Details

Time bar (total: 25.2s)

sample151.0ms

Algorithm
intervals
Results
57.0ms81×body1280valid
49.0ms26×body2560valid
16.0ms56×body640valid
5.0ms33×body320valid
4.0ms93×body80valid
3.0ms88×body80nan
1.0ms12×body160valid

simplify44.0ms

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: 42.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite945.0ms

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:
328.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
332.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
333.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
232.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)
319.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune963.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.6b

localize9.0ms

Local error

Found 3 expressions with local error:

1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
40×add-sqr-sqrt
35×add-cube-cbrt
31×times-frac
24×prod-diff
21×unpow-prod-down
16×add-exp-log
15×add-cbrt-cube
13×associate-/r*
8×fma-neg
6×cbrt-undiv div-exp sqr-pow
5×distribute-lft-out add-log-exp
4×pow1
3×expm1-log1p-u pow-unpow log1p-expm1-u div-inv difference-of-squares
2×flip3-- associate-*r/ prod-exp flip-- cbrt-unprod associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log pow-exp clear-num associate-/r/ associate-/l* distribute-lft-out--
Counts
3 → 120
Calls
3 calls:
219.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
224.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series738.0ms

Counts
3 → 9
Calls
3 calls:
224.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
185.0ms
(pow (+ 1.0 (/ i n)) n)
328.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify88.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
06611232
13202958
25002952

prune287.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.5b

localize14.0ms

Local error

Found 4 expressions with local error:

6.4b
(cbrt (+ 1.0 (/ i n)))
6.4b
(cbrt (+ 1.0 (/ i n)))
6.4b
(cbrt (+ 1.0 (/ i n)))
9.2b
(/ (* 100.0 (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0))) (/ i n))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
27×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt
16×add-exp-log add-cbrt-cube
13×associate-/r*
12×cbrt-prod
6×cbrt-undiv cbrt-div div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ div-inv distribute-lft-out
2×prod-exp cbrt-unprod
1×frac-2neg clear-num associate-/r/ associate-/l*
Counts
4 → 96
Calls
4 calls:
8.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
13.0ms
(/ (* 100.0 (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0))) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
220.0ms
(cbrt (+ 1.0 (/ i n)))
225.0ms
(cbrt (+ 1.0 (/ i n)))
217.0ms
(cbrt (+ 1.0 (/ i n)))
701.0ms
(/ (* 100.0 (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0))) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05261476
122861286
250011261

prune376.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

localize18.0ms

Local error

Found 4 expressions with local error:

6.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.3b
(pow (+ 1.0 (/ i n)) n)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

rewrite934.0ms

Algorithm
rewrite-expression-head
Rules
4525×times-frac
3383×add-sqr-sqrt
1961×*-un-lft-identity
1535×add-cube-cbrt
1356×unpow-prod-down
1344×difference-of-squares
1008×cube-prod
843×sqr-pow
210×distribute-lft-out--
143×div-inv
127×associate-/l*
42×difference-cubes
19×add-exp-log
16×add-cbrt-cube
13×associate-/r*
8×cbrt-undiv div-exp
7×pow1 pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out
2×div-sub
1×frac-2neg clear-num associate-/r/ associate-/l/
Counts
4 → 1872
Calls
4 calls:
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
18.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(pow (+ 1.0 (/ i n)) n)
645.0ms
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

series7.3s

Counts
4 → 12
Calls
4 calls:
231.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
188.0ms
(pow (+ 1.0 (/ i n)) n)
190.0ms
(pow (+ 1.0 (/ i n)) n)
6.7s
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

simplify623.0ms

Algorithm
egg-herbie
Counts
1884 → 1884
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500174375

prune4.7s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.5b

regimes135.0ms

Accuracy

51.4% (11.6b remaining)

Error of 30.8b against oracle of 19.2b and baseline of 43.0b

bsearch159.0ms

Steps
ItersRangePoint
8
1.537653969837454
6330.810310882262
2.5293961213262803
8
-3.87394257886499e-12
-2.117072550125069e-15
-3.796684874032534e-12

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04126
14126

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s1015×body2560valid
1.7s2487×body1280valid
443.0ms1605×body640valid
128.0ms849×body320valid
118.0ms3015×body80valid
61.0ms2238×body80nan
44.0ms469×body160valid
20.0ms6×body5120valid