Details

sample45.0ms

Algorithm

intervals

Results

10.0ms	43×	body	1280	valid
9.0ms	293×	body	80	nan
6.0ms	39×	body	640	valid
6.0ms	141×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	16×	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: 27.0b

localize6.0ms

Local error

Found 2 expressions with local error:

2.2b	(log (+ N 1.0))
4.2b	(- (log (+ N 1.0)) (log N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

4.0ms	(log (+ N 1.0))
12.0ms	(- (log (+ N 1.0)) (log N))

series142.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify54.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune96.0ms

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)
4.3b	(log (/ (+ N 1.0) N))

rewrite25.0ms

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×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

17.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series138.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune106.0ms

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	(sqrt (+ N 1.0))
0.1b	(/ (sqrt (+ N 1.0)) N)
2.2b	(log (sqrt (+ N 1.0)))
4.4b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

63×	`*-un-lft-identity`
42×	`times-frac`
40×	`add-sqr-sqrt` `sqrt-prod`
39×	`add-cube-cbrt` `log-prod`
25×	`associate-+r+`
14×	`distribute-lft-out`
11×	`pow1`
8×	`sqrt-div`
7×	`add-exp-log` `associate-+l+` `log-pow` `associate-/l*`
6×	`add-cbrt-cube`
5×	`log-div` `flip3-+` `flip-+`
4×	`add-log-exp`
3×	`associate-/r*`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `rem-sqrt-square` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

4 → 131

Calls

4 calls:

7.0ms	(sqrt (+ N 1.0))
17.0ms	(/ (sqrt (+ N 1.0)) N)
5.0ms	(log (sqrt (+ N 1.0)))
22.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ N 1.0))
73.0ms	(/ (sqrt (+ N 1.0)) N)
82.0ms	(log (sqrt (+ N 1.0)))
229.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify53.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	488	1120
1	1508	1022
2	5001	928

prune297.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(log (sqrt (+ N 1.0)))
4.4b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
4.4b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
4.4b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

103×	`log-prod`
92×	`*-un-lft-identity`
75×	`associate-+r+`
63×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`sqrt-prod`
25×	`distribute-lft-out`
21×	`associate-+l+`
18×	`pow1`
15×	`log-pow`
11×	`log-div`
8×	`sqrt-div`
7×	`flip3-+` `flip-+`
6×	`associate-+l-`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`+-commutative` `associate-+r-` `sum-log` `div-inv`
1×	`sqrt-pow1` `pow1/2` `rem-log-exp`

Counts

4 → 170

Calls

4 calls:

7.0ms	(log (sqrt (+ N 1.0)))
22.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
22.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
26.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

series774.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(log (sqrt (+ N 1.0)))
227.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
232.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
231.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))

simplify111.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 3 (91.0ms)

Iter	Nodes	Cost
0	380	1825
1	1042	1659
2	4110	1430
3	5001	1409

prune528.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch37.0ms

Steps

Iters	Range		Point
10	177.7519823634673	3845520655822.575	8816.358696954578

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

415.0ms	1744×	body	1280	valid
176.0ms	7890×	body	80	nan
176.0ms	1226×	body	640	valid
164.0ms	4117×	body	80	valid
57.0ms	613×	body	320	valid
19.0ms	300×	body	160	valid