Details

sample47.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
7.0ms	46×	body	640	valid
6.0ms	256×	body	80	nan
5.0ms	119×	body	80	valid
1.0ms	14×	body	320	valid
1.0ms	11×	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: 31.9b

localize7.0ms

Local error

Found 2 expressions with local error:

1.8b	(log (+ N 1.0))
2.4b	(- (log (+ N 1.0)) (log N))

rewrite10.0ms

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:

3.0ms	(log (+ N 1.0))
6.0ms	(- (log (+ N 1.0)) (log N))

series138.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
92.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

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

prune109.0ms

Pruning

3 alts after pruning (3 fresh and 0 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))
0.0b	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.4b	(/ 1 (pow N 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-l`
23×	`unpow-prod-down`
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×	`distribute-rgt-in` `frac-times` `sub-neg` `associate-+l+` `flip3--` `distribute-lft-in` `associate-*r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `associate-*l/` `cbrt-unprod` `div-inv` `difference-of-squares`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `*-commutative` `flip-+` `distribute-lft-out--` `inv-pow`

Counts

3 → 150

Calls

3 calls:

20.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
42.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
4.0ms	(/ 1 (pow N 2))

series123.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
76.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify72.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	583	1087
1	2726	904
2	5001	841

prune278.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.7b	(log (/ (+ N 1.0) N))

rewrite17.0ms

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:

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

series130.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
85.0ms	(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

prune122.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
1.8b	(log (+ N 1.0))
23.7b	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `associate--l+`
9×	`cbrt-prod`
6×	`pow1` `associate--r+` `add-log-exp`
5×	`add-exp-log`
4×	`add-cbrt-cube`
3×	`diff-log`
2×	`sub-neg` `log-div` `pow1/3` `log-pow` `distribute-lft-out` `distribute-lft-out--`
1×	`associate--l-` `flip3--` `flip3-+` `rem-log-exp` `flip--` `flip-+` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

0.0ms	(cbrt N)
0.0ms	(cbrt N)
2.0ms	(log (+ N 1.0))
20.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt N)
182.0ms	(cbrt N)
40.0ms	(log (+ N 1.0))
93.0ms	(- (- (log (+ N 1.0)) (* 2 (log (cbrt N)))) (log (cbrt N)))

simplify131.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	322	540
1	990	485
2	4018	429
3	5001	422

prune211.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes28.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.1b

bsearch29.0ms

Steps

Iters	Range		Point
9	168.70424079671096	29129170.846978452	7004.853881128945

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

437.0ms	1779×	body	1280	valid
200.0ms	1295×	body	640	valid
194.0ms	7958×	body	80	nan
171.0ms	4015×	body	80	valid
64.0ms	636×	body	320	valid
17.0ms	275×	body	160	valid