Details

Time bar (total: 25.0s)

sample249.0ms

Algorithm
intervals
Results
106.0ms41×body2560valid
85.0ms83×body1280valid
19.0ms50×body640valid
7.0ms98×body80valid
7.0ms28×body320valid
3.0ms71×body80nan
2.0ms10×body160valid

simplify557.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.1b
(pow (+ 1.0 (/ i n)) n)
12.9b
(/ (- (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:
528.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
247.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms
(pow (+ 1.0 (/ i n)) n)
395.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
475.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
322.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
341.0ms
(pow (+ 1.0 (/ i n)) n)
508.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify638.0ms

Counts
293 → 293

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 23.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.1b
(pow (+ 1.0 (/ i n)) n)

rewrite1.6s

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:
860.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
478.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
207.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
31.0ms
(pow (+ 1.0 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
525.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
238.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
376.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
347.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.0s

Counts
111 → 111

prune386.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
0.0b
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
7.3b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.7b
(* (pow i 2) (log 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×unpow-prod-down pow-prod-down add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*l/ pow-exp clear-num log-pow flip--
Counts
4 → 117
Calls
4 calls:
365.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
408.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
393.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
19.0ms
(* (pow i 2) (log 1.0))

series876.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
267.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
209.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
191.0ms
(* (pow i 2) (log 1.0))

simplify1.1s

Counts
129 → 129

prune502.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
2.2b
(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
7.7b
(* (pow i 2) (log 1.0))
13.7b
(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×pow1 associate-*l*
10×associate-*r* prod-exp
8×cbrt-unprod
6×distribute-rgt-in log-prod distribute-lft-in associate-*r/
5×unswap-sqr
4×unpow-prod-down pow-prod-down associate-*l/ add-log-exp
3×cbrt-undiv flip3-- times-frac div-exp associate-/r* *-commutative flip--
2×sub-neg associate--l+ associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 105
Calls
4 calls:
313.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
390.0ms
(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
15.0ms
(* (pow i 2) (log 1.0))
446.0ms
(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

series746.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
166.0ms
(* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
207.0ms
(* (pow i 2) (log 1.0))
241.0ms
(/ (* (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)

simplify1.2s

Counts
117 → 117

prune378.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.0b

regimes186.0ms

Accuracy

53.5% (10.4b remaining)

Error of 21.0b against oracle of 10.7b and baseline of 32.9b

bsearch306.0ms

Steps
ItersRangePoint
8
1.251734353427841e-184
4.7398570652317846e-181
1.6570160255762519e-183
10
-4.886702096579331e-303
4.1025949495244904e-302
5.74305082628592e-309
8
-1.0405383496838098e+71
-2.1293241434994903e+67
-2.0189248305682152e+68

simplify990.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.2s1004×body2560valid
2.1s2519×body1280valid
650.0ms1621×body640valid
606.0ms3109×body80valid
214.0ms853×body320valid
161.0ms2262×body80nan
54.0ms427×body160valid
38.0ms10×body5120valid