Details

sample210.0ms

Algorithm

intervals

Results

55.0ms	122×	body	1280	valid
43.0ms	68×	body	1280	nan
23.0ms	60×	body	640	nan
21.0ms	45×	body	10240	exit
16.0ms	50×	body	640	valid
9.0ms	224×	body	80	nan
7.0ms	26×	body	320	nan
7.0ms	32×	body	320	valid
4.0ms	95×	body	80	valid
3.0ms	21×	body	160	nan
2.0ms	16×	body	160	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
14×	`unpow-prod-down`
13×	`pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube` `distribute-lft-out`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 52

Calls

2 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series408.0ms

Counts

2 → 6

Calls

2 calls:

138.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify35.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	359	490
1	1141	475
2	5002	466

prune166.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
0.1b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.1b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.7b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

rewrite198.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
114×	`add-sqr-sqrt`
88×	`*-un-lft-identity`
86×	`pow-unpow`
78×	`add-cube-cbrt`
28×	`unpow-prod-down`
24×	`difference-of-squares`
16×	`associate-r` `sqr-pow`
8×	`pow1` `add-exp-log` `div-inv`
6×	`sqrt-prod` `add-cbrt-cube` `add-log-exp`
4×	`frac-times` `flip3--` `associate-l` `flip--`
3×	`sub-neg` `flip3-+` `flip-+` `distribute-lft-out`
2×	`distribute-rgt-in` `pow-to-exp` `pow-pow` `distribute-lft-in` `associate-r/` `associate-l/` `pow-exp` `distribute-lft-out--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 185

Calls

4 calls:

161.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
8.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
11.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))) (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
138.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
423.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

simplify97.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	912	2444
1	3939	2286
2	5003	2261

prune729.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
0.1b	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
0.1b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
3.9b	(- (pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2)) (sqrt (pow (sqrt x) (/ 1.0 n))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

720×	`times-frac`
362×	`add-sqr-sqrt`
348×	`*-un-lft-identity`
340×	`add-cube-cbrt`
309×	`pow-unpow`
30×	`div-inv`
23×	`unpow-prod-down`
15×	`sqrt-prod` `difference-of-squares`
11×	`sqr-pow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 382

Calls

4 calls:

18.0ms	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
17.0ms	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
9.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
16.0ms	(- (pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2)) (sqrt (pow (sqrt x) (/ 1.0 n))))

series984.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
145.0ms	(pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2))
149.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
539.0ms	(- (pow (+ x 1.0) (/ (/ (/ 1.0 n) 2) 2)) (sqrt (pow (sqrt x) (/ 1.0 n))))

simplify61.0ms

Algorithm

egg-herbie

Counts

394 → 394

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1569	3664
1	5001	3536

prune2.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
0.1b	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))
2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
36×	`difference-of-squares`
34×	`unpow-prod-down`
32×	`log-prod`
23×	`*-un-lft-identity`
22×	`sqr-pow`
16×	`exp-sum`
15×	`add-cube-cbrt`
13×	`pow-unpow`
9×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`add-exp-log` `add-log-exp`
4×	`log-div` `exp-prod` `add-cbrt-cube`
3×	`flip3--` `flip--` `distribute-lft-out--`
2×	`exp-diff` `log-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `div-inv` `rem-exp-log` `distribute-lft-out`

Counts

4 → 110

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
11.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))
16.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.7s

Counts

4 → 12

Calls

4 calls:

145.0ms	(pow (+ x 1.0) (/ 1.0 n))
447.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))))
1.6s	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n)))))
448.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	637	1851
1	2091	1782
2	5001	1755

prune419.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

regimes212.0ms

Accuracy

79.8% (2.2b remaining)

Error of 24.3b against oracle of 22.1b and baseline of 33.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	83
1	56	83
2	56	83

end0.0ms

sample6.4s

Algorithm

intervals

Results

1.8s	3910×	body	1280	valid
1.2s	2178×	body	1280	nan
734.0ms	1824×	body	640	nan
618.0ms	1421×	body	10240	exit
598.0ms	1838×	body	640	valid
264.0ms	6366×	body	80	nan
228.0ms	902×	body	320	nan
196.0ms	881×	body	320	valid
144.0ms	3099×	body	80	valid
64.0ms	456×	body	160	nan
60.0ms	444×	body	160	valid