Details

sample46.0ms

Algorithm

intervals

Results

14.0ms	57×	body	1280	valid
9.0ms	259×	body	80	nan
6.0ms	40×	body	640	valid
6.0ms	139×	body	80	valid
1.0ms	14×	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: 27.4b

localize7.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (log (+ N 1.0)) (log N))
1.6b	(log (+ N 1.0))

rewrite11.0ms

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:

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

series141.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (log (+ N 1.0)) (log N))
46.0ms	(log (+ N 1.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1874	250
3	5001	247

prune102.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.6b	(log (+ N 1.0))
1.6b	(log (+ N 1.0))
1.6b	(log (+ N 1.0))
18.6b	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`log-div`
5×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+` `distribute-lft-out` `associate--r+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 60

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
10.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

series225.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(log (+ N 1.0))
40.0ms	(log (+ N 1.0))
45.0ms	(log (+ N 1.0))
92.0ms	(- (* (* (cbrt (log (+ N 1.0))) (cbrt (log (+ N 1.0)))) (cbrt (log (+ N 1.0)))) (log N))

simplify62.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	217	609
1	595	492
2	2061	435
3	5001	417

prune178.0ms

Pruning

2 alts after pruning (1 fresh and 1 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))
0.8b	(/ 1 (pow N 2))

rewrite48.0ms

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))
17.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms	(/ 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))
77.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify71.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (59.0ms)

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

prune256.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
0.2b	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
0.8b	(/ 1 (pow N 2))
17.4b	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
64×	`add-sqr-sqrt`
62×	`add-exp-log`
52×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
31×	`associate-*l/`
26×	`prod-exp`
18×	`div-exp`
16×	`pow1` `associate-r`
14×	`associate-l`
13×	`swap-sqr`
12×	`unpow-prod-down` `associate-/l/`
10×	`frac-add` `cbrt-unprod`
9×	`associate-/r*`
8×	`cbrt-undiv`
7×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
6×	`pow-to-exp` `rec-exp` `flip3--` `1-exp` `pow-exp` `flip--` `div-inv` `associate-/l*`
4×	`pow-prod-down` `unpow2` `add-log-exp` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative`
1×	`pow2` `pow-flip` `pow-plus` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 192

Calls

4 calls:

28.0ms	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
10.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
8.0ms	(/ 1 (pow N 2))
16.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

series226.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (+ (* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N) (* (+ (/ 0.3333333333333333 N) 0.5) 1.0)) (* (+ (/ 0.3333333333333333 N) 0.5) N))
25.0ms	(* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))
21.0ms	(/ 1 (pow N 2))
97.0ms	(* (* (/ 1 (pow N 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) N)

simplify47.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1034	1857
1	5001	1571

prune460.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 30.0b

bsearch38.0ms

Steps

Iters	Range		Point
9	0.10207175935539815	6041963.123514823	3541.91441017856

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	30
1	39	30

end0.0ms

sample1.3s

Algorithm

intervals

Results

439.0ms	1754×	body	1280	valid
193.0ms	8043×	body	80	nan
186.0ms	1227×	body	640	valid
167.0ms	4058×	body	80	valid
63.0ms	639×	body	320	valid
20.0ms	322×	body	160	valid