Details

Time bar (total: 24.6s)

sample264.0ms

Algorithm
intervals
Results
113.0ms76×body1280valid
72.0ms24×body2560valid
29.0ms54×body640valid
8.0ms27×body320valid
8.0ms98×body80valid
6.0ms96×body80nan
4.0ms19×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b
(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:
491.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
300.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms
(pow (+ 1.0 (/ i n)) n)
481.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts
4 → 12
Calls
4 calls:
561.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
353.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
344.0ms
(pow (+ 1.0 (/ i n)) n)
505.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.1s

Counts
333 → 333
Iterations

Useful iterations: done (1.0s)

IterNodesCost
04797415
115206929
done50016480

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
0.1b
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.1b
(* (pow i 2) (log 1.0))
16.2b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 189
Calls
4 calls:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
53.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
14.0ms
(* (pow i 2) (log 1.0))
20.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series816.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
283.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
213.0ms
(* (pow i 2) (log 1.0))
257.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify621.0ms

Counts
201 → 201
Iterations

Useful iterations: done (612.0ms)

IterNodesCost
03296419
19506243
done50015768

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 11.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
3.3b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
10.3b
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
12.1b
(* (pow i 2) (log 1.0))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
127×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
53×add-exp-log
48×associate-*r*
32×add-cbrt-cube
23×div-exp
21×associate-*l*
13×prod-exp associate-/r*
12×cbrt-undiv unswap-sqr
10×div-inv
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×frac-times pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 218
Calls
4 calls:
1.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
23.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
61.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
14.0ms
(* (pow i 2) (log 1.0))

series715.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
176.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
277.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
202.0ms
(* (pow i 2) (log 1.0))

simplify693.0ms

Counts
230 → 230
Iterations

Useful iterations: done (680.0ms)

IterNodesCost
03707821
111747432
done50006547

prune952.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 11.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
3.0b
(* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
10.3b
(/ (* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)
12.1b
(* (pow i 2) (log 1.0))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
24×add-sqr-sqrt
22×add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
12×pow1 associate-*l*
10×associate-*r* prod-exp
9×distribute-rgt-in distribute-lft-in
8×cbrt-unprod
6×log-prod associate-*r/ prod-diff
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down associate-*l/ log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-- times-frac div-exp associate-/r* *-commutative flip--
2×sub-neg associate--l+ fma-udef associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 119
Calls
4 calls:
24.0ms
(* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
37.0ms
(* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
49.0ms
(/ (* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)
15.0ms
(* (pow i 2) (log 1.0))

series820.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
209.0ms
(* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n)
260.0ms
(/ (* (* 100.0 (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) n) i)
215.0ms
(* (pow i 2) (log 1.0))

simplify2.3s

Counts
131 → 131
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02363554
16053472
237132908
done50022844

prune839.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.4b

regimes442.0ms

Accuracy

53.8% (10.2b remaining)

Error of 21.2b against oracle of 10.9b and baseline of 33.1b

bsearch583.0ms

Steps
ItersRangePoint
8
1.7651294170037398e+141
1.8332650139728974e+145
5.064717226083426e+144
10
3.6038887973904155e-15
1575.9184687212278
18.662937204719956
0
3.894337894410089e-198
3.931641926837824e-198
3.912989910623956e-198
6
-1.8476729376770798e-255
-2.387276649835617e-256
-1.2354370687948715e-255
9
-3.309911606533295
-1.716801800522696e-06
-0.10408074195050146

simplify15.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
056167
170167
done70167

end0.0ms

sample6.8s

Algorithm
intervals
Results
2.7s2569×body1280valid
2.3s945×body2560valid
652.0ms1634×body640valid
190.0ms839×body320valid
178.0ms2934×body80valid
173.0ms2223×body80nan
93.0ms424×body160valid
18.0ms5×body5120valid