Details

sample203.0ms

Algorithm

intervals

Results

55.0ms	123×	body	1280	valid
38.0ms	66×	body	1280	nan
21.0ms	53×	body	640	nan
18.0ms	57×	body	640	valid
18.0ms	54×	body	10240	exit
8.0ms	34×	body	320	nan
8.0ms	180×	body	80	nan
7.0ms	34×	body	320	valid
5.0ms	102×	body	80	valid
3.0ms	22×	body	160	valid
2.0ms	15×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series479.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
60.0ms	(pow x (/ 1.0 n))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune334.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ (/ 1.0 n) 2))
0.1b	(pow x (/ (/ 1.0 n) 2))
5.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
99×	`pow-unpow`
94×	`*-un-lft-identity`
90×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
19×	`unpow-prod-down`
9×	`div-inv`
8×	`fma-neg` `prod-diff`
7×	`pow1` `add-exp-log`
6×	`add-log-exp` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 181

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
7.0ms	(pow x (/ (/ 1.0 n) 2))
6.0ms	(pow x (/ (/ 1.0 n) 2))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

series714.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(pow (+ x 1.0) (/ 1.0 n))
55.0ms	(pow x (/ (/ 1.0 n) 2))
58.0ms	(pow x (/ (/ 1.0 n) 2))
458.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	778	1570
1	3047	1335
2	5001	1324

prune629.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.1b	(pow x (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(pow x (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
17.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(pow (+ x 1.0) (/ 1.0 n))
59.0ms	(pow x (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune536.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
0.6b	(cbrt (/ 1.0 n))
5.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) 1)) (/ (cbrt (/ 1.0 n)) 2))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
33×	`*-un-lft-identity`
29×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
8×	`unpow-prod-down` `fma-neg` `prod-diff`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`distribute-lft-out` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 102

Calls

4 calls:

2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
2.0ms	(cbrt (/ 1.0 n))
7.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) 1)) (/ (cbrt (/ 1.0 n)) 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (/ 1.0 n))
196.0ms	(cbrt (/ 1.0 n))
203.0ms	(cbrt (/ 1.0 n))
610.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ (/ 1.0 n) 2)) (pow (pow x (/ (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))) 1)) (/ (cbrt (/ 1.0 n)) 2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	343	1442
1	1127	1270
2	5001	1259

prune472.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.4b

regimes227.0ms

Accuracy

79% (2.2b remaining)

Error of 25.0b against oracle of 22.8b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	49
1	52	49

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.8s	3883×	body	1280	valid
1.3s	2258×	body	1280	nan
762.0ms	1889×	body	640	nan
627.0ms	1829×	body	640	valid
616.0ms	1394×	body	10240	exit
273.0ms	6193×	body	80	nan
244.0ms	909×	body	320	nan
202.0ms	904×	body	320	valid
159.0ms	3121×	body	80	valid
68.0ms	468×	body	160	nan
62.0ms	436×	body	160	valid