Details

Time bar (total: 20.5s)

sample190.0ms

Algorithm
intervals
Results
69.0ms28×body2560valid
66.0ms71×body1280valid
15.0ms45×body640valid
7.0ms123×body80valid
6.0ms33×body320valid
5.0ms1×body5120valid
4.0ms15×body160valid
3.0ms67×body80nan

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize8.0ms

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))

rewrite637.0ms

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:
241.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
133.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
229.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
368.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
276.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms
(pow (+ 1.0 (/ i n)) n)
350.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify62.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune841.0ms

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))

rewrite580.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
163×times-frac
134×*-un-lft-identity
94×add-cube-cbrt
45×difference-of-squares
35×unpow-prod-down
24×add-exp-log prod-diff
23×add-cbrt-cube
20×sqr-pow
15×distribute-lft-out--
13×associate-/r*
10×pow1
9×div-inv
8×fma-neg
7×prod-exp cbrt-unprod associate-/l*
6×cbrt-undiv div-exp associate-*l* add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 229
Calls
4 calls:
189.0ms
(* (sqrt 100.0) (* (sqrt 100.0) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))))
133.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
234.0ms
(/ (- (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))))
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)
354.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify54.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
011512942
150012611

prune640.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

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))

rewrite490.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
528×*-un-lft-identity
296×add-sqr-sqrt add-cube-cbrt
116×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*
12×unpow-prod-down
8×cbrt-undiv fma-def div-exp add-log-exp
6×pow1 div-sub
4×expm1-log1p-u pow-unpow log1p-expm1-u
3×sqr-pow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 410
Calls
4 calls:
92.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
13.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
12.0ms
(pow (+ 1.0 (/ i n)) n)
343.0ms
(/ (/ (+ (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:
269.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (- (* 1.0 1.0)))
223.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
211.0ms
(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))

simplify124.0ms

Algorithm
egg-herbie
Counts
422 → 422
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0188610118
150019695

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 21.4b

localize21.0ms

Local error

Found 4 expressions with local error:

7.1b
(cbrt (+ 1.0 (/ i n)))
7.1b
(cbrt (+ 1.0 (/ i n)))
8.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) (* 2 n)) (pow (cbrt (+ 1.0 (/ i n))) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
573×times-frac
343×*-un-lft-identity
253×add-sqr-sqrt add-cube-cbrt
45×distribute-lft-out
34×div-inv
29×associate-/r/
18×associate-/l*
17×add-exp-log
16×flip3-+ add-cbrt-cube flip-+
13×associate-/r*
8×cbrt-undiv cbrt-prod div-exp
5×pow1
4×expm1-log1p-u unpow-prod-down cbrt-div log1p-expm1-u add-log-exp
3×pow-unpow
2×pow1/3
1×pow-to-exp pow-pow frac-2neg pow-exp clear-num associate-/l/ sqr-pow
Counts
4 → 339
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 (/ i n)))
6.0ms
(cbrt (+ 1.0 (/ i n)))
14.0ms
(pow (+ 1.0 (/ i n)) n)
152.0ms
(/ (/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) (* 2 n)) (pow (cbrt (+ 1.0 (/ i n))) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series3.5s

Counts
4 → 12
Calls
4 calls:
241.0ms
(cbrt (+ 1.0 (/ i n)))
238.0ms
(cbrt (+ 1.0 (/ i n)))
210.0ms
(pow (+ 1.0 (/ i n)) n)
2.8s
(/ (/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) (* 2 n)) (pow (cbrt (+ 1.0 (/ i n))) (* 2 n)) (- (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify136.0ms

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0186413601
1500113322

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.4b

regimes128.0ms

Accuracy

45% (11.6b remaining)

Error of 33.3b against oracle of 21.6b and baseline of 42.8b

bsearch329.0ms

Steps
ItersRangePoint
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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067114
167114

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.7s2515×body1280valid
1.6s932×body2560valid
436.0ms1588×body640valid
138.0ms865×body320valid
132.0ms3108×body80valid
76.0ms2275×body80nan
47.0ms458×body160valid
25.0ms8×body5120valid