Details

sample143.0ms

Algorithm

intervals

Results

48.0ms	108×	body	1280	valid
22.0ms	45×	body	10240	exit
16.0ms	48×	body	640	valid
10.0ms	22×	body	1280	nan
8.0ms	25×	body	640	nan
8.0ms	157×	body	80	valid
6.0ms	160×	body	80	nan
5.0ms	23×	body	320	valid
2.0ms	9×	body	320	nan
1.0ms	9×	body	160	valid
0.0ms	3×	body	160	nan

simplify36.0ms

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: 27.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.2b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite64.0ms

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:

49.0ms	(- (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))

series482.0ms

Counts

3 → 9

Calls

3 calls:

273.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
60.0ms	(pow x (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify67.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (49.0ms)

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

prune339.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.7b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.2b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite176.0ms

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:

49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
104.0ms	(log (exp (- (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))

series867.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
266.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
59.0ms	(pow x (/ 1.0 n))
272.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify88.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	835	3935
1	2475	2885
2	5001	2880

prune515.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow x (/ 1.0 n))
1.2b	(pow x (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(pow (+ x 1.0) (/ 1.0 n))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

52×	`pow-unpow`
40×	`*-un-lft-identity`
36×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
14×	`unpow-prod-down`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
2×	`distribute-lft-out`

Counts

4 → 118

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))

series401.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ 1.0 n))
58.0ms	(pow x (/ 1.0 n))
139.0ms	(pow (+ x 1.0) (/ 1.0 n))
145.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify38.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	353	662
1	1217	644
2	5001	632

prune448.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 19.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* x n))
2.0b	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
8.2b	(* (pow x 2) n)
9.2b	(* x (pow n 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

7.0ms	(/ 1 (* x n))
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	(* (pow x 2) n)
6.0ms	(* x (pow n 2))

series146.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ 1 (* x n))
88.0ms	(fma 1.0 (/ 1 (* x n)) (- (fma 0.5 (/ 1 (* (pow x 2) n)) (* 1.0 (/ (log (/ 1 x)) (* x (pow n 2)))))))
17.0ms	(* (pow x 2) n)
29.0ms	(* x (pow n 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	383	546
1	1807	466
2	5001	459

prune321.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.1b

regimes218.0ms

Accuracy

82% (1.6b remaining)

Error of 22.2b against oracle of 20.6b and baseline of 29.5b

bsearch212.0ms

Steps

Iters	Range		Point
10	1.7888545263047805e-09	29129170.846978452	1358332.5394366088
11	-13600.963204601821	-3.148161800826367e-19	-13450.546323696572

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	38
1	48	38

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3193×	body	1280	valid
517.0ms	1496×	body	640	valid
489.0ms	1155×	body	10240	exit
286.0ms	620×	body	1280	nan
247.0ms	4707×	body	80	valid
230.0ms	682×	body	640	nan
199.0ms	865×	body	320	valid
185.0ms	4992×	body	80	nan
61.0ms	435×	body	160	valid
60.0ms	312×	body	320	nan
19.0ms	177×	body	160	nan