Details

sample48.0ms

Algorithm

intervals

Results

16.0ms	66×	body	1280	valid
8.0ms	256×	body	80	nan
7.0ms	46×	body	640	valid
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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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:

2.0ms	(log (+ N 1.0))
8.0ms	(- (log (+ N 1.0)) (log N))

series141.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify126.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (120.0ms)

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

prune133.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.4b	(/ 1 (pow N 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*`
6×	`div-exp`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 69

Calls

2 calls:

0.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms	(/ 1 (pow N 2))

series53.0ms

Counts

2 → 6

Calls

2 calls:

33.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
20.0ms	(/ 1 (pow N 2))

simplify33.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	208	384
1	789	315
2	5001	269

prune109.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (log (exp (/ 1 (pow N 2)))) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.4b	(/ 1 (pow N 2))
2.4b	(log (exp (/ 1 (pow N 2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`log-pow`
28×	`exp-prod`
21×	`unpow-prod-down`
12×	`add-exp-log`
8×	`associate-/r*`
7×	`unpow2` `sqr-pow`
6×	`div-exp`
5×	`add-cbrt-cube`
4×	`pow1`
3×	`expm1-log1p-u` `pow-to-exp` `rec-exp` `log-prod` `1-exp` `pow-exp` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`div-inv`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `rem-log-exp` `clear-num` `fma-udef` `inv-pow`

Counts

3 → 111

Calls

3 calls:

0.0ms	(fma (log (exp (/ 1 (pow N 2)))) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
4.0ms	(/ 1 (pow N 2))
10.0ms	(log (exp (/ 1 (pow N 2))))

series69.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(fma (log (exp (/ 1 (pow N 2)))) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
16.0ms	(/ 1 (pow N 2))
20.0ms	(log (exp (/ 1 (pow N 2))))

simplify35.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	281	579
1	866	477
2	5002	396

prune243.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

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))

simplify111.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune120.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

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

bsearch32.0ms

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	21	9
1	21	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

440.0ms	1779×	body	1280	valid
199.0ms	1295×	body	640	valid
175.0ms	7958×	body	80	nan
166.0ms	4015×	body	80	valid
62.0ms	636×	body	320	valid
17.0ms	275×	body	160	valid