Details

Time bar (total: 10.5s)

sample47.0ms

Algorithm
intervals
Results
14.0ms56×body1280valid
10.0ms52×body640valid
6.0ms276×body80nan
5.0ms127×body80valid
1.0ms12×body320valid
1.0ms9×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(log (+ N 1.0))
2.8b
(- (log (+ N 1.0)) (log N))

rewrite12.0ms

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:
2.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

series134.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(log (+ N 1.0))
91.0ms
(- (log (+ N 1.0)) (log N))

simplify1.3s

Counts
71 → 71
Iterations

Useful iterations: 3 (484.0ms)

IterNodesCost
01271052
1277855
2715705
32303614
done5001614

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.6b
(log (+ 1.0 N))
2.6b
(log (+ N 1.0))
2.6b
(log (+ N 1.0))
2.7b
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
26×log-prod
21×*-un-lft-identity
11×add-sqr-sqrt add-cube-cbrt
8×associate--l+
7×pow1 add-exp-log distribute-rgt-in distribute-lft-in
6×log-div associate--r+ add-log-exp
5×distribute-lft-out
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-+ rem-log-exp log-pow flip-+
1×sub-neg flip3-- fma-neg diff-log prod-diff flip-- difference-of-squares
Counts
4 → 82
Calls
4 calls:
2.0ms
(log (+ 1.0 N))
2.0ms
(log (+ N 1.0))
2.0ms
(log (+ N 1.0))
8.0ms
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

series263.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(log (+ 1.0 N))
45.0ms
(log (+ N 1.0))
41.0ms
(log (+ N 1.0))
136.0ms
(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))

simplify1.7s

Counts
94 → 94
Iterations

Useful iterations: 3 (773.0ms)

IterNodesCost
01881317
14381217
212951094
344861065
done50001065

prune289.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.3b
(/ 0.5 (* N N))
10.8b
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
115×*-un-lft-identity
82×times-frac
60×add-sqr-sqrt
56×add-cube-cbrt
35×prod-diff
19×distribute-lft-out
14×add-exp-log
13×fma-def associate-/r*
12×unpow-prod-down cube-prod
11×add-cbrt-cube add-log-exp
8×div-inv
6×associate-/l*
5×fma-neg div-exp
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u sqr-pow
3×cbrt-undiv frac-sub
2×frac-2neg flip3-+ diff-log frac-add clear-num sum-log flip-+ distribute-lft-out-- difference-of-squares
1×+-commutative pow-to-exp sub-neg flip3-- pow-exp prod-exp associate--l+ flip-- cbrt-unprod
Counts
4 → 182
Calls
4 calls:
34.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
4.0ms
(/ 0.3333333333333333 (pow N 3))
3.0ms
(/ 0.5 (* N N))
353.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

series178.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3)))
35.0ms
(/ 0.3333333333333333 (pow N 3))
29.0ms
(/ 0.5 (* N N))
30.0ms
(- (+ (/ 1.0 N) (/ 0.3333333333333333 (pow N 3))) (/ 0.5 (* N N)))

simplify1.1s

Counts
194 → 194
Iterations

Useful iterations: 2 (475.0ms)

IterNodesCost
02643729
16133122
221452772
done50002772

prune349.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.3b
(/ 0.5 (* N N))
10.8b
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite247.0ms

Algorithm
rewrite-expression-head
Rules
843×times-frac
560×prod-diff
554×add-sqr-sqrt
537×*-un-lft-identity
528×add-cube-cbrt
282×associate-+r+
149×unpow-prod-down cube-prod
98×div-inv
51×sqr-pow
50×cube-mult
49×unpow3
40×fma-neg
14×add-exp-log
13×fma-def associate-/r*
11×add-cbrt-cube add-log-exp
10×difference-of-squares
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv frac-add distribute-lft-out--
2×sub-neg flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- distribute-lft-out
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 752
Calls
4 calls:
119.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
4.0ms
(/ 0.3333333333333333 (pow N 3))
3.0ms
(/ 0.5 (* N N))
54.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series187.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
40.0ms
(/ 0.3333333333333333 (pow N 3))
24.0ms
(/ 0.5 (* N N))
93.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify1.8s

Counts
764 → 764
Iterations

Useful iterations: 2 (1.1s)

IterNodesCost
068424628
1149519119
2347816816
done500016816

prune985.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.4b

bsearch27.0ms

Steps
ItersRangePoint
7
1766.3470775505596
94269.73169533648
3632.967761108044

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02338
12638
done2638

end0.0ms

sample1.3s

Algorithm
intervals
Results
430.0ms1744×body1280valid
196.0ms1269×body640valid
192.0ms8134×body80nan
170.0ms4056×body80valid
61.0ms613×body320valid
20.0ms318×body160valid