Details

Time bar (total: 3.8s)

sample43.0ms

Algorithm
intervals
Results
13.0ms52×body1280valid
7.0ms276×body80nan
6.0ms139×body80valid
4.0ms28×body640valid
3.0ms27×body320valid
1.0ms10×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: 26.8b

localize7.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (log (+ N 1.0)) (log N))
3.2b
(log (+ N 1.0))

rewrite14.0ms

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))

series142.0ms

Counts
2 → 6
Calls
2 calls:
94.0ms
(- (log (+ N 1.0)) (log N))
48.0ms
(log (+ N 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune147.0ms

Filtered
71 candidates to 43 candidates (60.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
16.3b
(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
19.0b
(log (+ (pow N 3) (pow 1.0 3)))
21.3b
(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
109×*-un-lft-identity
68×pow1
64×prod-diff log-pow
54×add-sqr-sqrt
47×associate--l+
42×distribute-lft-out--
40×add-cube-cbrt
36×log-prod
15×distribute-lft-out
12×unpow-prod-down fma-neg cube-prod
10×log-div
7×difference-of-squares
6×add-exp-log associate--r+
5×flip3-+ flip-+ add-log-exp
4×expm1-log1p-u diff-log add-cbrt-cube log1p-expm1-u associate--r-
3×associate--l- sub-neg sum-cubes
2×flip3-- rem-log-exp flip--
Counts
4 → 192
Calls
4 calls:
26.0ms
(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
10.0ms
(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
13.0ms
(log (+ (pow N 3) (pow 1.0 3)))
54.0ms
(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))

series661.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
71.0ms
(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
260.0ms
(log (+ (pow N 3) (pow 1.0 3)))
185.0ms
(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))

simplify93.0ms

Algorithm
egg-herbie
Counts
204 → 204
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06483728
125382815
250022779

prune533.0ms

Filtered
204 candidates to 110 candidates (53.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N))
0.2b
(/ 1 (pow N 3))
0.4b
(/ 1 (pow N 2))
15.0b
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
46×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
20×associate-/r*
12×cube-prod div-exp
8×add-cbrt-cube sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u unpow2 add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num fma-udef div-inv inv-pow
Counts
4 → 154
Calls
4 calls:
0.0ms
(fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N))
5.0ms
(/ 1 (pow N 3))
4.0ms
(/ 1 (pow N 2))
0.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N)))

series170.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N))
31.0ms
(/ 1 (pow N 3))
16.0ms
(/ 1 (pow N 2))
40.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N)))

simplify57.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0348793
11771580
25001557

prune265.0ms

Filtered
166 candidates to 69 candidates (41.6%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 31.5b

bsearch45.0ms

Steps
ItersRangePoint
9
2.027436157277799
7103758.057079569
3753.003344783202

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03521
13521

end0.0ms

sample1.3s

Algorithm
intervals
Results
467.0ms1832×body1280valid
202.0ms1279×body640valid
193.0ms7781×body80nan
179.0ms3993×body80valid
63.0ms603×body320valid
19.0ms293×body160valid