Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	50×	body	1280	valid
8.0ms	52×	body	640	valid
6.0ms	227×	body	80	nan
5.0ms	122×	body	80	valid
4.0ms	6×	body	160	valid
2.0ms	26×	body	320	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.4b	(log (+ N 1.0))
2.5b	(- (log (+ N 1.0)) (log N))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

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

series138.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(log (+ N 1.0))
97.0ms	(- (log (+ N 1.0)) (log N))

simplify60.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 3 (50.0ms)

Iter	Nodes	Cost
0	214	284
1	573	270
2	1945	256
3	5001	253

prune105.0ms

Filtered

50 candidates to 33 candidates (66.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Merged error: 0.0b

Counts

51 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 0.3333333333333333 N) 0.5)
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))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

396×	`frac-add`
380×	`associate-/r*`
280×	`frac-times`
244×	`add-sqr-sqrt`
233×	`*-un-lft-identity`
225×	`associate-/l*`
216×	`add-cube-cbrt`
151×	`flip3--` `flip--`
140×	`associate-*l/`
113×	`unpow-prod-down`
75×	`frac-2neg` `clear-num`
60×	`times-frac`
39×	`unpow2` `sqr-pow`
33×	`add-exp-log`
31×	`associate-l`
20×	`associate-*r/`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unswap-sqr`
8×	`pow1` `add-log-exp`
6×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `associate-r` `pow-exp`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `distribute-lft-out` `difference-of-squares`
3×	`pow-unpow` `div-inv`
2×	`cbrt-undiv` `cbrt-unprod` `distribute-lft-out--`
1×	`+-commutative` `pow-pow` `flip3-+` `diff-log` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `inv-pow`

Counts

4 → 604

Calls

4 calls:

9.0ms	(- (/ 0.3333333333333333 N) 0.5)
76.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
23.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
6.0ms	(/ 1 (pow N 2))

series166.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 0.3333333333333333 N) 0.5)
31.0ms	(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
79.0ms	(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
16.0ms	(/ 1 (pow N 2))

simplify182.0ms

Algorithm

egg-herbie

Counts

616 → 616

Iterations

Useful iterations: 1 (76.0ms)

Iter	Nodes	Cost
0	4227	10924
1	5001	10475

prune1.1s

Filtered

616 candidates to 292 candidates (47.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	615	1	616
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	615	4	619

Merged error: 0.0b

Counts

619 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.5b	(cbrt N)
1.1b	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
9.4b	(* (* (/ 1 (pow (* (cbrt N) (cbrt N)) 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) (cbrt N))

rewrite489.0ms

Algorithm

rewrite-expression-head

Rules

652×	`add-sqr-sqrt`
347×	`associate-l`
324×	`unpow-prod-down`
294×	`times-frac`
231×	`cbrt-prod`
228×	`*-un-lft-identity`
220×	`unswap-sqr`
180×	`add-cube-cbrt`
154×	`associate-*l/`
128×	`associate-/r*`
119×	`associate-r`
93×	`swap-sqr`
76×	`frac-times`
65×	`add-exp-log`
45×	`difference-of-squares`
39×	`flip3--` `flip--`
33×	`prod-exp`
32×	`*-commutative`
21×	`add-cbrt-cube`
18×	`pow1`
16×	`div-exp` `unpow2` `sqr-pow`
14×	`pow-flip`
12×	`pow-exp` `associate-/l*`
10×	`cbrt-unprod`
9×	`pow-pow`
8×	`rec-exp` `pow1/3` `1-exp`
6×	`pow-to-exp`
5×	`pow-prod-down` `distribute-lft-out--`
4×	`frac-2neg` `clear-num` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow`
2×	`associate-*r/` `pow-sqr` `pow-prod-up` `div-inv`
1×	`pow2` `pow-plus` `inv-pow`

Counts

4 → 578

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
24.0ms	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
409.0ms	(* (* (/ 1 (pow (* (cbrt N) (cbrt N)) 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) (cbrt N))

series724.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt N)
177.0ms	(cbrt N)
230.0ms	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
134.0ms	(* (* (/ 1 (pow (* (cbrt N) (cbrt N)) 2)) (- (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (* 0.5 0.5))) (cbrt N))

simplify120.0ms

Algorithm

egg-herbie

Counts

590 → 590

Iterations

Useful iterations: 1 (44.0ms)

Iter	Nodes	Cost
0	1927	7641
1	5002	7188

prune1.9s

Filtered

590 candidates to 366 candidates (62.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	589	1	590
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	590	4	594

Merged error: 0.0b

Counts

594 → 4

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt N)
0.5b	(cbrt N)
1.1b	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
2.2b	(log (exp (/ 1 (pow (* (cbrt N) (cbrt N)) 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

200×	`add-sqr-sqrt`
192×	`times-frac`
189×	`unpow-prod-down`
144×	`add-cube-cbrt` `*-un-lft-identity`
118×	`cbrt-prod`
101×	`log-pow`
100×	`exp-prod`
42×	`swap-sqr` `associate-r` `associate-l`
32×	`associate-/r*`
28×	`unswap-sqr`
21×	`add-exp-log`
14×	`pow1` `pow-flip`
9×	`pow-pow`
8×	`pow1/3` `div-exp`
7×	`*-commutative` `unpow2` `sqr-pow`
6×	`pow-exp` `add-cbrt-cube`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `log-prod` `prod-exp` `associate-/l*`
2×	`rem-log-exp` `pow-prod-down` `pow-sqr` `pow-prod-up` `div-inv`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `clear-num` `inv-pow`

Counts

4 → 304

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
18.0ms	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
25.0ms	(log (exp (/ 1 (pow (* (cbrt N) (cbrt N)) 2))))

series837.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt N)
188.0ms	(cbrt N)
236.0ms	(/ 1 (pow (* (cbrt N) (cbrt N)) 2))
232.0ms	(log (exp (/ 1 (pow (* (cbrt N) (cbrt N)) 2))))

simplify80.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	690	2375
1	2644	1799
2	5003	1418

prune932.0ms

Filtered

316 candidates to 168 candidates (53.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	315	1	316
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	316	4	320

Merged error: 0b

Counts

320 → 4

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.3b

bsearch39.0ms

Steps

Iters	Range		Point
9	0.3235305135594418	61404.87568264329	3345.380548053578

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	20
1	38	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

411.0ms	1670×	body	1280	valid
191.0ms	8087×	body	80	nan
187.0ms	1246×	body	640	valid
173.0ms	4159×	body	80	valid
64.0ms	631×	body	320	valid
18.0ms	294×	body	160	valid