Details

sample122.0ms

Algorithm

intervals

Results

48.0ms	107×	body	1280	valid
17.0ms	49×	body	640	valid
13.0ms	30×	body	10240	exit
6.0ms	130×	body	80	valid
6.0ms	17×	body	1280	nan
5.0ms	129×	body	80	nan
4.0ms	21×	body	320	valid
2.0ms	13×	body	320	nan
2.0ms	18×	body	160	valid
2.0ms	7×	body	640	nan
0.0ms	3×	body	160	nan

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: 31.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
44.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series464.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))
265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune233.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
0.5b	(pow x (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
47×	`unpow-prod-down`
46×	`cbrt-prod`
33×	`*-un-lft-identity`
27×	`difference-of-squares`
26×	`pow-unpow`
25×	`add-cube-cbrt`
23×	`sqr-pow`
18×	`times-frac`
17×	`cube-prod`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube`
3×	`distribute-lft-out`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`cube-mult` `sub-neg` `flip3--` `pow1/3` `diff-log` `unpow3` `flip--` `rem-cbrt-cube` `distribute-lft-out--`

Counts

4 → 126

Calls

4 calls:

9.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
100.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3))
59.0ms	(pow x (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))
267.0ms	(- (cbrt (pow (pow (+ x 1.0) (/ 1.0 n)) 3)) (pow x (/ 1.0 n)))

simplify58.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	596	1222
1	2112	1179
2	5001	1176

prune352.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.3b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ (* (log x) 1.0) (* x (pow n 2)))
1.5b	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
7.9b	(* x (pow n 2))
9.0b	(/ (/ 0.5 n) (pow x 2))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
113×	`add-sqr-sqrt`
103×	`*-un-lft-identity`
98×	`add-cube-cbrt`
46×	`add-exp-log` `unpow-prod-down`
23×	`add-cbrt-cube`
17×	`div-exp`
16×	`unpow2` `sqr-pow`
14×	`associate-/l*`
13×	`prod-exp`
11×	`div-inv`
9×	`associate-/r*` `add-log-exp`
8×	`associate-r`
7×	`cbrt-undiv`
5×	`pow-to-exp` `pow-exp` `cbrt-unprod`
4×	`pow1` `frac-sub` `unswap-sqr`
3×	`diff-log` `associate-l` `distribute-lft-out--` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--` `associate--r+`
1×	`*-commutative` `associate-/l/` `associate--r-`

Counts

4 → 220

Calls

4 calls:

5.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
196.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
6.0ms	(* x (pow n 2))
12.0ms	(/ (/ 0.5 n) (pow x 2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (* (log x) 1.0) (* x (pow n 2)))
68.0ms	(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
28.0ms	(* x (pow n 2))
30.0ms	(/ (/ 0.5 n) (pow x 2))

simplify50.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1112	2049
1	5001	1858

prune637.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.3b

localize22.0ms

Local error

Found 4 expressions with local error:

9.0b	(/ (/ 0.5 n) (pow x 2))
16.8b	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
16.8b	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
16.8b	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))

rewrite562.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
125×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
98×	`add-cube-cbrt`
42×	`unpow-prod-down`
24×	`cbrt-prod`
17×	`add-exp-log`
15×	`cbrt-div`
14×	`unpow2` `sqr-pow`
13×	`associate-/l*`
12×	`frac-sub`
10×	`div-inv`
9×	`div-exp` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*`
6×	`flip3--` `flip--`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `pow1/3`
2×	`pow-to-exp` `pow-exp`
1×	`frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 207

Calls

4 calls:

8.0ms	(/ (/ 0.5 n) (pow x 2))
179.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
182.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
182.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))

series704.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (/ 0.5 n) (pow x 2))
229.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
227.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))
223.0ms	(cbrt (- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	990	3317
1	4100	3120
2	5001	3105

prune901.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 18.3b

regimes263.0ms

Accuracy

82.6% (1.5b remaining)

Error of 21.7b against oracle of 20.2b and baseline of 28.9b

bsearch148.0ms

Steps

Iters	Range		Point
6	19876726218860.492	105140736935169.5	20201670204046.145
8	-1132915.5505216778	-22.912385628196162	-946530.0438019232

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	63
1	44	63

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.4s	3134×	body	1280	valid
537.0ms	1576×	body	640	valid
459.0ms	1104×	body	10240	exit
311.0ms	681×	body	1280	nan
255.0ms	4783×	body	80	valid
212.0ms	651×	body	640	nan
183.0ms	841×	body	320	valid
178.0ms	5079×	body	80	nan
69.0ms	370×	body	320	nan
56.0ms	410×	body	160	valid
20.0ms	184×	body	160	nan