Details

Time bar (total: 9.6s)

sample43.0ms

Algorithm
intervals
Results
11.0ms45×body1280valid
7.0ms45×body640valid
6.0ms275×body80nan
6.0ms140×body80valid
1.0ms13×body320valid
1.0ms13×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: 27.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b
(log (+ N 1.0))
3.7b
(- (log (+ N 1.0)) (log N))

rewrite15.0ms

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))
8.0ms
(- (log (+ N 1.0)) (log N))

series133.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(log (+ N 1.0))
92.0ms
(- (log (+ N 1.0)) (log N))

simplify1.5s

Counts
71 → 71
Iterations

Useful iterations: 3 (410.0ms)

IterNodesCost
01271052
1273855
2737705
33055614
done5001614

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.6b
(log (/ (+ N 1.0) N))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×expm1-log1p-u div-exp rem-log-exp log1p-expm1-u div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 64
Calls
2 calls:
8.0ms
(/ (+ N 1.0) N)
3.0ms
(log (/ (+ N 1.0) N))

series129.0ms

Counts
2 → 6
Calls
2 calls:
48.0ms
(/ (+ N 1.0) N)
81.0ms
(log (/ (+ N 1.0) N))

simplify1.4s

Counts
70 → 70
Iterations

Useful iterations: 3 (571.0ms)

IterNodesCost
0112749
1240708
2667660
33011647
done5000647

prune115.0ms

Pruning

2 alts after pruning (1 fresh and 1 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))))
0.3b
(/ 0.5 (* N N))
0.5b
(/ 0.3333333333333333 (pow N 3))
14.0b
(- (/ 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:
124.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
55.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series185.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (/ 1.0 N) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
24.0ms
(/ 0.5 (* N N))
38.0ms
(/ 0.3333333333333333 (pow N 3))
93.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify1.4s

Counts
764 → 764
Iterations

Useful iterations: 2 (669.0ms)

IterNodesCost
068424628
1138319119
2387216216
done500016216

prune928.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (/ 1 (sqrt N)) (/ 1.0 (sqrt N)) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
0.3b
(/ 0.5 (* N N))
0.5b
(/ 0.3333333333333333 (pow N 3))
14.0b
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
462×times-frac
313×add-sqr-sqrt
291×*-un-lft-identity
287×add-cube-cbrt
280×prod-diff
86×unpow-prod-down cube-prod
50×div-inv
40×fma-neg
30×sqr-pow
29×cube-mult
28×unpow3
14×add-exp-log
13×associate-/r*
11×add-cbrt-cube
10×difference-of-squares
6×associate-/l* add-log-exp
5×div-exp
4×pow1 expm1-log1p-u log1p-expm1-u
3×cbrt-undiv
2×frac-2neg clear-num distribute-lft-out--
1×pow-to-exp sub-neg flip3-- diff-log pow-exp prod-exp frac-sub flip-- cbrt-unprod fma-udef
Counts
4 → 447
Calls
4 calls:
0.0ms
(fma (/ 1 (sqrt N)) (/ 1.0 (sqrt N)) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
3.0ms
(/ 0.5 (* N N))
4.0ms
(/ 0.3333333333333333 (pow N 3))
55.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

series264.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(fma (/ 1 (sqrt N)) (/ 1.0 (sqrt N)) (- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N))))
24.0ms
(/ 0.5 (* N N))
37.0ms
(/ 0.3333333333333333 (pow N 3))
92.0ms
(- (/ 0.3333333333333333 (pow N 3)) (/ 0.5 (* N N)))

simplify1.0s

Counts
459 → 459
Iterations

Useful iterations: done (987.0ms)

IterNodesCost
045915786
188812075
2290610451
done500110404

prune559.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes21.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.0b

bsearch32.0ms

Steps
ItersRangePoint
10
0.0005333266348582408
117627206.70733242
10132.834563235498

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01825
12025
done2025

end0.0ms

sample1.3s

Algorithm
intervals
Results
444.0ms1761×body1280valid
192.0ms1221×body640valid
188.0ms7968×body80nan
178.0ms4126×body80valid
64.0ms596×body320valid
23.0ms296×body160valid