Details

Time bar (total: 29.4s)

sample160.0ms

Algorithm
intervals
Results
61.0ms32×body2560valid
60.0ms82×body1280valid
14.0ms46×body640valid
6.0ms31×body320valid
5.0ms107×body80valid
2.0ms62×body80nan
1.0ms9×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite91.0ms

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:
33.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
381.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
220.0ms
(pow (+ 1.0 (/ i n)) n)
354.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify69.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
013193734
150023446

prune924.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
78×add-sqr-sqrt
72×prod-diff
66×add-cube-cbrt
46×unpow-prod-down
31×times-frac
26×distribute-rgt-in distribute-lft-in
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* sqr-pow
11×distribute-lft-out
8×fma-neg
7×pow1 associate-*r*
6×cbrt-undiv div-exp add-log-exp difference-of-squares
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg pow-unpow flip3-- associate-*l* prod-exp flip-- cbrt-unprod div-inv
2×associate-/l/ distribute-lft-out--
1×pow-to-exp pow-pow frac-2neg diff-log pow-prod-down pow-exp clear-num associate-/r/ *-commutative associate-/l* unswap-sqr
Counts
4 → 198
Calls
4 calls:
15.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
11.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
23.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
276.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
220.0ms
(pow (+ 1.0 (/ i n)) n)
378.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify115.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
07922367
139171720
250021708

prune384.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
6.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (/ (* (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
285×times-frac
150×*-un-lft-identity
114×add-sqr-sqrt add-cube-cbrt
29×associate-/r/
27×add-exp-log
26×div-inv
25×add-cbrt-cube
18×distribute-lft-out
15×flip3-+ flip-+
13×cbrt-undiv div-exp associate-/r*
12×unpow-prod-down
10×associate-/l*
8×fma-def add-log-exp
6×pow1
4×expm1-log1p-u pow-unpow log1p-expm1-u
3×sqr-pow
2×pow-to-exp pow-pow pow-exp prod-exp sum-log cbrt-unprod
1×+-commutative neg-sub0 associate-+r- frac-2neg unsub-neg neg-log clear-num associate-/l/
Counts
4 → 243
Calls
4 calls:
12.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
7.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
7.0ms
(pow (+ 1.0 (/ i n)) n)
29.0ms
(/ (/ (* (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series2.8s

Counts
4 → 12
Calls
4 calls:
275.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
221.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
215.0ms
(pow (+ 1.0 (/ i n)) n)
2.1s
(/ (/ (* (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify86.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
015145059
150014711

prune887.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

localize22.0ms

Local error

Found 4 expressions with local error:

6.8b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
6.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (/ (* (/ (+ (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))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
285×times-frac
147×*-un-lft-identity
113×add-sqr-sqrt add-cube-cbrt
39×add-exp-log
36×add-cbrt-cube
29×associate-/r/
26×div-inv
20×cbrt-undiv div-exp
17×distribute-lft-out
14×flip3-+ flip-+
13×associate-/r*
12×unpow-prod-down
10×associate-/l*
7×pow1
5×pow-unpow
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×frac-2neg clear-num associate-/l/
Counts
4 → 239
Calls
4 calls:
7.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
7.0ms
(pow (+ 1.0 (/ i n)) n)
43.0ms
(/ (/ (* (/ (+ (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))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series15.0s

Counts
4 → 12
Calls
4 calls:
210.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
207.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
198.0ms
(pow (+ 1.0 (/ i n)) n)
14.3s
(/ (/ (* (/ (+ (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))) 100.0) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify91.0ms

Algorithm
egg-herbie
Counts
251 → 251
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
016227980
150017438

prune949.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.6b

regimes136.0ms

Accuracy

46.7% (12.9b remaining)

Error of 31.4b against oracle of 18.5b and baseline of 42.7b

bsearch546.0ms

Steps
ItersRangePoint
8
2.6233364391768453e+215
7.559003031217257e+219
7.395559138739582e+219
7
8.449789709258891e+21
1.927335547477129e+23
8.532543483832935e+21
6
3.1399496998840866e-125
3.7800925651486635e-124
6.02622510223327e-125
7
1.4967481787327182e-161
2.5387026277821525e-160
2.515912909264607e-160
8
-1.4252965457371644e-10
-5.035330346103121e-14
-1.3992561866449662e-10
8
-1.6450582212898727e+137
-4.094290472995023e+133
-2.561401665352169e+135

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
098111
1108111
2116111
3130111
4130111

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.7s2560×body1280valid
1.7s942×body2560valid
452.0ms1643×body640valid
134.0ms871×body320valid
122.0ms3062×body80valid
64.0ms2190×body80nan
38.0ms396×body160valid
28.0ms8×body5120valid