Details

Time bar (total: 14.4s)

sample176.0ms

Algorithm
intervals
Results
71.0ms36×body2560valid
59.0ms72×body1280valid
15.0ms46×body640valid
5.0ms114×body80valid
4.0ms1×body5120valid
4.0ms22×body320valid
3.0ms75×body80nan
2.0ms18×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
11.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite607.0ms

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:
222.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
123.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
235.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
363.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
205.0ms
(pow (+ 1.0 (/ i n)) n)
345.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify250.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune881.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
2.8b
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))
6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite365.0ms

Algorithm
rewrite-expression-head
Rules
85×*-un-lft-identity
74×add-sqr-sqrt
59×add-cube-cbrt
48×prod-diff
38×unpow-prod-down
31×times-frac
27×sqrt-prod
26×pow-unpow
16×associate-*r*
12×distribute-lft-out
11×add-exp-log sqr-pow
9×add-cbrt-cube
8×pow1 fma-neg
6×add-log-exp difference-of-squares
4×expm1-log1p-u log1p-expm1-u
3×associate-*l* div-inv
2×pow-to-exp pow-pow pow-exp prod-exp cbrt-unprod unswap-sqr
1×cbrt-undiv sub-neg flip3-- diff-log associate-*r/ div-exp pow-prod-down *-commutative flip-- distribute-lft-out--
Counts
4 → 174
Calls
4 calls:
206.0ms
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
126.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
14.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
12.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

series844.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
250.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
222.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
212.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

simplify75.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
06142231
123561740
250021736

prune507.0ms

Filtered
186 candidates to 113 candidates (60.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n))
0.3b
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))
12.3b
(* (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i)) (/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n)))

rewrite484.0ms

Algorithm
rewrite-expression-head
Rules
163×times-frac
106×*-un-lft-identity
103×add-sqr-sqrt
98×add-cube-cbrt
79×add-exp-log
60×associate-*r*
50×add-cbrt-cube
30×div-exp
27×prod-exp
17×cbrt-unprod
16×cbrt-undiv
13×pow-unpow associate-/r*
12×pow1
11×div-inv
4×expm1-log1p-u unpow-prod-down rec-exp 1-exp associate-*r/ associate-*l* pow-prod-down log1p-expm1-u distribute-lft-out add-log-exp
3×associate-/l*
2×associate-/r/ *-commutative unswap-sqr
1×frac-times pow-to-exp pow-pow frac-2neg associate-*l/ pow-exp clear-num sqr-pow
Counts
4 → 225
Calls
4 calls:
5.0ms
(/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n))
208.0ms
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
12.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
249.0ms
(* (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i)) (/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n)))

series1.1s

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n))
173.0ms
(* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))
223.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
592.0ms
(* (* 100.0 (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i)) (/ (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) (/ 1 n)))

simplify64.0ms

Algorithm
egg-herbie
Counts
237 → 237
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013173862
150013324

prune939.0ms

Filtered
237 candidates to 157 candidates (66.2%)
Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 10.4b

localize19.0ms

Local error

Found 2 expressions with local error:

6.1b
(pow (+ 1.0 (/ i n)) (/ n 2))
12.2b
(* (* (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) n) (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
21×times-frac
18×add-sqr-sqrt add-cube-cbrt
16×associate-*r*
15×add-exp-log
14×add-cbrt-cube
13×pow-unpow
8×pow1
6×prod-exp cbrt-unprod
4×unpow-prod-down distribute-lft-out
3×pow-prod-down
2×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u div-inv add-log-exp
1×pow-to-exp pow-pow associate-*r/ associate-*l* pow-exp *-commutative sqr-pow
Counts
2 → 68
Calls
2 calls:
11.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
164.0ms
(* (* (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) n) (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))

series728.0ms

Counts
2 → 6
Calls
2 calls:
220.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
507.0ms
(* (* (fma i 0.5 (- (fma 1/2 (* (log 1.0) n) 1) (sqrt 1.0))) n) (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i))

simplify73.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06061092
12810926
25001925

prune265.0ms

Filtered
74 candidates to 52 candidates (70.3%)
Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 10.4b

regimes625.0ms

Accuracy

52.6% (10.1b remaining)

Error of 21.4b against oracle of 11.3b and baseline of 32.6b

bsearch148.0ms

Steps
ItersRangePoint
9
8.394657237176314e-23
9.45688979760406e-18
9.343203234098088e-18
4
-0.041603525395973645
-0.02085603301560968
-0.02815481255422397

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04523
14523

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s957×body2560valid
1.8s2539×body1280valid
482.0ms1636×body640valid
141.0ms850×body320valid
133.0ms3037×body80valid
75.0ms2255×body80nan
43.0ms428×body160valid
30.0ms8×body5120valid