Details

Time bar (total: 10.6s)

sample199.0ms

Algorithm
intervals
Results
73.0ms80×body1280valid
64.0ms31×body2560valid
27.0ms66×body640valid
8.0ms28×body320valid
6.0ms79×body80valid
3.0ms23×body160valid
3.0ms63×body80nan

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0528115

prune9.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 45.6b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
0.0b
(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.7b
(pow (+ 1.0 (/ i n)) n)

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
26×associate-*r*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×associate-*l* add-log-exp
5×sqr-pow
4×pow-prod-down distribute-lft-out--
3×pow-unpow associate-*r/
2×cbrt-undiv div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
15.0ms
(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
17.0ms
(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
10.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)

series195.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* 100.0 (* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)))
56.0ms
(* n (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
32.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
27.0ms
(pow (+ 1.0 (/ i n)) n)

simplify64.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
049872283
149872283

prune332.0ms

Filtered
82 candidates to 111 candidates (-35.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1029111
Fresh101
Picked101
Done000
Total1049113

Merged error: 9.5b

Counts
113 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
0.1b
(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
10.6b
(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
11.1b
(* (* i i) (* 0.5 (log 1.0)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
23×pow1
19×times-frac
15×associate-*r* prod-exp cbrt-unprod
12×distribute-rgt-in log-prod distribute-lft-in pow-prod-down
7×associate-*l*
4×add-log-exp
3×cbrt-undiv associate-*r/ div-exp associate-/r* *-commutative associate-/l*
2×associate-+r- div-inv associate-/l/ unswap-sqr
1×frac-2neg flip3-+ div-sub clear-num flip-+
Counts
4 → 117
Calls
4 calls:
14.0ms
(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
14.0ms
(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
21.0ms
(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
14.0ms
(* (* i i) (* 0.5 (log 1.0)))

series79.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i))
26.0ms
(* 100.0 (* n (/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)))
14.0ms
(/ (+ (* 1.0 i) (+ (* n (log 1.0)) (- (* i (* i 0.5)) (* (* i i) (* 0.5 (log 1.0)))))) i)
13.0ms
(* (* i i) (* 0.5 (log 1.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
050882897

prune322.0ms

Filtered
84 candidates to 129 candidates (-53.6%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1218129
Fresh088
Picked101
Done000
Total12216138

Merged error: 9.5b

Counts
138 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
10.6b
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.6b
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.6b
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
35×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-prod
10×add-exp-log add-cbrt-cube
9×associate-/r* associate-/l*
6×associate-/l/
4×pow1 div-inv add-log-exp
3×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+
1×cbrt-div pow1/3
Counts
4 → 109
Calls
4 calls:
6.0ms
(cbrt (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
10.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series110.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(cbrt (/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
17.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
14.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
14.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify121.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (100.0ms)

IterNodesCost
051033424

prune828.0ms

Filtered
104 candidates to 121 candidates (-16.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1201121
Fresh01515
Picked101
Done000
Total12116137

Merged error: 9.5b

Counts
137 → 16

localize30.0ms

Local error

Found 4 expressions with local error:

10.6b
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.6b
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
10.6b
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
10.6b
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
12×add-exp-log associate-/r* add-cbrt-cube associate-/l*
8×associate-/l/
4×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
4 → 116
Calls
4 calls:
10.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
9.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
7.0ms
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
8.0ms
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

series77.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
15.0ms
(/ (+ (* i 1.0) (+ (* (log 1.0) n) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
23.0ms
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)
22.0ms
(/ (+ (* (log 1.0) n) (* i (+ 1.0 (* i (- 0.5 (* (log 1.0) 0.5)))))) i)

simplify77.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
053543418

prune1.0s

Filtered
104 candidates to 128 candidates (-23.1%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New1280128
Fresh01515
Picked011
Done000
Total12816144

Merged error: 9.5b

Counts
144 → 16

regimes368.0ms

Accuracy

67.8% (6.5b remaining)

Error of 15.8b against oracle of 9.3b and baseline of 29.4b

bsearch172.0ms

Steps
ItersRangePoint
8
1.0246170479537303e-11
1.3927731282034702e-07
3.6906872116354498e-09
8
-12322.514085840688
-0.2101619750885166
-0.409830999825773

simplify8.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
0498364
1498364

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.5s2974×body1280valid
2.0s963×body2560valid
715.0ms1761×body640valid
222.0ms849×body320valid
174.0ms2438×body80valid
94.0ms2182×body80nan
70.0ms445×body160valid
35.0ms9×body5120valid

Profiling

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