Details

sample121.0ms

Algorithm

intervals

Results

49.0ms	109×	body	1280	valid
17.0ms	52×	body	640	valid
9.0ms	155×	body	80	valid
8.0ms	37×	body	320	valid
6.0ms	158×	body	80	nan
5.0ms	5×	body	1280	nan
4.0ms	69×	body	80	overflowed
3.0ms	6×	body	640	nan
2.0ms	7×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	5×	body	160	nan

simplify33.0ms

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 2 expressions with local error:

0.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite51.0ms

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:

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

series430.0ms

Counts

2 → 6

Calls

2 calls:

278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
152.0ms	(pow (+ x 1.0) (/ 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

prune151.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 22.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
37×	`sqrt-prod`
35×	`*-un-lft-identity`
26×	`pow-unpow`
24×	`unpow-prod-down`
22×	`add-cube-cbrt`
18×	`times-frac`
16×	`difference-of-squares`
12×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out--`
3×	`rem-sqrt-square` `distribute-lft-out`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `flip--`

Counts

4 → 107

Calls

4 calls:

2.0ms	(sqrt (pow x (/ 1.0 n)))
49.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))

series866.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (pow x (/ 1.0 n)))
363.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify44.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	475	1013
1	1524	978
2	5001	970

prune400.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 22.4b

localize32.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
2.3b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
7.7b	(* x (pow n 2))
8.2b	(* (pow x 2) n)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
18×	`associate-l`
17×	`associate-*r/`
16×	`add-exp-log` `frac-add`
15×	`associate-r`
14×	`flip3-+` `flip-+`
12×	`add-cube-cbrt` `unpow-prod-down` `distribute-neg-frac`
10×	`frac-times` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`add-log-exp`
7×	`prod-exp` `distribute-lft-out`
6×	`pow1` `sqrt-prod`
4×	`unpow2` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-neg-in` `distribute-lft-in` `associate-*l/` `pow-exp` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-prod-down` `neg-log`

Counts

4 → 115

Calls

4 calls:

21.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
199.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
5.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series605.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
466.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
30.0ms	(* x (pow n 2))
21.0ms	(* (pow x 2) n)

simplify46.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	944	2456
1	5002	2289

prune657.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 22.3b

localize32.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
2.4b	(* (sqrt (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
7.7b	(* x (pow n 2))
8.2b	(* (pow x 2) n)

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
21×	`associate-l`
17×	`associate-*r/`
16×	`add-exp-log` `frac-add`
15×	`associate-r`
14×	`flip3-+` `sqrt-prod` `flip-+`
13×	`add-cube-cbrt`
12×	`unpow-prod-down` `sqrt-div` `distribute-neg-frac`
10×	`frac-times` `add-cbrt-cube` `unswap-sqr`
8×	`add-log-exp`
7×	`prod-exp` `distribute-lft-out`
6×	`pow1`
4×	`unpow2` `sqr-pow`
3×	`*-commutative` `cbrt-unprod`
2×	`distribute-rgt-in` `pow-to-exp` `associate-+l+` `distribute-neg-in` `distribute-lft-in` `associate-*l/` `pow-exp` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `pow-prod-down` `neg-log`

Counts

4 → 119

Calls

4 calls:

24.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
189.0ms	(* (sqrt (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
6.0ms	(* x (pow n 2))
6.0ms	(* (pow x 2) n)

series892.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x))
755.0ms	(* (sqrt (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
30.0ms	(* x (pow n 2))
18.0ms	(* (pow x 2) n)

simplify150.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	955	2765
1	4672	2603
2	5001	2598

prune707.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 22.3b

regimes318.0ms

Accuracy

83% (1.5b remaining)

Error of 21.6b against oracle of 20.1b and baseline of 29.0b

bsearch220.0ms

Steps

Iters	Range		Point
8	214.50772926448735	166023.53156923671	163568.2823176695
11	-5516994550455459.0	-0.0002940191646985452	-119271701237.4661

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	54
1	68	54
2	72	54
3	72	54

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	3140×	body	1280	valid
525.0ms	1501×	body	640	valid
251.0ms	4669×	body	80	valid
204.0ms	891×	body	320	valid
191.0ms	5033×	body	80	nan
161.0ms	171×	body	1280	nan
132.0ms	2291×	body	80	overflowed
113.0ms	232×	body	640	nan
63.0ms	457×	body	160	valid
37.0ms	156×	body	320	nan
11.0ms	87×	body	160	nan