Details

Time bar (total: 1.8m)

sample200.0ms

Algorithm
intervals
Results
72.0ms74×body1280valid
56.0ms24×body2560valid
22.0ms53×body640valid
16.0ms104×body80valid
7.0ms27×body320valid
3.0ms18×body160valid
3.0ms58×body80nan

simplify513.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 281
Calls
4 calls:
444.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
215.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
27.0ms
(pow (+ 1.0 (/ i n)) n)
474.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
486.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
282.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
232.0ms
(pow (+ 1.0 (/ i n)) n)
427.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify672.0ms

Counts
293 → 293

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 23.0b

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite866.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
524×*-un-lft-identity
294×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv unpow-prod-down div-exp add-log-exp
6×pow1 div-sub
4×pow-unpow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log sqr-pow
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
171.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
22.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
22.0ms
(pow (+ 1.0 (/ i n)) n)
604.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series3.7s

Counts
4 → 12
Calls
4 calls:
369.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
329.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
290.0ms
(pow (+ 1.0 (/ i n)) n)
2.7s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.0s

Counts
406 → 406

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.0b

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.1b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
3405×times-frac
2121×*-un-lft-identity
1275×add-sqr-sqrt add-cube-cbrt
423×distribute-lft-out
150×div-inv
141×associate-/r/
78×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
9×div-sub
7×pow1
5×pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1182
Calls
4 calls:
35.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
37.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
34.0ms
(pow (+ 1.0 (/ i n)) n)
1.1s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series18.9s

Counts
4 → 12
Calls
4 calls:
244.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
247.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
239.0ms
(pow (+ 1.0 (/ i n)) n)
18.2s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.9s

Counts
1194 → 1194

prune4.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.0b

localize33.0ms

Local error

Found 4 expressions with local error:

7.1b
(pow (+ 1.0 (/ i n)) n)
7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
8.4b
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (+ (* (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
6405×times-frac
4795×*-un-lft-identity
2185×add-sqr-sqrt add-cube-cbrt
1305×distribute-lft-out
684×unpow-prod-down
672×cube-prod
210×div-inv
168×sum-cubes
141×associate-/r/
138×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
7×pow1
6×div-sub
5×pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
2×cube-neg
1×frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 2021
Calls
4 calls:
17.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
1.2s
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (+ (* (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series49.7s

Counts
4 → 12
Calls
4 calls:
239.0ms
(pow (+ 1.0 (/ i n)) n)
256.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
262.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
49.0s
(/ (/ (/ (+ (pow (pow (+ 1.0 (/ i n)) (* 2 n)) 3) (pow (- (* 1.0 1.0)) 3)) (+ (* (- (* 1.0 1.0)) (- (- (* 1.0 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify3.8s

Counts
2033 → 2033

prune6.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.0b

regimes143.0ms

Accuracy

44.1% (11.7b remaining)

Error of 33.3b against oracle of 21.7b and baseline of 42.6b

bsearch893.0ms

Steps
ItersRangePoint
10
84517967325.35463
1.9680762236544087e+23
85896130569.3759
10
1.761934526793414e-195
2.1477908055279466e-185
3.7329467397055525e-195
9
-1.5161657059709947e-251
-2.6825235325208276e-257
-5.829000262711808e-257
9
-177737.9005252096
-1.1154561922801245
-1.3343306970279527

simplify723.0ms

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.1s2456×body1280valid
1.8s957×body2560valid
590.0ms1652×body640valid
474.0ms2209×body80nan
159.0ms3034×body80valid
156.0ms811×body320valid
55.0ms452×body160valid
42.0ms12×body5120valid