Details

Time bar (total: 14.5s)

sample179.0ms

Algorithm
intervals
Results
69.0ms96×body1280valid
65.0ms32×body2560valid
17.0ms50×body640valid
5.0ms30×body320valid
5.0ms81×body80valid
3.0ms74×body80nan
2.0ms14×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1597
21417
33467
411717
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: 47.7b

Counts
2 → 1

localize9.0ms

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)
4.4b
(pow (+ 1.0 (/ i n)) n)
11.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
329×times-frac
306×add-sqr-sqrt
215×*-un-lft-identity
152×add-cube-cbrt
104×associate-*r*
87×difference-of-squares
33×unpow-prod-down
32×associate-/r*
30×distribute-lft-out-- sqr-pow
25×associate-*r/
22×associate-/l*
19×add-exp-log
18×associate-/r/ add-cbrt-cube div-inv
7×pow1
6×cbrt-undiv div-exp add-log-exp
5×clear-num
4×frac-2neg associate-/l/
3×pow-unpow flip3-- associate-*l* prod-exp un-div-inv flip-- cbrt-unprod unswap-sqr
1×pow-to-exp sub-neg pow-pow diff-log div-sub pow-prod-down pow-exp *-commutative distribute-lft-out
Counts
4 → 324
Calls
4 calls:
37.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms
(pow (+ 1.0 (/ i n)) n)
21.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
372.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
268.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
226.0ms
(pow (+ 1.0 (/ i n)) n)
379.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify78.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
013313564
150023443

prune695.0ms

Filtered
336 candidates to 254 candidates (75.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3297336
Fresh000
Picked101
Done000
Total3307337

Merged error: 22.9b

Counts
337 → 7

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 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
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
3623×*-un-lft-identity
1737×times-frac
1664×associate-*l*
1508×distribute-lft-out
1153×add-sqr-sqrt
870×distribute-lft-out--
606×add-cube-cbrt
524×associate-*r*
259×unswap-sqr
240×pow1
233×log-pow
168×difference-of-squares
115×associate-/l*
82×div-inv
57×associate-*r/
32×unpow-prod-down associate-/r* un-div-inv
30×unpow2 sqr-pow
22×add-exp-log
19×add-cbrt-cube
18×log-prod associate-/r/
15×distribute-rgt-in distribute-lft-in
13×div-sub
12×associate--r+
6×cbrt-undiv div-exp prod-exp
5×clear-num
4×frac-2neg cbrt-unprod associate-/l/
3×add-log-exp
2×flip3-- pow-prod-down *-commutative flip--
1×pow-to-exp pow-exp
Counts
3 → 1262
Calls
3 calls:
369.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
7.0ms
(* (pow i 2) (log 1.0))
85.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series544.0ms

Counts
3 → 9
Calls
3 calls:
219.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
133.0ms
(* (pow i 2) (log 1.0))
192.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify229.0ms

Algorithm
egg-herbie
Counts
1271 → 1271
Iterations

Useful iterations: 1 (50.0ms)

IterNodesCost
0196517600
1500217281

prune1.3s

Filtered
1271 candidates to 305 candidates (24.0%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New1260111271
Fresh066
Picked101
Done000
Total1261171278

Merged error: 10.6b

Counts
1278 → 17

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* (/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
11.1b
(/ (* 100.0 (- (+ (* 1.0 i) (+ (* 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))

rewrite316.0ms

Algorithm
rewrite-expression-head
Rules
1071×*-un-lft-identity
696×associate-*l*
468×distribute-lft-out
358×associate-*r*
339×add-sqr-sqrt
290×times-frac
270×distribute-lft-out--
135×add-cube-cbrt
98×unswap-sqr
96×associate-/l*
83×pow1
73×log-pow
56×associate-*l/
54×difference-of-squares
25×add-exp-log
22×add-cbrt-cube
13×unpow-prod-down
11×*-commutative unpow2 sqr-pow
9×distribute-rgt-in distribute-lft-in prod-exp
8×associate--l+
7×cbrt-unprod
6×log-prod associate-*r/ associate-/r*
4×cbrt-undiv +-commutative associate-+r+ div-exp associate-/l/ add-log-exp
3×flip3-- pow-prod-down flip--
2×sub-neg frac-2neg clear-num div-inv
1×pow-to-exp pow-exp
Counts
4 → 539
Calls
4 calls:
69.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
102.0ms
(* (/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
81.0ms
(/ (* 100.0 (- (+ (* 1.0 i) (+ (* 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))

series642.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
222.0ms
(* (/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
158.0ms
(/ (* 100.0 (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
136.0ms
(* (pow i 2) (log 1.0))

simplify115.0ms

Algorithm
egg-herbie
Counts
551 → 551
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
011608010
150027434

prune828.0ms

Filtered
551 candidates to 216 candidates (39.2%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New5465551
Fresh21416
Picked101
Done000
Total54919568

Merged error: 10.6b

Counts
568 → 19

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2))))
0.1b
(* (/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i) n)
11.1b
(/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i)
11.6b
(* (log 1.0) (- n (* 0.5 (pow i 2))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
278×associate-*l*
237×*-un-lft-identity
109×times-frac
108×distribute-lft-out
77×add-sqr-sqrt
56×add-cube-cbrt
46×associate-*l/
43×*-commutative
36×associate-/l*
33×associate-*r*
27×pow1
20×associate-*r/
18×distribute-rgt-out
17×log-pow
15×add-exp-log add-cbrt-cube
12×associate-/l/
8×frac-add unswap-sqr
7×flip3-+ flip-+
6×associate-/r*
5×flip3-- flip-- difference-of-squares
4×distribute-rgt-in distribute-lft-in prod-exp cbrt-unprod add-log-exp
3×pow-prod-down unpow2
2×cbrt-undiv +-commutative sub-neg frac-2neg div-exp clear-num div-inv distribute-lft-out--
1×unpow-prod-down sqr-pow
Counts
4 → 261
Calls
4 calls:
20.0ms
(* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2))))
91.0ms
(* (/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i) n)
81.0ms
(/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i)
13.0ms
(* (log 1.0) (- n (* 0.5 (pow i 2))))

series646.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2))))
225.0ms
(* (/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i) n)
154.0ms
(/ (+ (* 100.0 (+ (* 1.0 i) (* 0.5 (pow i 2)))) (* (* (* (log 1.0) (- n (* 0.5 (pow i 2)))) 1) 100.0)) i)
171.0ms
(* (log 1.0) (- n (* 0.5 (pow i 2))))

simplify178.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 2 (134.0ms)

IterNodesCost
08763661
147083354
250033344

prune426.0ms

Filtered
273 candidates to 123 candidates (45.1%)
Pruning

19 alts after pruning (18 fresh and 1 done)

PrunedKeptTotal
New2703273
Fresh31518
Picked011
Done000
Total27319292

Merged error: 10.6b

Counts
292 → 19

regimes446.0ms

Accuracy

64.3% (6.4b remaining)

Error of 17.6b against oracle of 11.1b and baseline of 29.1b

bsearch444.0ms

Steps
ItersRangePoint
8
1.1041122235818434e+43
1.550445775864617e+46
1.1157873681258683e+43
8
-5.836795344528573e-218
-5.275162429883666e-221
-1.0328055327868427e-218
9
-0.05767290693153419
-6.132196241634436e-08
-0.001601341064536709

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09184
19784
210484
310684
410684

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.1s2929×body1280valid
1.8s944×body2560valid
563.0ms1805×body640valid
158.0ms894×body320valid
119.0ms2410×body80valid
82.0ms2268×body80nan
50.0ms476×body160valid
27.0ms7×body5120valid