Details

Time bar (total: 5.4s)

sample44.0ms

Algorithm
intervals
Results
14.0ms57×body1280valid
6.0ms43×body640valid
6.0ms245×body80nan
5.0ms121×body80valid
3.0ms26×body320valid
1.0ms9×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (log (+ N 1.0)) (log N))
4.0b
(log (+ N 1.0))

rewrite13.0ms

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:
8.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series133.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(- (log (+ N 1.0)) (log N))
43.0ms
(log (+ N 1.0))

simplify127.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (120.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune128.0ms

Filtered
71 candidates to 43 candidates (60.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.1b
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.7b
(/ 1 (pow N 2))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
242×add-sqr-sqrt
222×*-un-lft-identity
214×add-cube-cbrt
202×times-frac
195×prod-diff
82×distribute-rgt-in associate-+l+ distribute-lft-in
33×add-exp-log
28×associate-*l*
23×unpow-prod-down
18×div-inv
13×fma-neg
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r* add-log-exp
6×pow1 pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×sub-neg flip3-- frac-add flip--
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u difference-of-squares
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod distribute-lft-out--
1×+-commutative pow-flip fma-def frac-2neg flip3-+ diff-log pow-prod-down clear-num sum-log *-commutative flip-+ inv-pow
Counts
4 → 382
Calls
4 calls:
33.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
14.0ms
(- (/ 0.3333333333333333 N) 0.5)
54.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms
(/ 1 (pow N 2))

series158.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
33.0ms
(- (/ 0.3333333333333333 N) 0.5)
73.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
21.0ms
(/ 1 (pow N 2))

simplify129.0ms

Algorithm
egg-herbie
Counts
394 → 394
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010364191
145582787
250012787

prune758.0ms

Filtered
394 candidates to 223 candidates (56.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1 (pow N 2))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
21×cbrt-div
15×frac-add
13×add-exp-log
12×unpow-prod-down
9×cbrt-prod
8×associate-/r*
6×frac-times flip3-- associate-*r/ div-exp add-cbrt-cube flip--
4×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×pow-to-exp rec-exp flip3-+ pow1/3 1-exp associate-*l/ pow-exp flip-+ associate-/l*
1×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
Counts
4 → 119
Calls
4 calls:
4.0ms
(/ 1 (pow N 2))
16.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
19.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
17.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
151.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
150.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
153.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify69.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05351600
121751494
250011430

prune377.0ms

Filtered
131 candidates to 90 candidates (68.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

4.2b
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
13.5b
(fma 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)) (- (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (fma 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N)))))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
18.3b
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-div
10×frac-add
6×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×pow1 add-exp-log expm1-log1p-u frac-times flip3-- associate-*r/ add-cbrt-cube flip-- log1p-expm1-u
2×flip3-+ pow1/3 exp-sum associate-*l/ flip-+
1×distribute-rgt-in exp-prod exp-to-pow distribute-lft-in fma-udef rem-exp-log
Counts
4 → 64
Calls
4 calls:
2.0ms
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
0.0ms
(fma 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)) (- (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (fma 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N)))))
17.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
20.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

series804.0ms

Counts
4 → 12
Calls
4 calls:
304.0ms
(exp (* 1/3 (+ (log 1.0) (log (/ 1 N)))))
191.0ms
(fma 0.125 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (pow N 2)) (- (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (fma 0.041666666666666664 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) (* (pow N 2) (pow 1.0 2))) (* 0.16666666666666666 (/ (exp (* 1/3 (+ (log 1.0) (log (/ 1 N))))) N)))))
156.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))
153.0ms
(cbrt (+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N)))

simplify57.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
05041511
118681363
250011330

prune534.0ms

Filtered
76 candidates to 68 candidates (89.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

regimes30.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.6b

bsearch30.0ms

Steps
ItersRangePoint
7
481.02071266823316
19555.519105776155
8616.086423541381

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.3s

Algorithm
intervals
Results
428.0ms1753×body1280valid
193.0ms8037×body80nan
188.0ms1238×body640valid
171.0ms4084×body80valid
66.0ms625×body320valid
18.0ms300×body160valid