Details

Time bar (total: 35.5s)

sample149.0ms

Algorithm
intervals
Results
55.0ms28×body2560valid
51.0ms71×body1280valid
12.0ms45×body640valid
5.0ms123×body80valid
5.0ms33×body320valid
4.0ms1×body5120valid
2.0ms67×body80nan
1.0ms15×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite573.0ms

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:
232.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
107.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms
(pow (+ 1.0 (/ i n)) n)
204.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
357.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
246.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
209.0ms
(pow (+ 1.0 (/ i n)) n)
350.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012263285
150023166

prune790.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
153×add-sqr-sqrt
110×*-un-lft-identity
78×add-cube-cbrt
45×difference-of-squares
24×add-exp-log
23×add-cbrt-cube
19×unpow-prod-down
16×sqr-pow
15×distribute-lft-out--
13×associate-/r*
10×pow1
9×div-inv
7×prod-exp cbrt-unprod associate-/l*
6×cbrt-undiv div-exp associate-*l* add-log-exp
3×pow-unpow pow-prod-down sqrt-prod
2×flip3-- associate-*r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r* pow-exp clear-num associate-/r/ *-commutative distribute-lft-out
Counts
4 → 189
Calls
4 calls:
179.0ms
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))
105.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
200.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
748.0ms
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))
251.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
241.0ms
(pow (+ 1.0 (/ i n)) n)
369.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify117.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
010562485
146862324
250022319

prune589.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.5b

localize16.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
8.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
8.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite462.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
524×*-un-lft-identity
294×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv unpow-prod-down div-exp add-log-exp
6×pow1 div-sub
4×pow-unpow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log sqr-pow
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
77.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) n)
332.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.7s

Counts
4 → 12
Calls
4 calls:
276.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
216.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
224.0ms
(pow (+ 1.0 (/ i n)) n)
2.0s
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify127.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0186410059
150029637

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.5b

localize22.0ms

Local error

Found 4 expressions with local error:

8.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
8.3b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
8.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite659.0ms

Algorithm
rewrite-expression-head
Rules
3405×times-frac
2121×*-un-lft-identity
1275×add-sqr-sqrt add-cube-cbrt
423×distribute-lft-out
150×div-inv
141×associate-/r/
78×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
9×div-sub
7×pow1
5×pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1182
Calls
4 calls:
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
13.0ms
(pow (+ 1.0 (/ i n)) n)
498.0ms
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series15.2s

Counts
4 → 12
Calls
4 calls:
216.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
218.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
211.0ms
(pow (+ 1.0 (/ i n)) n)
14.5s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (- (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify448.0ms

Algorithm
egg-herbie
Counts
1194 → 1194
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
0500154232

prune3.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.5b

regimes145.0ms

Accuracy

43.9% (13.2b remaining)

Error of 32.4b against oracle of 19.2b and baseline of 42.7b

bsearch548.0ms

Steps
ItersRangePoint
9
1.1168519270995823e+164
1.1325633587695186e+169
6.446019370922723e+168
8
1.5128407297750358e-128
5.974300878502234e-124
1.5472591010965058e-128
6
-1.3492760744583381e-217
-9.636105299026902e-219
-9.803758796411594e-219
9
-1.3904126925433413e+188
-1.265931623886742e+180
-7.3291384716741e+181

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
096108
199108
299108

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s2515×body1280valid
1.7s932×body2560valid
437.0ms1588×body640valid
138.0ms865×body320valid
127.0ms3108×body80valid
66.0ms2275×body80nan
44.0ms458×body160valid
26.0ms8×body5120valid