Details

sample49.0ms

Algorithm

intervals

Results

17.0ms	257×	body	80	valid
5.0ms	11×	body	640	valid
5.0ms	83×	body	80	overflowed
3.0ms	4×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.8b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.8b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series126.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
60.0ms	(- (log (+ 1.0 (exp x))) (* x y))
59.0ms	(log (+ 1.0 (exp x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune110.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.5b

Counts

55 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 (exp x)))
0.0b	(sqrt (+ 1.0 (exp x)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`*-un-lft-identity`
16×	`sqrt-prod`
14×	`log-prod`
12×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt`
8×	`sqrt-div`
6×	`add-exp-log` `log-pow`
4×	`log-div` `sqrt-pow1` `flip3-+` `pow1/2` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
2×	`rem-sqrt-square` `rem-log-exp`

Counts

4 → 72

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 (exp x)))
3.0ms	(sqrt (+ 1.0 (exp x)))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (+ 1.0 (exp x)))
30.0ms	(sqrt (+ 1.0 (exp x)))
106.0ms	(log (sqrt (+ 1.0 (exp x))))
125.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	162	564
1	453	528
2	1549	508
3	5001	496

prune200.0ms

Filtered

84 candidates to 60 candidates (71.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	84	4	88

Merged error: 0.5b

Counts

88 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
7.6b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

5.0ms	(* 1/2 (pow x 2))
8.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
6.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/2 (pow x 2))
76.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
17.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
54.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune174.0ms

Filtered

83 candidates to 61 candidates (73.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.5b

Counts

87 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (pow x 2) (sqrt 2.0))
0.5b	(/ x (sqrt 2.0))
1.4b	(log (sqrt (+ 1.0 (exp x))))
8.2b	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
56×	`*-un-lft-identity`
54×	`add-sqr-sqrt` `add-cube-cbrt`
43×	`sqrt-prod`
21×	`unpow-prod-down`
13×	`add-exp-log`
12×	`associate-/r*`
11×	`associate-/l*`
10×	`log-prod`
8×	`add-cbrt-cube`
7×	`pow1` `unpow2` `sqr-pow`
6×	`log-div`
4×	`div-exp` `log-pow` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `associate-*r/` `rem-log-exp` `frac-add` `clear-num` `div-inv`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `distribute-lft-out`

Counts

4 → 151

Calls

4 calls:

6.0ms	(/ (pow x 2) (sqrt 2.0))
8.0ms	(/ x (sqrt 2.0))
4.0ms	(log (sqrt (+ 1.0 (exp x))))
8.0ms	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ (pow x 2) (sqrt 2.0))
67.0ms	(/ x (sqrt 2.0))
109.0ms	(log (sqrt (+ 1.0 (exp x))))
211.0ms	(log (+ (* 1/2 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 1/4 (/ 1/8 2.0))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	623	1438
1	2400	1267
2	5003	1254

prune721.0ms

Filtered

163 candidates to 100 candidates (61.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	162	5	167

Merged error: 0.5b

Counts

167 → 5

regimes88.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 12.2b

bsearch55.0ms

Steps

Iters	Range		Point
9	-5.855776674212404	-7.74497267090904e-05	-0.0008614003792471078

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	30
1	44	30

end0.0ms

sample898.0ms

Algorithm

intervals

Results

388.0ms	8391×	body	80	valid
102.0ms	2450×	body	80	overflowed
78.0ms	244×	body	640	valid
69.0ms	126×	body	1280	valid
37.0ms	198×	body	320	valid
11.0ms	99×	body	160	valid