Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	58×	body	1280	valid
6.0ms	284×	body	80	nan
6.0ms	38×	body	640	valid
6.0ms	136×	body	80	valid
2.0ms	17×	body	320	valid
0.0ms	7×	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: 28.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(log (+ N 1.0))
3.0b	(- (log (+ N 1.0)) (log N))

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:

3.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series137.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

simplify124.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune125.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b	(log (/ (+ N 1.0) N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
15×	`*-un-lft-identity`
12×	`times-frac`
9×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log`
3×	`distribute-lft-out`
2×	`pow1` `rem-log-exp`
1×	`expm1-log1p-u` `log-div` `div-exp` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

4.0ms

(log (/ (+ N 1.0) N))

series84.0ms

Counts

1 → 3

Calls

1 calls:

84.0ms

(log (/ (+ N 1.0) N))

simplify59.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	172	216
1	471	200
2	2042	190
3	5002	187

prune59.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ 1 (sqrt N)))
0.2b	(/ 1 (sqrt N))
0.4b	(/ (+ N 1.0) (sqrt N))
3.4b	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
102×	`times-frac`
78×	`add-sqr-sqrt` `add-cube-cbrt`
72×	`log-prod`
57×	`sqrt-prod`
28×	`associate-+r+`
22×	`associate-+l+`
17×	`distribute-lft-out`
16×	`pow1`
15×	`add-exp-log`
14×	`log-pow`
12×	`associate-/r*`
9×	`pow-flip`
8×	`fma-def` `add-cbrt-cube`
7×	`associate-/l*`
5×	`div-exp` `div-inv`
4×	`expm1-log1p-u` `rem-log-exp` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `sqrt-pow1` `pow1/2` `inv-pow`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l-` `associate-+r-` `log-rec` `sum-log`

Counts

4 → 216

Calls

4 calls:

3.0ms	(log (/ 1 (sqrt N)))
3.0ms	(/ 1 (sqrt N))
9.0ms	(/ (+ N 1.0) (sqrt N))
19.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log (/ 1 (sqrt N)))
30.0ms	(/ 1 (sqrt N))
50.0ms	(/ (+ N 1.0) (sqrt N))
178.0ms	(+ (log (/ 1 (sqrt N))) (log (/ (+ N 1.0) (sqrt N))))

simplify63.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	613	1607
1	2627	1415
2	5001	1323

prune418.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (+ N 1.0) N))
0.5b	(cbrt (/ (+ N 1.0) N))
2.9b	(log (cbrt (/ (+ N 1.0) N)))
2.9b	(log (cbrt (/ (+ N 1.0) N)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
62×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `cbrt-div` `pow1/3` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 118

Calls

4 calls:

3.0ms	(cbrt (/ (+ N 1.0) N))
3.0ms	(cbrt (/ (+ N 1.0) N))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))
4.0ms	(log (cbrt (/ (+ N 1.0) N)))

series665.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(cbrt (/ (+ N 1.0) N))
125.0ms	(cbrt (/ (+ N 1.0) N))
209.0ms	(log (cbrt (/ (+ N 1.0) N)))
201.0ms	(log (cbrt (/ (+ N 1.0) N)))

simplify108.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	278	1088
1	803	1024
2	3528	998
3	5002	962

prune366.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes35.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch29.0ms

Steps

Iters	Range		Point
7	3268.458992709865	89650.56729712563	5876.780919713783

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	14
1	26	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

438.0ms	1743×	body	1280	valid
198.0ms	1273×	body	640	valid
191.0ms	8040×	body	80	nan
172.0ms	4090×	body	80	valid
63.0ms	590×	body	320	valid
19.0ms	304×	body	160	valid