Details

Time bar (total: 14.7s)

sample71.0ms

Algorithm
intervals
Results
32.0ms72×body1280valid
13.0ms48×body640valid
8.0ms24×body2560valid
4.0ms25×body320valid
3.0ms77×body80valid
1.0ms10×body160valid

simplify5.0ms

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: 53.5b

localize16.0ms

Local error

Found 3 expressions with local error:

1.1b
(+ x (sqrt (+ (* x x) 1.0)))
1.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.2b
(sqrt (+ (* x x) 1.0))

rewrite112.0ms

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:
32.0ms
(+ x (sqrt (+ (* x x) 1.0)))
58.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
21.0ms
(sqrt (+ (* x x) 1.0))

series352.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(+ x (sqrt (+ (* x x) 1.0)))
222.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
56.0ms
(sqrt (+ (* x x) 1.0))

simplify2.0s

Counts
51 → 51
Iterations

Useful iterations: done (2.0s)

IterNodesCost
0133761
1308691
2848618
32737602
done5001590

prune250.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite158.0ms

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:
107.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
44.0ms
(* -1/6 (/ (* x x) 1.0))

series302.0ms

Counts
2 → 6
Calls
2 calls:
272.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
30.0ms
(* -1/6 (/ (* x x) 1.0))

simplify1.6s

Counts
80 → 80
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01621283
14111174
215501066
done50001034

prune337.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.2b
(/ 0.125 (pow x 3))
9.5b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
17.9b
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite538.0ms

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:
9.0ms
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
383.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
129.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 0.0625 (pow x 5))
59.0ms
(/ 0.125 (pow x 3))
258.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
183.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify1.4s

Counts
179 → 179
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03382966
16792667
218582553
done50002541

prune477.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

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))
0.2b
(/ 0.125 (pow x 3))
8.3b
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

rewrite686.0ms

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:
47.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
392.0ms
(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
8.0ms
(/ 0.125 (pow x 3))
233.0ms
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

series420.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
52.0ms
(+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x))
39.0ms
(/ 0.125 (pow x 3))
217.0ms
(log (+ (- (/ 0.5 x) (/ 0.125 (pow x 3))) (* 2 x)))

simplify1.0s

Counts
131 → 131
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02202024
14691818
213401704
done50011686

prune300.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.5b

bsearch104.0ms

Steps
ItersRangePoint
9
0.0033303272193615503
311302.39110615524
0.8999222701664713
9
-7.35943201301068
-4.403108084983288e-07
-1.004740488829904

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03756
14556
done4556

end0.0ms

sample3.9s

Algorithm
intervals
Results
2.1s2317×body1280valid
710.0ms1560×body640valid
509.0ms844×body2560valid
228.0ms784×body320valid
123.0ms2101×body80valid
55.0ms394×body160valid