Details

Time bar (total: 50.2s)

sample293.0ms

Algorithm
intervals
Results
102.0ms74×body1280valid
93.0ms28×body2560valid
39.0ms60×body640valid
12.0ms33×body320valid
10.0ms109×body80valid
7.0ms81×body80nan
3.0ms12×body160valid

simplify5.2s

Counts
1 → 1
Iterations
IterNodes
done5000
63388
5834
4309
3135
259
125
010

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.8s

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:
727.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
359.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
37.0ms
(pow (+ 1.0 (/ i n)) n)
655.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.2s

Counts
4 → 12
Calls
4 calls:
693.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
460.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
387.0ms
(pow (+ 1.0 (/ i n)) n)
640.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify5.8s

Counts
293 → 293
Iterations
IterNodes
done5002
24653
11388
0437

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0b
(pow (+ 1.0 (/ i n)) n)

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
28×associate-*r*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×add-log-exp
5×sqr-pow
4×associate-*l* pow-prod-down distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
763.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
603.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
329.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
45.0ms
(pow (+ 1.0 (/ i n)) n)

series1.9s

Counts
4 → 12
Calls
4 calls:
727.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
299.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
501.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
417.0ms
(pow (+ 1.0 (/ i n)) n)

simplify3.0s

Counts
111 → 111
Iterations
IterNodes
done5000
21987
1607
0224

prune929.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
0.1b
(* (* 100.0 (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)) n)
12.1b
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
12.8b
(* (log 1.0) (- n (* (* 0.5 i) i)))

rewrite765.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-sqr-sqrt add-cbrt-cube
15×add-cube-cbrt *-un-lft-identity
12×pow1
9×times-frac add-log-exp
6×associate-*r* prod-exp cbrt-unprod
5×associate-*l*
4×pow-prod-down
3×associate-*r/ associate-/r* sum-log associate-/l*
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in flip3-+ div-exp *-commutative flip-+ associate-/l/
1×+-commutative associate-+r+ flip3-- frac-2neg associate-*l/ clear-num log-pow flip-- div-inv unswap-sqr
Counts
4 → 88
Calls
4 calls:
85.0ms
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
337.0ms
(* (* 100.0 (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)) n)
300.0ms
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
38.0ms
(* (log 1.0) (- n (* (* 0.5 i) i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
168.0ms
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
393.0ms
(* (* 100.0 (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)) n)
268.0ms
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
288.0ms
(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify3.6s

Counts
100 → 100
Iterations
IterNodes
done5000
22174
1527
0188

prune942.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.7b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
0.1b
(* 100.0 (* (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i) n))
12.1b
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
12.8b
(* (log 1.0) (- n (* (* 0.5 i) i)))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
17×add-exp-log add-sqr-sqrt add-cbrt-cube
15×add-cube-cbrt *-un-lft-identity
12×pow1
9×times-frac add-log-exp
7×associate-*l*
6×prod-exp cbrt-unprod
4×associate-*r* pow-prod-down
3×associate-*r/ associate-/r* sum-log associate-/l*
2×cbrt-undiv distribute-rgt-in sub-neg distribute-lft-in flip3-+ div-exp *-commutative flip-+ associate-/l/
1×+-commutative associate-+r+ flip3-- frac-2neg associate-*l/ clear-num log-pow flip-- div-inv unswap-sqr
Counts
4 → 88
Calls
4 calls:
91.0ms
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
277.0ms
(* 100.0 (* (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i) n))
292.0ms
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
34.0ms
(* (log 1.0) (- n (* (* 0.5 i) i)))

series1.1s

Counts
4 → 12
Calls
4 calls:
162.0ms
(+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i)))))
341.0ms
(* 100.0 (* (/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i) n))
222.0ms
(/ (+ (* i 1.0) (+ (* (* 0.5 i) i) (* (log 1.0) (- n (* (* 0.5 i) i))))) i)
326.0ms
(* (log 1.0) (- n (* (* 0.5 i) i)))

simplify3.4s

Counts
100 → 100
Iterations
IterNodes
done5000
22098
1511
0186

prune804.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.7b

regimes652.0ms

Accuracy

57.1% (10.6b remaining)

Error of 19.1b against oracle of 8.5b and baseline of 33.2b

bsearch577.0ms

Steps
ItersRangePoint
7
4.4391554391661806e+188
1.0183500025446565e+191
2.5651303341965514e+190
9
2.6925018084722774e-16
6.402043939282351e-10
6.305809243265488e-10
10
-5.212462118803251e-11
-2.0980722130609105e-21
-5.1633600557877234e-11

simplify28.0ms

Iterations
IterNodes
done57
157
041

end0.0ms

sample10.8s

Algorithm
intervals
Results
4.1s2501×body1280valid
3.7s933×body2560valid
1.3s1594×body640valid
380.0ms902×body320valid
358.0ms3054×body80valid
184.0ms2280×body80nan
104.0ms457×body160valid
45.0ms7×body5120valid