Details

Time bar (total: 13.1s)

sample208.0ms

Algorithm
intervals
Results
87.0ms39×body2560valid
70.0ms82×body1280valid
20.0ms55×body640valid
7.0ms93×body80valid
5.0ms20×body320valid
4.0ms73×body80nan
3.0ms20×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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.9b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b
(pow (+ 1.0 (/ i n)) n)
9.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite89.0ms

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:
35.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms
(- (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))

series1.2s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
218.0ms
(pow (+ 1.0 (/ i n)) n)
351.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify69.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune797.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New32211333
Fresh000
Picked101
Done000
Total32311334

Merged error: 21.3b

Counts
334 → 11

localize20.0ms

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))
19.1b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite36.0ms

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)))))
14.0ms
(* 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))

series649.0ms

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)))))
218.0ms
(* 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)))
138.0ms
(* (pow i 2) (log 1.0))
196.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify119.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07343209
137502968
250012968

prune722.0ms

Filtered
198 candidates to 152 candidates (76.8%)
Pruning

23 alts after pruning (23 fresh and 0 done)

PrunedKeptTotal
New18513198
Fresh01010
Picked101
Done000
Total18623209

Merged error: 10.9b

Counts
209 → 23

localize16.0ms

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)
7.0ms
(* (pow i 2) (log 1.0))

series701.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
216.0ms
(* 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))
142.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms
(* (pow i 2) (log 1.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04761783
120111521
250011513

prune423.0ms

Filtered
134 candidates to 92 candidates (68.7%)
Pruning

22 alts after pruning (21 fresh and 1 done)

PrunedKeptTotal
New1331134
Fresh22022
Picked011
Done000
Total13522157

Merged error: 10.9b

Counts
157 → 22

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
2.9b
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
11.6b
(* (pow i 2) (log 1.0))
12.5b
(/ (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)) i)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity associate-*l*
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod
5×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 times-frac div-exp associate-/r* *-commutative
2×unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 101
Calls
4 calls:
5.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
4.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
6.0ms
(* (pow i 2) (log 1.0))
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))))) n)) i)

series664.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n))
151.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
140.0ms
(* (pow i 2) (log 1.0))
216.0ms
(/ (* 100.0 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)) i)

simplify73.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
04401426
121411157
250021157

prune285.0ms

Filtered
113 candidates to 73 candidates (64.6%)
Pruning

21 alts after pruning (19 fresh and 2 done)

PrunedKeptTotal
New1103113
Fresh41620
Picked011
Done011
Total11421135

Merged error: 10.9b

Counts
135 → 21

regimes361.0ms

Accuracy

69.1% (5.6b remaining)

Error of 16.1b against oracle of 10.5b and baseline of 28.8b

bsearch241.0ms

Steps
ItersRangePoint
7
0.00022027325057658872
0.008784522488119305
0.005619708242321016
10
-18784469646.78796
-0.08793709934347878
-0.21878848523850206

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05947
15947

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.5s2886×body1280valid
2.1s1003×body2560valid
747.0ms1746×body640valid
235.0ms908×body320valid
188.0ms2475×body80valid
103.0ms2304×body80nan
70.0ms436×body160valid
11.0ms3×body5120valid

Profiling

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