Details

Time bar (total: 16.2s)

sample147.0ms

Algorithm
intervals
Results
57.0ms79×body1280valid
48.0ms25×body2560valid
19.0ms65×body640valid
4.0ms100×body80valid
3.0ms18×body320valid
3.0ms85×body80nan
1.0ms12×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 42.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
9.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite660.0ms

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:
258.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
135.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
235.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
210.0ms
(pow (+ 1.0 (/ i n)) n)
545.0ms
(/ (- (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
150013446

prune868.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
1.9b
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
5.6b
(pow (+ 1.0 (/ i n)) (/ n 2))
5.6b
(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite808.0ms

Algorithm
rewrite-expression-head
Rules
84×*-un-lft-identity
68×add-sqr-sqrt
58×add-cube-cbrt
48×prod-diff
38×unpow-prod-down
30×times-frac
27×sqrt-prod
26×pow-unpow
18×add-exp-log
16×associate-*l* add-cbrt-cube
12×distribute-lft-out
11×pow1 sqr-pow
8×fma-neg
6×prod-exp cbrt-unprod add-log-exp difference-of-squares
5×associate-*l/
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow-prod-down flip-- div-inv
2×cbrt-undiv frac-times pow-to-exp pow-pow associate-*r/ div-exp pow-exp
1×sub-neg diff-log associate-*r* *-commutative distribute-lft-out--
Counts
4 → 179
Calls
4 calls:
632.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
139.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
13.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
16.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
603.0ms
(* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n))
257.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
239.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
221.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

simplify92.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
06892685
127181980
250011895

prune531.0ms

Filtered
191 candidates to 117 candidates (61.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 11.9b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 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))) n)))
5.6b
(pow (+ 1.0 (/ i n)) (/ n 2))
13.7b
(* (/ (+ (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))) n))

rewrite444.0ms

Algorithm
rewrite-expression-head
Rules
34×add-exp-log
33×add-cbrt-cube
28×*-un-lft-identity
21×times-frac
20×add-sqr-sqrt add-cube-cbrt
19×associate-*l*
18×pow1
17×prod-exp cbrt-unprod
13×pow-unpow
9×pow-prod-down
4×cbrt-undiv unpow-prod-down div-exp distribute-lft-out
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×associate-*r* associate-*l/ *-commutative div-inv
1×pow-to-exp pow-pow associate-*r/ pow-exp sqr-pow
Counts
3 → 96
Calls
3 calls:
185.0ms
(* 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))) n)))
12.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
243.0ms
(* (/ (+ (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))) n))

series1.3s

Counts
3 → 9
Calls
3 calls:
579.0ms
(* 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))) n)))
226.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
533.0ms
(* (/ (+ (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))) n))

simplify87.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08101919
133201552
250011542

prune425.0ms

Filtered
105 candidates to 70 candidates (66.7%)
Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.8b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 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)))) n))
0.1b
(* (/ (+ (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))))
5.6b
(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite869.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
26×add-sqr-sqrt
23×add-exp-log
22×times-frac add-cbrt-cube
21×add-cube-cbrt
19×associate-*l*
15×pow1
13×pow-unpow
11×prod-exp cbrt-unprod
7×pow-prod-down
4×unpow-prod-down associate-*r* distribute-lft-out
3×expm1-log1p-u associate-*l/ log1p-expm1-u add-log-exp
2×cbrt-undiv div-exp *-commutative fma-udef div-inv unswap-sqr
1×distribute-rgt-in pow-to-exp pow-pow distribute-lft-in associate-*r/ pow-exp sqr-pow
Counts
3 → 95
Calls
3 calls:
612.0ms
(* 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)))) n))
237.0ms
(* (/ (+ (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))))
16.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

series1.2s

Counts
3 → 9
Calls
3 calls:
601.0ms
(* 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)))) n))
404.0ms
(* (/ (+ (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))))
222.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

simplify95.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
08411801
134601539
250011535

prune391.0ms

Filtered
104 candidates to 74 candidates (71.2%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.8b

regimes254.0ms

Accuracy

52.3% (10.5b remaining)

Error of 21.6b against oracle of 11.1b and baseline of 33.1b

bsearch240.0ms

Steps
ItersRangePoint
9
1.560051953962792e-13
3.9524390088012255e-07
5.88981601408303e-08
9
-6.956871504263554e-09
-9.165072888214816e-14
-6.8977356701701615e-09

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05143
15143

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.0s1005×body2560valid
1.8s2464×body1280valid
486.0ms1630×body640valid
145.0ms854×body320valid
130.0ms3054×body80valid
72.0ms2270×body80nan
47.0ms460×body160valid