Details

sample55.0ms

Algorithm

intervals

Results

16.0ms	52×	body	1280	valid
10.0ms	273×	body	80	nan
9.0ms	46×	body	640	valid
7.0ms	132×	body	80	valid
3.0ms	20×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

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))

rewrite16.0ms

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:

11.0ms	(- (log (+ N 1.0)) (log N))
3.0ms	(log (+ N 1.0))

series134.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (log (+ N 1.0)) (log N))
41.0ms	(log (+ N 1.0))

simplify124.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune137.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.6b	(log (/ (+ N 1.0) N))

rewrite14.0ms

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:

8.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series132.0ms

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)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune121.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (log (sqrt (+ N 1.0))) (log N))
2.7b	(+ (log (sqrt (+ N 1.0))) (- (log (sqrt (+ N 1.0))) (log N)))
2.8b	(log (sqrt (+ N 1.0)))
2.8b	(log (sqrt (+ N 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
65×	`log-pow`
57×	`pow1`
48×	`prod-diff`
39×	`add-sqr-sqrt`
38×	`log-prod`
37×	`add-cube-cbrt`
33×	`associate-+r+`
20×	`sqrt-prod`
15×	`distribute-lft-out`
14×	`associate--l+`
12×	`sqrt-pow1` `pow1/2` `distribute-lft-out--`
8×	`log-div` `sqrt-div`
7×	`associate-+l+`
6×	`add-exp-log` `fma-def` `fma-neg`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--r+`
2×	`associate--l-` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--` `difference-of-squares`

Counts

4 → 178

Calls

4 calls:

10.0ms	(- (log (sqrt (+ N 1.0))) (log N))
28.0ms	(+ (log (sqrt (+ N 1.0))) (- (log (sqrt (+ N 1.0))) (log N)))
3.0ms	(log (sqrt (+ N 1.0)))
3.0ms	(log (sqrt (+ N 1.0)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (log (sqrt (+ N 1.0))) (log N))
124.0ms	(+ (log (sqrt (+ N 1.0))) (- (log (sqrt (+ N 1.0))) (log N)))
83.0ms	(log (sqrt (+ N 1.0)))
83.0ms	(log (sqrt (+ N 1.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	482	1801
1	1396	1430
2	5001	1124

prune342.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.1b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.5b	(/ 1 (pow N 2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
178×	`*-un-lft-identity`
172×	`add-cube-cbrt`
165×	`times-frac`
156×	`prod-diff`
82×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
14×	`div-inv`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `associate-r` `pow-exp`
5×	`pow1` `frac-add` `add-log-exp`
4×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `difference-of-squares`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 313

Calls

3 calls:

30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
53.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series121.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
75.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify121.0ms

Algorithm

egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1021	3505
1	4524	2419
2	5001	2419

prune657.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes25.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch33.0ms

Steps

Iters	Range		Point
9	0.25638013280504446	27058.00354315718	7441.562923621332

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.7s

Algorithm

intervals

Results

566.0ms	1807×	body	1280	valid
282.0ms	8186×	body	80	nan
254.0ms	1235×	body	640	valid
229.0ms	4064×	body	80	valid
82.0ms	604×	body	320	valid
24.0ms	290×	body	160	valid