Details

Time bar (total: 3.3s)

sample41.0ms

Algorithm
intervals
Results
11.0ms45×body1280valid
7.0ms45×body640valid
6.0ms140×body80valid
6.0ms275×body80nan
1.0ms13×body320valid
1.0ms13×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

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))

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))

series133.0ms

Counts
2 → 6
Calls
2 calls:
40.0ms
(log (+ N 1.0))
93.0ms
(- (log (+ N 1.0)) (log N))

simplify123.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001343

prune123.0ms

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))

series125.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (+ N 1.0) N)
79.0ms
(log (/ (+ N 1.0) N))

simplify101.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (95.0ms)

IterNodesCost
0243383
1808358
23663347
35001344

prune114.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.3b
(/ 1 (pow N 2))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
11×add-exp-log
8×associate-/r*
6×div-exp
4×add-cbrt-cube unpow2 sqr-pow
3×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv pow-flip frac-2neg clear-num fma-udef div-inv inv-pow
Counts
2 → 69
Calls
2 calls:
0.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms
(/ 1 (pow N 2))

series50.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
15.0ms
(/ 1 (pow N 2))

simplify32.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0208384
1789315
25001269

prune98.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))) (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
23.1b
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
23.1b
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
23.1b
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
5.0ms
(* (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))) (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
0.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
0.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
1.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

series604.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))) (cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))))
152.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
152.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))
152.0ms
(cbrt (fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N)))

simplify48.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03701581
112781469
250021258

prune284.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

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

bsearch31.0ms

Steps
ItersRangePoint
10
0.0005333266348582408
117627206.70733242
10132.834563235498

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219
1219

end0.0ms

sample1.2s

Algorithm
intervals
Results
429.0ms1761×body1280valid
188.0ms1221×body640valid
178.0ms7968×body80nan
174.0ms4126×body80valid
59.0ms596×body320valid
18.0ms296×body160valid