Details

sample41.0ms

Algorithm

intervals

Results

12.0ms	52×	body	1280	valid
6.0ms	276×	body	80	nan
6.0ms	139×	body	80	valid
4.0ms	28×	body	640	valid
3.0ms	27×	body	320	valid
1.0ms	10×	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: 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))

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))
45.0ms	(log (+ N 1.0))

simplify122.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

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

prune139.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))

rewrite71.0ms

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:

23.0ms	(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
5.0ms	(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
11.0ms	(log (+ (pow N 3) (pow 1.0 3)))
24.0ms	(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))

series643.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0)))))
65.0ms	(log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))
248.0ms	(log (+ (pow N 3) (pow 1.0 3)))
181.0ms	(- (- (log (+ (pow N 3) (pow 1.0 3))) (log (+ (* N N) (- (* 1.0 1.0) (* N 1.0))))) (log N))

simplify94.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	648	3728
1	2538	2815
2	5002	2779

prune500.0ms

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)))

rewrite17.0ms

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 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N))
6.0ms	(/ 1 (pow N 3))
5.0ms	(/ 1 (pow N 2))
1.0ms	(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N))
31.0ms	(/ 1 (pow N 3))
20.0ms	(/ 1 (pow N 2))
34.0ms	(fma (- 0.5) (/ 1 (pow N 2)) (fma 0.33333333333333337 (/ 1 (pow N 3)) (/ 1.0 N)))

simplify52.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	348	793
1	1771	580
2	5001	557

prune262.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

100% (0.0b remaining)

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

bsearch41.0ms

Steps

Iters	Range		Point
9	2.027436157277799	7103758.057079569	3753.003344783202

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.3s

Algorithm

intervals

Results

440.0ms	1832×	body	1280	valid
190.0ms	1279×	body	640	valid
184.0ms	7781×	body	80	nan
161.0ms	3993×	body	80	valid
58.0ms	603×	body	320	valid
18.0ms	293×	body	160	valid