Details

Time bar (total: 14.6s)

sample200.0ms

Algorithm
intervals
Results
76.0ms89×body1280valid
70.0ms31×body2560valid
24.0ms63×body640valid
7.0ms29×body320valid
6.0ms77×body80valid
3.0ms71×body80nan
1.0ms10×body160valid

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 47.0b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (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))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
33.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
16.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
385.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
261.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
228.0ms
(pow (+ 1.0 (/ i n)) n)
366.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify59.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012263285
150023166

prune730.0ms

Filtered
293 candidates to 223 candidates (76.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New28310293
Fresh000
Picked101
Done000
Total28410294

Merged error: 21.7b

Counts
294 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
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))

rewrite53.0ms

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 add-log-exp
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×unpow-prod-down cbrt-unprod
3×distribute-rgt-in distribute-lft-in sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 186
Calls
4 calls:
6.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
19.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
6.0ms
(* (pow i 2) (log 1.0))
13.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series660.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
256.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
160.0ms
(* (pow i 2) (log 1.0))
202.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify148.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09293604
148183341
250013341

prune668.0ms

Filtered
198 candidates to 150 candidates (75.8%)
Pruning

20 alts after pruning (20 fresh and 0 done)

PrunedKeptTotal
New18612198
Fresh189
Picked101
Done000
Total18820208

Merged error: 10.7b

Counts
208 → 20

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
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))
11.0b
(/ (- (+ (* 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))

rewrite42.0ms

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×unpow-prod-down pow-prod-down add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 117
Calls
4 calls:
11.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
11.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.0ms
(/ (- (+ (* 1.0 i) (+ (* 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))

series709.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
220.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
147.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms
(* (pow i 2) (log 1.0))

simplify85.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05291979
124351684
250011679

prune397.0ms

Filtered
129 candidates to 87 candidates (67.4%)
Pruning

20 alts after pruning (19 fresh and 1 done)

PrunedKeptTotal
New1290129
Fresh01919
Picked011
Done000
Total12920149

Merged error: 10.7b

Counts
149 → 20

localize29.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* (/ (- (+ (* 1.0 i) (+ (* 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
(* (/ (- (+ (* 1.0 i) (+ (* 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
(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite79.0ms

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×associate-/l* add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/l/
2×frac-2neg associate-*l/ clear-num *-commutative
1×flip3-- div-sub associate-/r/ log-pow flip--
Counts
4 → 286
Calls
4 calls:
25.0ms
(/ (* (/ (- (+ (* 1.0 i) (+ (* 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)))
19.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 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)))
14.0ms
(/ (- (+ (* 1.0 i) (+ (* 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))

series895.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(/ (* (/ (- (+ (* 1.0 i) (+ (* 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)))
159.0ms
(* (/ (- (+ (* 1.0 i) (+ (* 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)))
386.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (pow (cbrt i) 2))
144.0ms
(* (pow i 2) (log 1.0))

simplify87.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015817202
150016617

prune1.2s

Filtered
298 candidates to 217 candidates (72.8%)
Pruning

23 alts after pruning (22 fresh and 1 done)

PrunedKeptTotal
New2917298
Fresh31518
Picked101
Done011
Total29523318

Merged error: 10.7b

Counts
318 → 23

regimes430.0ms

Accuracy

66.3% (6.1b remaining)

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

bsearch472.0ms

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
08273
18273

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.6s2980×body1280valid
2.1s979×body2560valid
710.0ms1728×body640valid
225.0ms881×body320valid
184.0ms2400×body80valid
105.0ms2266×body80nan
70.0ms434×body160valid
51.0ms12×body5120valid