
9556.682540875734
0.8981400227354687
9
-1501.2167507114543
-0.006495210018506858
-1.017049376431383

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03557
14057
done4057

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.9s2224×body1280valid
625.0ms1649×body640valid
346.0ms836×body2560valid
278.0ms820×body320valid
101.0ms2075×body80valid
48.0ms396×body160valid