Details

sample70.0ms

Algorithm

intervals

Results

43.0ms	232×	body	10240	exit
6.0ms	198×	body	80	valid
3.0ms	29×	body	320	valid
2.0ms	16×	body	640	valid
1.0ms	17×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (+ wj 1))
0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
5.4b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite527.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

10.0ms	(/ x (+ wj 1))
10.0ms	(/ wj (+ wj 1))
23.0ms	(/ (/ x (+ wj 1)) (exp wj))
477.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series151.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ x (+ wj 1))
24.0ms	(/ wj (+ wj 1))
41.0ms	(/ (/ x (+ wj 1)) (exp wj))
62.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify86.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5001	1469

prune427.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate-r` `associate--l+` `sum-log` `*-commutative` `flip--`

Counts

2 → 32

Calls

2 calls:

72.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
15.0ms	(* 2 (* wj x))

series52.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
20.0ms	(* 2 (* wj x))

simplify128.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	162	196
1	645	179
2	3837	177
3	5001	177

prune68.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (* (exp wj) (+ wj 1)))
0.0b	(/ wj (+ wj 1))
0.0b	(* (exp wj) (+ wj 1))
5.4b	(- (+ (/ x (* (exp wj) (+ wj 1))) wj) (/ wj (+ wj 1)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

32×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`times-frac`
13×	`add-cbrt-cube`
11×	`add-exp-log`
9×	`add-log-exp`
6×	`pow1` `distribute-lft-out` `associate-/l*`
5×	`associate-/r*`
4×	`flip3-+` `associate-r/` `associate-r*` `associate-/r/` `flip-+`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`frac-2neg` `diff-log` `prod-exp` `clear-num` `frac-sub` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/ x (* (exp wj) (+ wj 1)))
11.0ms	(/ wj (+ wj 1))
24.0ms	(* (exp wj) (+ wj 1))
249.0ms	(- (+ (/ x (* (exp wj) (+ wj 1))) wj) (/ wj (+ wj 1)))

series160.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ x (* (exp wj) (+ wj 1)))
21.0ms	(/ wj (+ wj 1))
37.0ms	(* (exp wj) (+ wj 1))
59.0ms	(- (+ (/ x (* (exp wj) (+ wj 1))) wj) (/ wj (+ wj 1)))

simplify66.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	493	762
1	2288	711
2	5001	708

prune235.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (- (+ x (pow wj 2)) (* 2 (* wj x))))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))
3.2b	(exp (log (- (+ x (pow wj 2)) (* 2 (* wj x)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-exp-log`
9×	`add-cbrt-cube` `add-log-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`log-prod`
4×	`log-div` `exp-prod`
3×	`flip3--` `associate-l` `exp-sum` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`exp-diff` `diff-log` `log-pow`
1×	`sub-neg` `rem-log-exp` `associate-r` `associate--l+` `sum-log` `*-commutative` `rem-exp-log`

Counts

4 → 63

Calls

4 calls:

40.0ms	(log (- (+ x (pow wj 2)) (* 2 (* wj x))))
71.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
15.0ms	(* 2 (* wj x))
44.0ms	(exp (log (- (+ x (pow wj 2)) (* 2 (* wj x)))))

series225.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(log (- (+ x (pow wj 2)) (* 2 (* wj x))))
31.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
23.0ms	(* 2 (* wj x))
32.0ms	(exp (log (- (+ x (pow wj 2)) (* 2 (* wj x)))))

simplify156.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	265	556
1	927	502
2	4911	487
3	5001	487

prune135.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

regimes62.0ms

Accuracy

67.7% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.1b

bsearch39.0ms

Steps

Iters	Range		Point
10	3.2716599026957865e-16	2.5556453819330236	4.160404689641217e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s	7548×	body	10240	exit
187.0ms	6299×	body	80	valid
78.0ms	793×	body	320	valid
70.0ms	489×	body	640	valid
32.0ms	493×	body	160	valid