Details

Time bar (total: 8.5s)

sample62.0ms

Algorithm
intervals
Results
27.0ms68×body1280valid
15.0ms63×body640valid
5.0ms20×body2560valid
3.0ms25×body320valid
2.0ms64×body80valid
1.0ms16×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
3.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(sqrt (+ (* x x) 1.0))

rewrite44.0ms

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)))
18.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series258.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
165.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
40.0ms
(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts
51 → 51
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0133761
1308691
2848618
32737602
done5001590

prune132.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
0.4b
(* -1/6 (/ (* x x) 1.0))

rewrite88.0ms

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:
68.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
17.0ms
(* -1/6 (/ (* x x) 1.0))

series197.0ms

Counts
2 → 6
Calls
2 calls:
169.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
28.0ms
(* -1/6 (/ (* x x) 1.0))

simplify918.0ms

Counts
80 → 80
Iterations

Useful iterations: done (916.0ms)

IterNodesCost
01621283
14111174
215501066
done50001034

prune176.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
0.3b
(/ 0.125 (pow x 3))
10.9b
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
36×times-frac
29×add-sqr-sqrt add-cube-cbrt
12×unpow-prod-down cube-prod associate-/r*
9×add-exp-log
8×add-log-exp
7×distribute-lft-out
6×log-prod
5×add-cbrt-cube
4×pow1 cube-mult unpow3 sqr-pow
3×div-exp associate-/l*
2×log-div associate-+r+ flip3-+ frac-add sum-log flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative pow-to-exp associate-+r- sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
3 → 101
Calls
3 calls:
72.0ms
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
8.0ms
(/ 0.125 (pow x 3))
199.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

series225.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
36.0ms
(/ 0.125 (pow x 3))
151.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

simplify724.0ms

Counts
110 → 110
Iterations

Useful iterations: done (720.0ms)

IterNodesCost
02061622
14641404
214001332
done50011328

prune183.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.9b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
19.0b
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

rewrite344.0ms

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:
7.0ms
(/ 0.0625 (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
245.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
77.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(/ 0.0625 (pow x 5))
41.0ms
(/ 0.125 (pow x 3))
180.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
127.0ms
(- (/ 0.125 (pow x 3)) (/ 0.0625 (pow x 5)))

simplify789.0ms

Counts
179 → 179
Iterations

Useful iterations: done (779.0ms)

IterNodesCost
03382966
16792667
218582553
done50002541

prune497.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.8b

bsearch88.0ms

Steps
ItersRangePoint
11
6.1632953816490534e-12
2923699147.8271213
0.8969712032463295
10
-21283307590.397102
-3.152803306627408e-07
-1.0282378261696905

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03656
14456
done4456

end0.0ms

sample1.9s

Algorithm
intervals
Results
945.0ms2341×body1280valid
365.0ms1576×body640valid
209.0ms779×body2560valid
105.0ms780×body320valid
64.0ms2121×body80valid
31.0ms403×body160valid