Details

sample133.0ms

Algorithm

intervals

Results

47.0ms	110×	body	1280	valid
19.0ms	37×	body	10240	exit
19.0ms	56×	body	640	valid
7.0ms	140×	body	80	valid
6.0ms	17×	body	1280	nan
6.0ms	170×	body	80	nan
4.0ms	21×	body	320	valid
4.0ms	15×	body	640	nan
3.0ms	16×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	5×	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: 28.0b

localize8.0ms

Local error

Found 3 expressions with local error:

1.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(pow x (/ 1.0 n))
2.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite73.0ms

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:

57.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series466.0ms

Counts

3 → 9

Calls

3 calls:

265.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
58.0ms	(pow x (/ 1.0 n))
142.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify65.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	654	2164
1	2162	1642
2	5002	1637

prune318.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.9b

localize12.0ms

Local error

Found 3 expressions with local error:

1.1b	(fma (pow 1 (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
1.2b	(pow x (/ 1.0 n))
2.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow-unpow`
21×	`*-un-lft-identity`
19×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
7×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
1×	`fma-udef` `distribute-lft-out`

Counts

3 → 69

Calls

3 calls:

0.0ms	(fma (pow 1 (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series7.0m

Counts

3 → 9

Calls

3 calls:

7.0m	(fma (pow 1 (/ 1.0 n)) (pow (+ x 1.0) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
53.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify42.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	478	525
1	1760	492
2	5001	485

prune232.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (log (/ 1 x)) (* x (pow n 2)))
1.5b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
9.2b	(* x (pow n 2))
9.7b	(* (pow x 2) n)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

10.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
0.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series191.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
80.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
27.0ms	(* x (pow n 2))
16.0ms	(* (pow x 2) n)

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	383	691
1	1703	592
2	5002	591

prune354.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (log (/ 1 x)) (* x (pow n 2)))
1.5b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (log1p (expm1 (* (pow x 2) n)))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
9.2b	(* x (pow n 2))
9.7b	(* (pow x 2) n)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

8.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
0.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (log1p (expm1 (* (pow x 2) n)))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series242.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ (log (/ 1 x)) (* x (pow n 2)))
127.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (log1p (expm1 (* (pow x 2) n)))) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
26.0ms	(* x (pow n 2))
19.0ms	(* (pow x 2) n)

simplify50.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	388	715
1	1715	609
2	5001	607

prune371.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.6b

regimes221.0ms

Accuracy

82.5% (1.5b remaining)

Error of 22.2b against oracle of 20.7b and baseline of 29.2b

bsearch117.0ms

Steps

Iters	Range		Point
4	35684799163967.39	65476467807244.016	38477768099274.57
8	-1.4656833132303516e+19	-5.137140036294433e+16	-5.194583831257681e+16

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	44	25

end0.0ms

sample3.8s

Algorithm

intervals

Results

1.3s	3139×	body	1280	valid
520.0ms	1607×	body	640	valid
396.0ms	1116×	body	10240	exit
278.0ms	647×	body	1280	nan
232.0ms	4738×	body	80	valid
210.0ms	675×	body	640	nan
185.0ms	865×	body	320	valid
171.0ms	5153×	body	80	nan
63.0ms	366×	body	320	nan
55.0ms	438×	body	160	valid
21.0ms	207×	body	160	nan

Details

sample133.0ms

simplify35.0ms

prune2.0ms

localize8.0ms

rewrite73.0ms

series466.0ms

simplify65.0ms

prune318.0ms

localize12.0ms

rewrite11.0ms

series7.0m

simplify42.0ms

prune232.0ms

localize19.0ms

rewrite25.0ms

series191.0ms

simplify50.0ms

prune354.0ms

localize21.0ms

rewrite23.0ms

series242.0ms

simplify50.0ms

prune371.0ms

regimes221.0ms

bsearch117.0ms

simplify1.0ms

end0.0ms

sample3.8s

end2.9m