Details

Time bar (total: 21.7s)

sample89.0ms

Algorithm
intervals
Results
22.0ms48×body1280valid
15.0ms54×body640valid
14.0ms286×body80nan
10.0ms122×body80valid
4.0ms20×body320valid
1.0ms12×body160valid

simplify25.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize20.0ms

Local error

Found 2 expressions with local error:

2.7b
(- (log (+ N 1.0)) (log N))
2.9b
(log (+ N 1.0))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
26.0ms
(- (log (+ N 1.0)) (log N))
8.0ms
(log (+ N 1.0))

series268.0ms

Counts
2 → 6
Calls
2 calls:
183.0ms
(- (log (+ N 1.0)) (log N))
85.0ms
(log (+ N 1.0))

simplify1.7s

Counts
71 → 71
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01271052
1288863
21086705
done5001614

prune403.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 N) (/ 0.5 (* N N)))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.4b
(/ 0.5 (* N N))
13.0b
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite404.0ms

Algorithm
rewrite-expression-head
Rules
292×times-frac
220×add-sqr-sqrt
217×*-un-lft-identity
210×add-cube-cbrt
182×prod-diff
93×associate-+r+
44×div-inv
40×fma-def
21×unpow-prod-down cube-prod
14×add-exp-log
13×fma-neg associate-/r*
11×add-cbrt-cube add-log-exp
7×cube-mult unpow3 sqr-pow
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×cbrt-undiv frac-add
2×sub-neg flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- distribute-lft-out distribute-lft-out--
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 367
Calls
4 calls:
73.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
25.0ms
(/ 0.3333333333333333 (pow N 3))
18.0ms
(/ 0.5 (* N N))
242.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series363.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
91.0ms
(/ 0.3333333333333333 (pow N 3))
51.0ms
(/ 0.5 (* N N))
74.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify1.1s

Counts
379 → 379
Iterations

Useful iterations: done (1.1s)

IterNodesCost
04448644
110617221
done50016378

prune2.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (pow (log (+ N 1.0)) 3))
0.4b
(pow (log (+ N 1.0)) 3)
2.7b
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
2.9b
(log (+ N 1.0))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
88×cbrt-prod
68×prod-diff
58×add-sqr-sqrt
54×*-un-lft-identity
49×add-cube-cbrt
38×pow1
33×log-pow
29×unpow-prod-down cube-prod
17×fma-neg
8×sqr-pow
7×cube-mult log-prod unpow3
6×add-exp-log
5×add-cbrt-cube add-log-exp difference-of-squares
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate--r+
2×log-div distribute-lft-out--
1×pow-to-exp sub-neg flip3-- pow-pow flip3-+ pow1/3 diff-log rem-log-exp pow-exp flip-- rem-cbrt-cube flip-+ distribute-lft-out rem-cube-cbrt
Counts
4 → 178
Calls
4 calls:
6.0ms
(cbrt (pow (log (+ N 1.0)) 3))
7.0ms
(pow (log (+ N 1.0)) 3)
90.0ms
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
11.0ms
(log (+ N 1.0))

series515.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(cbrt (pow (log (+ N 1.0)) 3))
180.0ms
(pow (log (+ N 1.0)) 3)
187.0ms
(- (cbrt (pow (log (+ N 1.0)) 3)) (log N))
75.0ms
(log (+ N 1.0))

simplify3.8s

Counts
190 → 190
Iterations

Useful iterations: done (3.7s)

IterNodesCost
02604129
17042635
237422047
done50002042

prune740.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize38.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 0.3333333333333333 (pow N 3))
13.0b
(+ (/ 0.3333333333333333 (pow N 3)) (/ (* N (- (* 1.0 N) 0.5)) (pow N 3)))
24.4b
(/ (* N (- (* 1.0 N) 0.5)) (pow N 3))

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
58×*-un-lft-identity
56×add-sqr-sqrt add-cube-cbrt
40×fma-def
27×unpow-prod-down cube-prod
24×associate-/r*
21×add-exp-log
10×add-cbrt-cube
9×cube-mult unpow3 div-exp sqr-pow
5×div-inv add-log-exp
4×associate-/l*
3×pow1 cbrt-undiv expm1-log1p-u pow-to-exp pow-exp prod-exp log1p-expm1-u
2×frac-2neg associate-*r/ clear-num associate-/l/
1×+-commutative distribute-rgt-out flip3-- flip3-+ frac-add sum-log flip-- cbrt-unprod flip-+ distribute-lft-out
Counts
3 → 170
Calls
3 calls:
16.0ms
(/ 0.3333333333333333 (pow N 3))
126.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (* N (- (* 1.0 N) 0.5)) (pow N 3)))
55.0ms
(/ (* N (- (* 1.0 N) 0.5)) (pow N 3))

series288.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ 0.3333333333333333 (pow N 3))
63.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (/ (* N (- (* 1.0 N) 0.5)) (pow N 3)))
153.0ms
(/ (* N (- (* 1.0 N) 0.5)) (pow N 3))

simplify4.6s

Counts
179 → 179
Iterations

Useful iterations: done (4.6s)

IterNodesCost
01981951
15201664
237761547
done50011533

prune883.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes65.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.3b

bsearch65.0ms

Steps
ItersRangePoint
9
0.5323112742081106
59347805.45921656
4627.670043607516

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02129
12329
done2329

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.2s1813×body1280valid
549.0ms7916×body80nan
524.0ms4039×body80valid
480.0ms1221×body640valid
140.0ms611×body320valid
45.0ms316×body160valid