Details

Time bar (total: 57.1s)

sample284.0ms

Algorithm
intervals
Results
99.0ms74×body1280valid
91.0ms28×body2560valid
37.0ms60×body640valid
11.0ms33×body320valid
10.0ms109×body80valid
6.0ms81×body80nan
3.0ms12×body160valid

simplify9.7s

Counts
1 → 1
Iterations
IterNodes
done5004
63477
5875
4318
3139
260
125
010

prune123.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize42.0ms

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))

rewrite2.4s

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:
736.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
414.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
39.0ms
(pow (+ 1.0 (/ i n)) n)
1.2s
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.2s

Counts
4 → 12
Calls
4 calls:
709.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
446.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
413.0ms
(pow (+ 1.0 (/ i n)) n)
661.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify6.0s

Counts
333 → 333
Iterations
IterNodes
done5000
11491
0479

prune3.1s

Pruning

7 alts after pruning (7 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)

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u 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
Counts
4 → 139
Calls
4 calls:
751.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
649.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
519.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
51.0ms
(pow (+ 1.0 (/ i n)) n)

series2.2s

Counts
4 → 12
Calls
4 calls:
740.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
289.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
653.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
460.0ms
(pow (+ 1.0 (/ i n)) n)

simplify3.8s

Counts
151 → 151
Iterations
IterNodes
done5000
22233
1713
0266

prune1.4s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×pow1
9×times-frac
6×associate-*r* prod-diff prod-exp cbrt-unprod
5×distribute-rgt-in distribute-lft-in associate-*l*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×associate-*r/ associate-/r* associate-/l*
2×cbrt-undiv sub-neg div-exp *-commutative
1×flip3-- frac-2neg associate-*l/ clear-num log-pow flip-- fma-udef div-inv unswap-sqr
Counts
4 → 95
Calls
4 calls:
1.0ms
(fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i))))))
51.0ms
(* (* 100.0 (/ (fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i)))))) i)) n)
6.0ms
(/ (fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i)))))) i)
38.0ms
(* (log 1.0) (- n (* 0.5 (* i i))))

series1.4s

Counts
4 → 12
Calls
4 calls:
322.0ms
(fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i))))))
380.0ms
(* (* 100.0 (/ (fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i)))))) i)) n)
258.0ms
(/ (fma 1.0 i (+ (* 0.5 (* i i)) (* (log 1.0) (- n (* 0.5 (* i i)))))) i)
429.0ms
(* (log 1.0) (- n (* 0.5 (* i i))))

simplify3.6s

Counts
107 → 107
Iterations
IterNodes
done5000
21683
1479
0191

prune1.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.7b

localize53.0ms

Local error

Found 2 expressions with local error:

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

rewrite224.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×associate-*r*
5×add-cube-cbrt *-un-lft-identity
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u flip3-+ associate-*l/ *-commutative flip-+ log1p-expm1-u add-log-exp
1×distribute-rgt-in distribute-lft-in unswap-sqr
Counts
2 → 46
Calls
2 calls:
93.0ms
(* 100.0 (+ (* i 0.5) (- (fma (/ (log 1.0) i) n 1.0) (* (log 1.0) (* i 0.5)))))
128.0ms
(* (* 100.0 (+ (* i 0.5) (- (fma (/ (log 1.0) i) n 1.0) (* (log 1.0) (* i 0.5))))) n)

series567.0ms

Counts
2 → 6
Calls
2 calls:
207.0ms
(* 100.0 (+ (* i 0.5) (- (fma (/ (log 1.0) i) n 1.0) (* (log 1.0) (* i 0.5)))))
361.0ms
(* (* 100.0 (+ (* i 0.5) (- (fma (/ (log 1.0) i) n 1.0) (* (log 1.0) (* i 0.5))))) n)

simplify3.3s

Counts
52 → 52
Iterations
IterNodes
done5001
21283
1327
0107

prune502.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 8.7b

regimes742.0ms

Accuracy

55.5% (11.2b remaining)

Error of 19.7b against oracle of 8.5b and baseline of 33.6b

bsearch596.0ms

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

simplify19.0ms

Iterations
IterNodes
done48
148
037

end0.0ms

sample11.5s

Algorithm
intervals
Results
3.9s2501×body1280valid
3.4s933×body2560valid
1.9s1594×body640valid
1.1s902×body320valid
290.0ms3054×body80valid
234.0ms2280×body80nan
103.0ms457×body160valid
42.0ms7×body5120valid