Details

Time bar (total: 11.9s)

sample88.0ms

Algorithm
intervals
Results
40.0ms63×body1280valid
20.0ms64×body640valid
8.0ms23×body2560valid
4.0ms24×body320valid
3.0ms69×body80valid
1.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
199
done99

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (+ (* x x) 1.0)))
3.5b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.1b
(sqrt (+ (* x x) 1.0))

rewrite83.0ms

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:
43.0ms
(+ x (sqrt (+ (* x x) 1.0)))
25.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0ms
(sqrt (+ (* x x) 1.0))

series365.0ms

Counts
3 → 9
Calls
3 calls:
79.0ms
(+ x (sqrt (+ (* x x) 1.0)))
225.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
61.0ms
(sqrt (+ (* x x) 1.0))

simplify1.5s

Counts
51 → 51
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0133761
1308691
2848618
32737602
done5001590

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite101.0ms

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:
79.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
19.0ms
(* -1/6 (/ (* x x) 1.0))

series268.0ms

Counts
2 → 6
Calls
2 calls:
240.0ms
(* (+ (* -1/6 (/ (* x x) 1.0)) 1) (/ x (sqrt 1.0)))
27.0ms
(* -1/6 (/ (* x x) 1.0))

simplify1.2s

Counts
80 → 80
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01621283
14111174
215501066
done50001034

prune206.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (/ (pow x 3) (/ 1.0 -1/6)))
0.1b
(/ (pow x 3) (/ 1.0 -1/6))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
273×times-frac
137×*-un-lft-identity
135×add-sqr-sqrt add-cube-cbrt
42×unpow-prod-down cube-prod
15×add-exp-log
14×cube-mult unpow3 div-inv sqr-pow
13×associate-/r*
12×associate-/l*
9×div-exp
7×add-cbrt-cube
4×add-log-exp
3×cbrt-undiv
2×pow1 pow-to-exp pow-exp
1×+-commutative frac-2neg flip3-+ clear-num sum-log associate-/r/ flip-+ distribute-lft-out
Counts
2 → 212
Calls
2 calls:
61.0ms
(+ x (/ (pow x 3) (/ 1.0 -1/6)))
15.0ms
(/ (pow x 3) (/ 1.0 -1/6))

series146.0ms

Counts
2 → 6
Calls
2 calls:
98.0ms
(+ x (/ (pow x 3) (/ 1.0 -1/6)))
48.0ms
(/ (pow x 3) (/ 1.0 -1/6))

simplify1.4s

Counts
218 → 218
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03223669
16352995
224992929
done50002927

prune523.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
0.0b
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
0.2b
(/ 0.125 (pow x 3))
14.1b
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

rewrite676.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
36×times-frac
30×add-sqr-sqrt add-cube-cbrt
18×add-log-exp
12×unpow-prod-down cube-prod associate-/r* distribute-lft-out
10×add-exp-log
7×sum-log
6×log-prod add-cbrt-cube
5×pow1
4×cube-mult unpow3 sqr-pow
3×associate-+r- associate-+r+ flip3-+ div-exp flip-+ associate-/l* distribute-lft-out--
2×+-commutative log-div diff-log frac-add
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg rem-log-exp pow-exp clear-num log-pow flip-- div-inv
Counts
4 → 119
Calls
4 calls:
287.0ms
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
80.0ms
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
8.0ms
(/ 0.125 (pow x 3))
293.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

series443.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3)))))
58.0ms
(+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))
58.0ms
(/ 0.125 (pow x 3))
258.0ms
(log (+ x (+ (/ 0.5 x) (- x (/ 0.125 (pow x 3))))))

simplify814.0ms

Counts
131 → 131
Iterations

Useful iterations: done (810.0ms)

IterNodesCost
02172010
14951774
215191664
done50011660

prune262.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.3b

bsearch85.0ms

Steps
ItersRangePoint
10
1.0194597579740466e-06
20796729.49276672
0.9017023301953626
8
-11.923248480236845
-0.0008047768791668974
-1.002814715336328

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03556
14254
done4254

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.8s2305×body1280valid
591.0ms1572×body640valid
322.0ms828×body2560valid
183.0ms771×body320valid
141.0ms2130×body80valid
48.0ms394×body160valid