Details

Time bar (total: 22.9s)

sample203.0ms

Algorithm
intervals
Results
77.0ms80×body1280valid
72.0ms28×body2560valid
22.0ms51×body640valid
7.0ms115×body80valid
5.0ms21×body320valid
4.0ms75×body80nan
2.0ms13×body160valid

simplify1.9s

Counts
1 → 1
Iterations
IterNodes
done5004
52473
4512
3150
258
128
010

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
1.3b
(- (pow (+ 1 (/ i n)) n) 1)
6.1b
(pow (+ 1 (/ i n)) n)
10.2b
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

rewrite449.0ms

Algorithm
rewrite-expression-head
Rules
584×times-frac
485×add-sqr-sqrt
366×*-un-lft-identity
224×add-cube-cbrt
174×associate-*r*
168×difference-of-squares
88×unpow-prod-down
85×sqr-pow
84×difference-of-sqr-1
29×div-inv
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* associate-/l*
7×pow1
6×cbrt-undiv div-exp add-log-exp
4×insert-posit16
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative distribute-lft-out
Counts
4 → 453
Calls
4 calls:
163.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
81.0ms
(- (pow (+ 1 (/ i n)) n) 1)
19.0ms
(pow (+ 1 (/ i n)) n)
173.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
462.0ms
(* 100 (/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n)))
309.0ms
(- (pow (+ 1 (/ i n)) n) 1)
260.0ms
(pow (+ 1 (/ i n)) n)
368.0ms
(/ (- (pow (+ 1 (/ i n)) n) 1) (/ i n))

simplify1.6s

Counts
465 → 465
Iterations
IterNodes
done5001
11702
0542

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (pow (+ 1 (/ i n)) n) (/ i n))
0.3b
(/ 1 (/ i n))
6.1b
(pow (+ 1 (/ i n)) n)
12.4b
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
395×times-frac
286×add-sqr-sqrt
233×*-un-lft-identity
153×add-cube-cbrt
70×unpow-prod-down
35×difference-of-squares
29×add-exp-log
26×associate-/r*
25×sqr-pow
24×div-inv
16×div-exp distribute-lft-out--
15×distribute-lft-out
14×add-cbrt-cube
11×associate-/l*
6×pow1 cbrt-undiv add-log-exp
5×distribute-rgt-out-- associate-/r/
4×insert-posit16
3×pow-to-exp pow-unpow pow-exp
2×rec-exp clear-num frac-2neg 1-exp
1×sub-neg pow-pow flip3-- diff-log frac-sub pow-flip flip-- inv-pow sub-div
Counts
4 → 312
Calls
4 calls:
56.0ms
(/ (pow (+ 1 (/ i n)) n) (/ i n))
13.0ms
(/ 1 (/ i n))
17.0ms
(pow (+ 1 (/ i n)) n)
100.0ms
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

series921.0ms

Counts
4 → 12
Calls
4 calls:
287.0ms
(/ (pow (+ 1 (/ i n)) n) (/ i n))
10.0ms
(/ 1 (/ i n))
254.0ms
(pow (+ 1 (/ i n)) n)
370.0ms
(- (/ (pow (+ 1 (/ i n)) n) (/ i n)) (/ 1 (/ i n)))

simplify1.8s

Counts
324 → 324
Iterations
IterNodes
done5003
23332
11236
0487

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 1/6 i) i)
0.3b
(* 1/6 i)
3.5b
(+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2))))
8.3b
(* n (* (* 1/6 i) i))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-cbrt-cube add-exp-log
10×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
9×add-log-exp
8×*-un-lft-identity add-cube-cbrt
7×associate-*r* associate-*l*
4×insert-posit16
3×sum-log *-commutative
1×+-commutative associate-+r+ flip3-+ flip-+ unswap-sqr
Counts
4 → 74
Calls
4 calls:
14.0ms
(* (* 1/6 i) i)
5.0ms
(* 1/6 i)
42.0ms
(+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2))))
35.0ms
(* n (* (* 1/6 i) i))

series134.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (* 1/6 i) i)
19.0ms
(* 1/6 i)
54.0ms
(+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2))))
33.0ms
(* n (* (* 1/6 i) i))

simplify984.0ms

Counts
86 → 86
Iterations
IterNodes
done5005
21169
1305
0110

prune276.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.3b

localize35.0ms

Local error

Found 4 expressions with local error:

8.3b
(* n (* (* 1/6 i) i))
12.6b
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
12.6b
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
12.6b
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-cbrt-cube add-exp-log
9×cbrt-prod
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×cbrt-div pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×flip3-+ pow1/3 associate-*l* flip-+
1×associate-*r* *-commutative
Counts
4 → 64
Calls
4 calls:
35.0ms
(* n (* (* 1/6 i) i))
34.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
34.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
38.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* n (* (* 1/6 i) i))
123.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
117.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))
117.0ms
(cbrt (+ (* n (* (* 1/6 i) i)) (+ n (* i (* n 1/2)))))

simplify1.3s

Counts
76 → 76
Iterations
IterNodes
done5000
21121
1305
0121

prune328.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.3b

regimes349.0ms

Accuracy

56.6% (11.7b remaining)

Error of 17.8b against oracle of 6.1b and baseline of 33.1b

bsearch231.0ms

Steps
ItersRangePoint
9
2.784564170770455e-12
0.0004981816479932727
0.0004866774544189746
8
-922.1020704437461
-0.5767180207385502
-1.8795028361709332

simplify9.0ms

Iterations
IterNodes
done48
148
034

end0.0ms

sample7.3s

Algorithm
intervals
Results
3.2s2514×body1280valid
2.4s1006×body2560valid
702.0ms1632×body640valid
276.0ms845×body320valid
230.0ms3013×body80valid
115.0ms2294×body80nan
66.0ms440×body160valid
35.0ms8×body5120valid