Details

Time bar (total: 14.4s)

sample200.0ms

Algorithm
intervals
Results
76.0ms89×body1280valid
68.0ms31×body2560valid
27.0ms63×body640valid
6.0ms29×body320valid
5.0ms77×body80valid
3.0ms71×body80nan
1.0ms10×body160valid

simplify41.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 47.0b

Counts
2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.6b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (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)))
14.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
365.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
271.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
244.0ms
(pow (+ 1.0 (/ i n)) n)
375.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify76.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013193734
150023446

prune772.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New32310333
Fresh000
Picked101
Done000
Total32410334

Merged error: 21.7b

Counts
334 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
11.6b
(* (pow i 2) (log 1.0))
19.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow fma-udef
Counts
4 → 186
Calls
4 calls:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
15.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
6.0ms
(* (pow i 2) (log 1.0))
6.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series646.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
214.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
139.0ms
(* (pow i 2) (log 1.0))
197.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify122.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07343209
137502968
250012968

prune691.0ms

Filtered
198 candidates to 152 candidates (76.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New18612198
Fresh189
Picked101
Done000
Total18820208

Merged error: 10.7b

Counts
208 → 20

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
0.1b
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
11.0b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.6b
(* (pow i 2) (log 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
6.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
6.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
3.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
6.0ms
(* (pow i 2) (log 1.0))

series755.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
275.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
139.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
143.0ms
(* (pow i 2) (log 1.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04761783
120111521
250011513

prune403.0ms

Filtered
134 candidates to 92 candidates (68.7%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh01919
Picked011
Done000
Total13420154

Merged error: 10.7b

Counts
154 → 20

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
2.7b
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
5.4b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
11.6b
(* (pow i 2) (log 1.0))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
183×times-frac
119×add-sqr-sqrt
115×add-exp-log
104×add-cube-cbrt *-un-lft-identity
94×cbrt-prod
51×associate-/r*
48×unpow-prod-down div-exp
45×associate-*l*
39×prod-exp add-cbrt-cube
22×cbrt-undiv
19×cbrt-unprod
10×pow1 unpow2 unswap-sqr sqr-pow
8×pow-to-exp pow-exp
6×log-prod
5×associate-*r* div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down
2×frac-2neg associate-*l/ clear-num *-commutative
1×associate-/r/ log-pow associate-/l/
Counts
4 → 291
Calls
4 calls:
20.0ms
(/ (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
14.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
6.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
6.0ms
(* (pow i 2) (log 1.0))

series711.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(/ (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n))) (/ (cbrt i) (cbrt n)))
165.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2)) (* (cbrt n) (cbrt n)))
204.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (pow (cbrt i) 2))
141.0ms
(* (pow i 2) (log 1.0))

simplify92.0ms

Algorithm
egg-herbie
Counts
303 → 303
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015136599
150015838

prune1.3s

Filtered
303 candidates to 225 candidates (74.3%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New2967303
Fresh31518
Picked101
Done011
Total30023323

Merged error: 10.7b

Counts
323 → 23

regimes433.0ms

Accuracy

66.2% (6.1b remaining)

Error of 16.6b against oracle of 10.5b and baseline of 28.7b

bsearch441.0ms

Steps
ItersRangePoint
10
6.590504763180255e+276
1.8061123366623828e+288
1.1844385083165567e+288
8
5.4299457571941195e+193
2.1453878748451765e+196
2.1137780374624336e+196
9
0.00615885028673163
18724.121991280714
11.046467195687415
9
-4.426567571666705e-08
-2.0731084483512764e-13
-4.3751650145781584e-08

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07273
17273

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.5s2980×body1280valid
2.0s979×body2560valid
690.0ms1728×body640valid
216.0ms881×body320valid
170.0ms2400×body80valid
98.0ms2266×body80nan
68.0ms434×body160valid
51.0ms12×body5120valid