Details

Time bar (total: 6.0s)

sample42.0ms

Algorithm
intervals
Results
14.0ms58×body1280valid
6.0ms284×body80nan
6.0ms136×body80valid
5.0ms38×body640valid
2.0ms17×body320valid
0.0ms7×body160valid

simplify10.0ms

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: 28.5b

localize7.0ms

Local error

Found 2 expressions with local error:

2.7b
(log (+ N 1.0))
3.0b
(- (log (+ N 1.0)) (log N))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
5×add-cube-cbrt log-pow
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
3.0ms
(log (+ N 1.0))
6.0ms
(- (log (+ N 1.0)) (log N))

series143.0ms

Counts
2 → 6
Calls
2 calls:
42.0ms
(log (+ N 1.0))
101.0ms
(- (log (+ N 1.0)) (log N))

simplify59.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (49.0ms)

IterNodesCost
0212281
1547264
21875250
35001247

prune98.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b
(log (/ (+ N 1.0) N))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
16×log-prod
15×*-un-lft-identity
12×times-frac
9×add-sqr-sqrt add-cube-cbrt
4×add-exp-log
3×distribute-lft-out
2×pow1 rem-log-exp
1×log-div div-exp log-pow add-cbrt-cube div-inv add-log-exp
Counts
1 → 27
Calls
1 calls:
3.0ms
(log (/ (+ N 1.0) N))

series92.0ms

Counts
1 → 3
Calls
1 calls:
92.0ms
(log (/ (+ N 1.0) N))

simplify57.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (13.0ms)

IterNodesCost
0167209
1455196
21964184
35002184

prune55.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.3b
(/ (cbrt (+ N 1.0)) (sqrt N))
0.3b
(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
2.9b
(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
120×*-un-lft-identity
96×times-frac
84×add-sqr-sqrt
76×cbrt-prod add-cube-cbrt
56×log-prod
54×sqrt-prod
46×associate-+r+
26×cbrt-div
23×distribute-lft-out
15×pow1
14×flip3-+ flip-+
13×add-exp-log
12×associate-/r*
10×associate-+l+ associate-/l/
9×swap-sqr
8×frac-times add-cbrt-cube associate-/l*
7×associate-*r* associate-*l*
6×pow1/3
4×associate-*r/ associate-*l/ log-pow div-inv add-log-exp unswap-sqr
3×cbrt-undiv div-exp
2×log-div frac-2neg pow-prod-down prod-exp clear-num pow-sqr pow-prod-up cbrt-unprod
1×+-commutative pow2 associate-+l- associate-+r- pow-plus sum-log *-commutative
Counts
4 → 230
Calls
4 calls:
19.0ms
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
9.0ms
(/ (cbrt (+ N 1.0)) (sqrt N))
10.0ms
(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
56.0ms
(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

series1.2s

Counts
4 → 12
Calls
4 calls:
113.0ms
(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
202.0ms
(/ (cbrt (+ N 1.0)) (sqrt N))
243.0ms
(/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))
595.0ms
(+ (log (/ (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (sqrt N))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

simplify102.0ms

Algorithm
egg-herbie
Counts
242 → 242
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
09532748
139542494
250012380

prune658.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
2.9b
(log (/ (cbrt (+ N 1.0)) (sqrt (* (cbrt N) (cbrt N)))))
3.0b
(+ (log (/ (cbrt (+ N 1.0)) (sqrt (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
145×log-prod
133×times-frac
131×*-un-lft-identity
103×cbrt-prod
89×add-sqr-sqrt add-cube-cbrt
70×sqrt-prod
67×associate-+l+
46×associate-+r+
23×distribute-lft-out
9×pow1
7×add-exp-log
5×log-pow
4×add-cbrt-cube add-log-exp
3×log-div div-inv
2×pow1/3 rem-log-exp
1×+-commutative associate-+l- associate-+r- flip3-+ div-exp sum-log flip-+
Counts
4 → 195
Calls
4 calls:
0.0ms
(cbrt N)
0.0ms
(cbrt N)
7.0ms
(log (/ (cbrt (+ N 1.0)) (sqrt (* (cbrt N) (cbrt N)))))
24.0ms
(+ (log (/ (cbrt (+ N 1.0)) (sqrt (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

series1.1s

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt N)
191.0ms
(cbrt N)
227.0ms
(log (/ (cbrt (+ N 1.0)) (sqrt (* (cbrt N) (cbrt N)))))
451.0ms
(+ (log (/ (cbrt (+ N 1.0)) (sqrt (cbrt N)))) (log (/ (cbrt (+ N 1.0)) (sqrt N))))

simplify70.0ms

Algorithm
egg-herbie
Counts
207 → 207
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
08172681
124682599
250012576

prune900.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes37.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch36.0ms

Steps
ItersRangePoint
7
3268.458992709865
89650.56729712563
5113.255823203994

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04730
14730

end0.0ms

sample1.2s

Algorithm
intervals
Results
417.0ms1743×body1280valid
186.0ms1273×body640valid
177.0ms8040×body80nan
164.0ms4090×body80valid
55.0ms590×body320valid
18.0ms304×body160valid