Details

Time bar (total: 3.4s)

sample42.0ms

Algorithm
intervals
Results
14.0ms57×body1280valid
6.0ms259×body80nan
6.0ms40×body640valid
6.0ms139×body80valid
1.0ms14×body320valid
0.0ms6×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: 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))

series136.0ms

Counts
2 → 6
Calls
2 calls:
90.0ms
(- (log (+ N 1.0)) (log N))
45.0ms
(log (+ N 1.0))

simplify123.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (117.0ms)

IterNodesCost
0277598
1837444
23748347
35001345

prune134.0ms

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
(log (log (+ N 1.0)))
0.6b
(exp (log (log (+ N 1.0))))
1.6b
(log (+ N 1.0))
22.9b
(- (exp (log (log (+ N 1.0)))) (log N))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×log-prod
31×*-un-lft-identity
30×add-sqr-sqrt
28×prod-diff
26×add-cube-cbrt
25×exp-sum
22×pow1
18×log-pow
7×fma-neg
6×add-exp-log
5×add-log-exp
4×expm1-log1p-u exp-prod add-cbrt-cube log1p-expm1-u
3×associate--r+
2×log-div rem-log-exp distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+ rem-exp-log distribute-lft-out
Counts
4 → 106
Calls
4 calls:
3.0ms
(log (log (+ N 1.0)))
2.0ms
(exp (log (log (+ N 1.0))))
3.0ms
(log (+ N 1.0))
11.0ms
(- (exp (log (log (+ N 1.0)))) (log N))

series265.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(log (log (+ N 1.0)))
43.0ms
(exp (log (log (+ N 1.0))))
40.0ms
(log (+ N 1.0))
93.0ms
(- (exp (log (log (+ N 1.0)))) (log N))

simplify49.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04481188
11481809
25001615

prune217.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
0.5b
(/ 1 (pow N 3))
0.8b
(/ 1 (pow N 2))
13.2b
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 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:
1.0ms
(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
5.0ms
(/ 1 (pow N 3))
5.0ms
(/ 1 (pow N 2))
1.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)))

series169.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N))
32.0ms
(/ 1 (pow N 3))
16.0ms
(/ 1 (pow N 2))
39.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)))

simplify56.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0348793
11771580
25001557

prune246.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (pow N 3))
0.8b
(/ 1 (pow N 2))
13.2b
(fma (- 0.5) (/ 1 (pow N 2)) (cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3)))
29.6b
(cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
49×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
22×add-exp-log
20×associate-/r*
15×cube-prod
12×cbrt-prod div-exp
9×sqr-pow
8×add-cbrt-cube
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
5×cube-mult unpow3
4×pow1 expm1-log1p-u log1p-expm1-u unpow2 add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num div-inv inv-pow
1×pow1/3 rem-cbrt-cube fma-udef
Counts
4 → 167
Calls
4 calls:
6.0ms
(/ 1 (pow N 3))
5.0ms
(/ 1 (pow N 2))
1.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3)))
2.0ms
(cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3))

series167.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1 (pow N 3))
15.0ms
(/ 1 (pow N 2))
39.0ms
(fma (- 0.5) (/ 1 (pow N 2)) (cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3)))
82.0ms
(cbrt (pow (fma 0.3333333333333333 (/ 1 (pow N 3)) (/ 1.0 N)) 3))

simplify63.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0387861
11954725
25003709

prune297.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

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

bsearch34.0ms

Steps
ItersRangePoint
9
0.10207175935539815
6041963.123514823
3438.684937725736

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
12714

end0.0ms

sample1.2s

Algorithm
intervals
Results
416.0ms1754×body1280valid
190.0ms8043×body80nan
180.0ms1227×body640valid
167.0ms4058×body80valid
61.0ms639×body320valid
19.0ms322×body160valid