Details

sample47.0ms

Algorithm

intervals

Results

19.0ms	110×	body	10240	exit
8.0ms	196×	body	80	valid
3.0ms	35×	body	320	valid
3.0ms	101×	body	80	overflowed
1.0ms	9×	body	640	valid
1.0ms	21×	body	160	valid

simplify47.0ms

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: 14.9b

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))
5.6b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite436.0ms

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:

5.0ms	(/ x (+ wj 1))
5.0ms	(/ wj (+ wj 1))
12.0ms	(/ (/ x (+ wj 1)) (exp wj))
401.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ x (+ wj 1))
22.0ms	(/ wj (+ wj 1))
38.0ms	(/ (/ x (+ wj 1)) (exp wj))
56.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify122.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (89.0ms)

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

prune511.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

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:

49.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
5.0ms	(+ x (pow wj 2))
6.0ms	(* 2 (* wj x))

series78.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
28.0ms	(+ x (pow wj 2))
19.0ms	(* 2 (* wj x))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

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

prune141.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 1 (fma wj wj x)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 38

Calls

2 calls:

3.0ms	(- (* 1 (fma wj wj x)) (* 2 (* wj x)))
6.0ms	(* 2 (* wj x))

series45.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (* 1 (fma wj wj x)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify38.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	199	225
1	871	190
2	5001	182

prune88.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))) (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))))
0.6b	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
0.6b	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
0.6b	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
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 → 95

Calls

4 calls:

18.0ms	(* (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))) (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))))
2.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
2.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
2.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))

series639.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))) (cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x)))))
154.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
157.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))
160.0ms	(cbrt (- (* 1 (fma wj wj x)) (* 2 (* wj x))))

simplify55.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	247	1441
1	1007	1340
2	5001	1261

prune288.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

regimes71.0ms

Accuracy

70.2% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.3b

bsearch34.0ms

Steps

Iters	Range		Point
8	9.879933556960907e-10	4.7559785702882385e-07	9.60333635941626e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	28	13
2	28	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

705.0ms	3896×	body	10240	exit
194.0ms	6350×	body	80	valid
106.0ms	3898×	body	80	overflowed
70.0ms	763×	body	320	valid
67.0ms	437×	body	640	valid
32.0ms	536×	body	160	valid