Details

Time bar (total: 5.3s)

sample42.0ms

Algorithm
intervals
Results
13.0ms57×body1280valid
6.0ms259×body80nan
6.0ms40×body640valid
6.0ms139×body80valid
1.0ms14×body320valid
0.0ms6×body160valid

simplify6.0ms

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: 27.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.3b
(- (log (+ N 1.0)) (log N))
1.6b
(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))

series134.0ms

Counts
2 → 6
Calls
2 calls:
89.0ms
(- (log (+ N 1.0)) (log N))
44.0ms
(log (+ N 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune130.0ms

Filtered
71 candidates to 43 candidates (60.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (log (+ N 1.0)))
0.5b
(expm1 (log1p (log (+ N 1.0))))
1.6b
(log (+ N 1.0))
24.1b
(- (expm1 (log1p (log (+ N 1.0)))) (log N))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
16×add-sqr-sqrt
14×add-cube-cbrt
12×prod-diff
9×pow1
7×log-prod
5×add-exp-log expm1-log1p-u log-pow add-log-exp
4×add-cbrt-cube log1p-expm1-u
3×fma-neg associate--r+
2×log-div distribute-lft-out-- expm1-udef
1×associate--l- sub-neg log1p-udef expm1-log1p flip3-- flip3-+ diff-log log1p-expm1 rem-log-exp flip-- flip-+ distribute-lft-out difference-of-squares
Counts
4 → 75
Calls
4 calls:
1.0ms
(log1p (log (+ N 1.0)))
1.0ms
(expm1 (log1p (log (+ N 1.0))))
3.0ms
(log (+ N 1.0))
5.0ms
(- (expm1 (log1p (log (+ N 1.0)))) (log N))

series482.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(log1p (log (+ N 1.0)))
127.0ms
(expm1 (log1p (log (+ N 1.0))))
40.0ms
(log (+ N 1.0))
214.0ms
(- (expm1 (log1p (log (+ N 1.0)))) (log N))

simplify58.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0556870
12211669
25002649

prune209.0ms

Filtered
87 candidates to 66 candidates (75.9%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (- 1 (log (/ 1 N))) 3)
0.8b
(/ 1 (pow N 2))
16.6b
(fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))
18.3b
(- (fma 0.3333333333333333 (/ 1 (* (- 1 (log (/ 1 N))) (pow N 3))) (* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))) (fma 5.551115123125783e-17 (/ 1 (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))) (fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
39×add-sqr-sqrt
31×add-cube-cbrt
24×times-frac
19×unpow-prod-down
14×add-exp-log
9×prod-diff
8×associate-/r*
7×pow1 cube-prod add-cbrt-cube
6×div-exp add-log-exp
5×distribute-lft-out-- difference-of-squares sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u unpow2
3×rec-exp pow-unpow fma-neg 1-exp fma-udef associate-/l*
2×cube-div flip3-- log-pow flip--
1×cbrt-undiv cube-mult sub-neg pow-flip pow-pow frac-2neg diff-log unpow3 associate--l+ clear-num div-inv associate--r+ inv-pow rem-cube-cbrt
Counts
4 → 134
Calls
4 calls:
6.0ms
(pow (- 1 (log (/ 1 N))) 3)
5.0ms
(/ 1 (pow N 2))
1.0ms
(fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))
4.0ms
(- (fma 0.3333333333333333 (/ 1 (* (- 1 (log (/ 1 N))) (pow N 3))) (* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))) (fma 5.551115123125783e-17 (/ 1 (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))) (fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))))

series2.0s

Counts
4 → 12
Calls
4 calls:
169.0ms
(pow (- 1 (log (/ 1 N))) 3)
17.0ms
(/ 1 (pow N 2))
442.0ms
(fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))
1.4s
(- (fma 0.3333333333333333 (/ 1 (* (- 1 (log (/ 1 N))) (pow N 3))) (* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))) (fma 5.551115123125783e-17 (/ 1 (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))) (fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))))

simplify112.0ms

Algorithm
egg-herbie
Counts
146 → 146
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
07003220
134712330
250032304

prune537.0ms

Filtered
146 candidates to 81 candidates (55.5%)
Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch48.0ms

Steps
ItersRangePoint
9
0.10207175935539815
6041963.123514823
3335.4554652729116

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04446
14446

end0.0ms

sample1.2s

Algorithm
intervals
Results
415.0ms1754×body1280valid
189.0ms8043×body80nan
183.0ms1227×body640valid
170.0ms4058×body80valid
65.0ms639×body320valid
19.0ms322×body160valid