Details

Time bar (total: 6.1s)

sample59.0ms

Algorithm
intervals
Results
19.0ms58×body1280valid
11.0ms250×body80nan
9.0ms43×body640valid
7.0ms129×body80valid
2.0ms16×body320valid
1.0ms10×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: 29.2b

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (log (+ N 1.0)) (log N))
2.8b
(log (+ N 1.0))

rewrite12.0ms

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:
7.0ms
(- (log (+ N 1.0)) (log N))
2.0ms
(log (+ N 1.0))

series136.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(- (log (+ N 1.0)) (log N))
40.0ms
(log (+ N 1.0))

simplify122.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune129.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(log1p (log (+ N 1.0)))
0.6b
(expm1 (log1p (log (+ N 1.0))))
2.8b
(log (+ N 1.0))
25.5b
(- (expm1 (log1p (log (+ N 1.0)))) (log N))

rewrite9.0ms

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:
0.0ms
(log1p (log (+ N 1.0)))
0.0ms
(expm1 (log1p (log (+ N 1.0))))
2.0ms
(log (+ N 1.0))
4.0ms
(- (expm1 (log1p (log (+ N 1.0)))) (log N))

series490.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(log1p (log (+ N 1.0)))
124.0ms
(expm1 (log1p (log (+ N 1.0))))
46.0ms
(log (+ N 1.0))
218.0ms
(- (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

prune215.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (pow N 2))
1.3b
(* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))
15.6b
(fma 0.3333333333333333 (/ (log (/ 1 N)) (* (- 1 (log (/ 1 N))) (pow N 3))) (* 0.5 (/ 1 (pow N 2))))
17.0b
(- (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))))))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
48×add-exp-log
35×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×times-frac
20×prod-exp
16×div-exp
15×add-cbrt-cube
12×unpow-prod-down associate-*r*
9×pow-to-exp prod-diff pow-exp
8×pow1 associate-/r*
6×add-log-exp
4×expm1-log1p-u cbrt-unprod log1p-expm1-u unpow2 sqr-pow
3×cbrt-undiv rec-exp fma-neg 1-exp associate-*l* log-pow fma-udef associate-/l*
2×cube-div flip3-- pow-flip associate-*l/ associate-/r/ flip-- div-inv inv-pow
1×sub-neg frac-2neg diff-log associate-*r/ distribute-frac-neg log-rec pow-prod-down associate--l+ clear-num *-commutative distribute-rgt-neg-out associate--r+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 142
Calls
4 calls:
4.0ms
(/ 1 (pow N 2))
46.0ms
(* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))
0.0ms
(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))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1 (pow N 2))
391.0ms
(* 5.551115123125783e-17 (/ (log (/ 1 N)) (* (pow (- 1 (log (/ 1 N))) 3) (pow N 3))))
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))))))

simplify141.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
08143539
143172612
250012605

prune580.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.2b

bsearch52.0ms

Steps
ItersRangePoint
9
0.8894813891870064
5702493.407928515
3680.1889511455383

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04446
14446

end0.0ms

sample1.7s

Algorithm
intervals
Results
598.0ms1848×body1280valid
273.0ms7795×body80nan
263.0ms1223×body640valid
236.0ms4036×body80valid
86.0ms603×body320valid
25.0ms290×body160valid