Details

Time bar (total: 30.5s)

sample229.0ms

Algorithm
intervals
Results
88.0ms82×body1280valid
75.0ms28×body2560valid
24.0ms49×body640valid
7.0ms97×body80valid
7.0ms26×body320valid
5.0ms91×body80nan
2.0ms13×body160valid

simplify4.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 321
Calls
4 calls:
441.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
22.0ms
(pow (+ 1.0 (/ i n)) n)
549.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts
4 → 12
Calls
4 calls:
493.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
308.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
320.0ms
(pow (+ 1.0 (/ i n)) n)
384.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.5s

Counts
333 → 333
Iterations

Useful iterations: done (2.5s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ n (/ i (- (pow (/ i n) n) 1.0)))
0.1b
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
1.1b
(- (pow (/ i n) n) 1.0)
4.6b
(pow (/ i n) n)

rewrite399.0ms

Algorithm
rewrite-expression-head
Rules
418×times-frac
393×add-sqr-sqrt
252×*-un-lft-identity
208×add-cube-cbrt
109×unpow-prod-down
95×associate-*r*
88×difference-of-squares
51×prod-diff
30×associate-/r*
27×sqr-pow
22×distribute-lft-out--
21×add-exp-log
18×add-cbrt-cube
17×fma-neg
16×associate-/r/
14×div-inv
8×flip3-- flip--
7×pow1 div-exp
6×cbrt-undiv add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod associate-/l* unswap-sqr
2×pow-exp
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 376
Calls
4 calls:
86.0ms
(/ n (/ i (- (pow (/ i n) n) 1.0)))
199.0ms
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
76.0ms
(- (pow (/ i n) n) 1.0)
10.0ms
(pow (/ i n) n)

series502.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(/ n (/ i (- (pow (/ i n) n) 1.0)))
177.0ms
(* 100.0 (/ n (/ i (- (pow (/ i n) n) 1.0))))
104.0ms
(- (pow (/ i n) n) 1.0)
59.0ms
(pow (/ i n) n)

simplify1.1s

Counts
388 → 388
Iterations

Useful iterations: done (1.1s)

IterNodesCost
06578161
115987226
done50016788

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 16.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
0.1b
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
1.1b
(- (pow (/ i n) n) 1.0)
4.6b
(pow (/ i n) n)

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
415×times-frac
383×add-sqr-sqrt
251×*-un-lft-identity
207×add-cube-cbrt
109×unpow-prod-down
95×associate-*r*
88×difference-of-squares
63×add-exp-log
51×prod-diff
30×associate-/r* add-cbrt-cube
27×sqr-pow
22×div-exp distribute-lft-out--
21×prod-exp
17×fma-neg
16×associate-/r/
14×div-inv
11×pow1
9×cbrt-undiv cbrt-unprod
8×flip3-- flip--
6×rec-exp 1-exp add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow pow-prod-down associate-/l*
2×pow-exp
1×pow-to-exp sub-neg pow-flip pow-pow frac-2neg diff-log associate-*r/ associate-*l* clear-num un-div-inv *-commutative inv-pow
Counts
4 → 393
Calls
4 calls:
93.0ms
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
181.0ms
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
99.0ms
(- (pow (/ i n) n) 1.0)
11.0ms
(pow (/ i n) n)

series462.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ 1 (/ i (- (pow (/ i n) n) 1.0)))
190.0ms
(* (* 100.0 n) (/ 1 (/ i (- (pow (/ i n) n) 1.0))))
108.0ms
(- (pow (/ i n) n) 1.0)
80.0ms
(pow (/ i n) n)

simplify2.8s

Counts
405 → 405
Iterations

Useful iterations: done (2.8s)

IterNodesCost
06618676
117697090
248406381
done50006376

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 16.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
0.8b
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))
6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
84×*-un-lft-identity
68×add-sqr-sqrt
58×add-cube-cbrt
48×prod-diff
38×unpow-prod-down
30×times-frac
27×sqrt-prod
26×pow-unpow
18×add-exp-log
16×associate-*l* add-cbrt-cube
12×distribute-lft-out
11×pow1 sqr-pow
8×fma-neg
6×prod-exp cbrt-unprod add-log-exp difference-of-squares
5×associate-*l/
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow-prod-down flip-- div-inv
2×cbrt-undiv frac-times pow-to-exp pow-pow associate-*r/ div-exp pow-exp
1×sub-neg diff-log associate-*r* *-commutative distribute-lft-out--
Counts
4 → 179
Calls
4 calls:
979.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
205.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
20.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
28.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

series1.6s

Counts
4 → 12
Calls
4 calls:
711.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
354.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
313.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
243.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

simplify998.0ms

Counts
191 → 191
Iterations

Useful iterations: done (991.0ms)

IterNodesCost
02735236
16753933
220073239
done50002988

prune486.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 16.7b

regimes199.0ms

Accuracy

51.7% (13.2b remaining)

Error of 30.0b against oracle of 16.8b and baseline of 44.1b

bsearch554.0ms

Steps
ItersRangePoint
7
1.466106254315184e+230
4.2050101804867395e+231
2.568245662391043e+231
11
3.173232095275158e+114
4.61796087672408e+142
9.944860624286458e+141
9
1.2167838917470026e-32
3.39002248453449e-27
3.332988420430884e-27
9
-123126161593.44334
-41918.349557210015
-42606.74875587942

simplify27.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
085193
1111193
done111193

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.5s2515×body1280valid
2.1s989×body2560valid
654.0ms1615×body640valid
277.0ms856×body320valid
224.0ms2973×body80valid
131.0ms2337×body80nan
56.0ms443×body160valid
16.0ms4×body5120valid