Details

Time bar (total: 14.4s)

sample100.0ms

Algorithm
intervals
Results
42.0ms74×body1280valid
24.0ms54×body640valid
11.0ms28×body2560valid
5.0ms23×body320valid
3.0ms62×body80valid
2.0ms15×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
4.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.8b
(sqrt (+ (* x x) 1.0))

rewrite113.0ms

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:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
34.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
19.0ms
(sqrt (+ (* x x) 1.0))

series362.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(+ x (sqrt (+ (* x x) 1.0)))
254.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
46.0ms
(sqrt (+ (* x x) 1.0))

simplify1.9s

Counts
51 → 51
Iterations

Useful iterations: done (1.9s)

IterNodesCost
0133761
1308691
2848618
32737602
done5001590

prune206.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
0.2b
(* -1/6 (/ (* x x) 1.0))

rewrite166.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
29×associate-*r*
24×times-frac
19×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
10×sqrt-prod
6×pow1 associate-*l* prod-exp cbrt-unprod
5×unswap-sqr
3×cbrt-undiv div-exp
2×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+ div-inv add-log-exp
Counts
2 → 74
Calls
2 calls:
126.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
34.0ms
(* -1/6 (/ (* x x) 1.0))

series269.0ms

Counts
2 → 6
Calls
2 calls:
241.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
28.0ms
(* -1/6 (/ (* x x) 1.0))

simplify1.5s

Counts
80 → 80
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01621283
14111174
215501066
done50001034

prune270.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
13.4b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
18.7b
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite593.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
94×times-frac
63×*-un-lft-identity
46×add-cube-cbrt
33×unpow-prod-down
22×difference-of-squares
19×associate-/r*
17×sqr-pow
16×cube-prod
15×add-exp-log
8×log-prod add-cbrt-cube
7×distribute-lft-out--
6×div-exp associate-/l* add-log-exp
5×pow1 log-div frac-sub
4×cube-mult unpow3
3×flip3-- flip--
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×sub-neg diff-log rem-log-exp log-pow
Counts
4 → 167
Calls
4 calls:
8.0ms
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
425.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
144.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series623.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ 0.0625 (pow x 5))
57.0ms
(/ 0.125 (pow x 3))
292.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
189.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify1.3s

Counts
179 → 179
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03382966
16792667
218582553
done50002541

prune589.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log 2) (/ 0.25 (* x x)))
0.1b
(/ 0.09375 (pow x 4))
0.2b
(/ 0.25 (* x x))
6.8b
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
50×*-un-lft-identity
25×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
15×distribute-lft-out--
14×add-exp-log
13×add-log-exp
12×unpow-prod-down
11×pow1 add-cbrt-cube
8×associate-/r* distribute-lft-out
7×log-pow
6×diff-log associate-/l*
5×div-exp
4×frac-sub sqr-pow
3×cbrt-undiv associate-+l+ log-prod flip3-- flip3-+ sum-log flip-- flip-+
2×sub-neg frac-2neg clear-num div-inv associate--r+
1×+-commutative pow-to-exp pow-exp prod-exp associate--l+ cbrt-unprod associate--r- difference-of-squares
Counts
4 → 115
Calls
4 calls:
21.0ms
(+ (log 2) (/ 0.25 (* x x)))
13.0ms
(/ 0.09375 (pow x 4))
15.0ms
(/ 0.25 (* x x))
212.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

series741.0ms

Counts
4 → 12
Calls
4 calls:
485.0ms
(+ (log 2) (/ 0.25 (* x x)))
66.0ms
(/ 0.09375 (pow x 4))
31.0ms
(/ 0.25 (* x x))
158.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

simplify1.1s

Counts
127 → 127
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02212041
15421896
218641780
done50001760

prune443.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes175.0ms

Accuracy

99.2% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch123.0ms

Steps
ItersRangePoint
9
3.244205803610274e-06
1902.9075791774285
0.9479026978334683
8
-45.38980787391071
-0.005411406272604966
-0.998226736869587

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04459
15159
done5159

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.8s2333×body1280valid
714.0ms1587×body640valid
394.0ms777×body2560valid
154.0ms755×body320valid
150.0ms2109×body80valid
53.0ms439×body160valid