Details

sample95.0ms

Algorithm

intervals

Results

47.0ms	129×	body	10240	exit
16.0ms	198×	body	80	valid
8.0ms	122×	body	80	overflowed
4.0ms	26×	body	320	valid
4.0ms	15×	body	640	valid
2.0ms	19×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	21	9
1	52	9
2	113	9
3	240	8
4	1625	8
5	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
0.0b	(/ x (+ wj 1))
4.6b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
175×	`times-frac`
129×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
72×	`prod-diff`
52×	`distribute-lft-out`
24×	`associate-/l*`
20×	`associate-/r/`
13×	`add-cbrt-cube`
11×	`add-exp-log` `flip3-+` `associate-/r*` `flip-+` `div-inv`
9×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
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 → 260

Calls

4 calls:

7.0ms	(/ wj (+ wj 1))
12.0ms	(/ (/ x (+ wj 1)) (exp wj))
5.0ms	(/ x (+ wj 1))
404.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ wj (+ wj 1))
39.0ms	(/ (/ x (+ wj 1)) (exp wj))
26.0ms	(/ x (+ wj 1))
54.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify123.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1015	4090
1	4555	3249
2	5001	3243

prune512.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`fma-neg` `prod-diff`
3×	`expm1-log1p-u` `fma-def` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
2×	`diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate-r` `associate--l+` `*-commutative` `flip--` `flip-+`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ x (pow wj 2))
47.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms	(* 2 (* wj x))

series81.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ x (pow wj 2))
29.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
22.0ms	(* 2 (* wj x))

simplify37.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	237	340
1	926	292
2	5001	274

prune144.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (fma wj wj x) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `associate--l+` `*-commutative` `flip--` `fma-udef`

Counts

2 → 41

Calls

2 calls:

3.0ms	(- (fma wj wj x) (* 2 (* wj x)))
8.0ms	(* 2 (* wj x))

series47.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(- (fma wj wj x) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify133.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	185	232
1	729	206
2	4842	196
3	5001	191

prune94.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

38.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
5.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
324.0ms	(cbrt (+ x (pow wj 2)))
318.0ms	(cbrt (+ x (pow wj 2)))
318.0ms	(cbrt (+ x (pow wj 2)))

simplify169.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	259	918
1	988	867
2	4915	790
3	5001	790

prune299.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

regimes84.0ms

Accuracy

63.8% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 2.4b

bsearch46.0ms

Steps

Iters	Range		Point
8	2.921432904961236e-10	1.5703764843175337e-06	9.06252678575456e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3816×	body	10240	exit
433.0ms	6236×	body	80	valid
239.0ms	3757×	body	80	overflowed
142.0ms	822×	body	320	valid
117.0ms	480×	body	640	valid
69.0ms	548×	body	160	valid