Details

Time bar (total: 5.4s)

sample43.0ms

Algorithm
intervals
Results
14.0ms63×body1280valid
6.0ms39×body640valid
6.0ms264×body80nan
5.0ms130×body80valid
1.0ms15×body320valid
1.0ms9×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: 29.6b

localize6.0ms

Local error

Found 2 expressions with local error:

2.4b
(- (log (+ N 1.0)) (log N))
3.2b
(log (+ N 1.0))

rewrite23.0ms

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:
16.0ms
(- (log (+ N 1.0)) (log N))
4.0ms
(log (+ N 1.0))

series130.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(- (log (+ N 1.0)) (log N))
40.0ms
(log (+ N 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune127.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
2.5b
(log (/ (+ N 1.0) N))

rewrite25.0ms

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:
17.0ms
(/ (+ N 1.0) N)
6.0ms
(log (/ (+ N 1.0) N))

series131.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (+ N 1.0) N)
82.0ms
(log (/ (+ N 1.0) N))

simplify104.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (99.0ms)

IterNodesCost
0243383
1808358
23663347
35001344

prune114.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
2.5b
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
2.5b
(log (/ (cbrt (+ N 1.0)) (cbrt N)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
96×cbrt-prod
92×log-prod
84×*-un-lft-identity times-frac
60×add-sqr-sqrt add-cube-cbrt
12×distribute-lft-out
10×add-exp-log
6×pow1
4×expm1-log1p-u rem-log-exp add-cbrt-cube log1p-expm1-u add-log-exp
2×log-div pow1/3 div-exp log-pow div-inv
Counts
4 → 144
Calls
4 calls:
1.0ms
(cbrt N)
1.0ms
(cbrt N)
8.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
8.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))

series755.0ms

Counts
4 → 12
Calls
4 calls:
169.0ms
(cbrt N)
171.0ms
(cbrt N)
207.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
207.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))

simplify39.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
03471510
110271458
250021418

prune461.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
2.5b
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
6.5b
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))
6.5b
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
240×cbrt-prod
234×log-prod
222×times-frac
196×*-un-lft-identity
186×sqrt-prod
148×add-sqr-sqrt add-cube-cbrt
24×distribute-lft-out
13×add-exp-log
7×pow1
6×rem-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×log-div div-exp log-pow div-inv
1×pow1/3
Counts
4 → 286
Calls
4 calls:
1.0ms
(cbrt N)
8.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
12.0ms
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))
12.0ms
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))

series765.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(cbrt N)
206.0ms
(log (/ (cbrt (+ N 1.0)) (cbrt N)))
185.0ms
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))
191.0ms
(log (/ (sqrt (cbrt (+ N 1.0))) (cbrt (sqrt N))))

simplify73.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
07754325
121784235
250024182

prune1.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch18.0ms

Steps
ItersRangePoint
6
6031.575547282502
27711.216442224475
7664.61661724573

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.2s

Algorithm
intervals
Results
422.0ms1805×body1280valid
172.0ms7948×body80nan
169.0ms1201×body640valid
158.0ms4077×body80valid
54.0ms598×body320valid
18.0ms319×body160valid