Details

sample90.0ms

Algorithm

intervals

Results

26.0ms	48×	body	1280	valid
22.0ms	326×	body	80	valid
14.0ms	35×	body	640	valid
6.0ms	26×	body	320	valid
5.0ms	73×	body	80	overflowed
1.0ms	6×	body	160	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (35.0ms)

Iter	Nodes	Cost
0	46	16
1	122	16
2	347	16
3	1295	16
4	5001	15

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 26.5b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.2b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.2b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.2b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
80×	`exp-neg` `frac-times`
60×	`neg-sub0` `exp-diff`
42×	`associate-*l/`
40×	`associate-*r/`
32×	`flip3--` `flip--`
30×	`flip3-+` `flip-+`
23×	`add-sqr-sqrt`
20×	`un-div-inv`
16×	`*-un-lft-identity`
15×	`associate-l`
10×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
9×	`associate-r`
8×	`add-exp-log`
6×	`add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `difference-of-squares` `unswap-sqr`
2×	`distribute-lft-out--`
1×	`sub-neg` `times-frac` `diff-log` `distribute-lft-out`

Counts

4 → 173

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
12.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
16.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
18.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series310.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- 1.0 eps) x)
45.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
49.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
186.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify150.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	1253	4065
1	4712	3787
2	5001	3778

prune404.0ms

Filtered

185 candidates to 95 candidates (51.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	183	3	186

Merged error: 0.6b

Counts

186 → 3

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log` `add-log-exp`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `diff-log` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `unpow3` `pow-exp` `associate--l+` `sum-log` `*-commutative` `flip--` `cbrt-unprod`

Counts

2 → 45

Calls

2 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* 0.6666666666666667 (pow x 3))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify36.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	207	273
1	894	245
2	5002	241

prune94.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	49	5	54

Merged error: 0.6b

Counts

54 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

3.3b	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
3.3b	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate--l+` `sum-log`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
11.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series186.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
52.0ms	(sqrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
41.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
37.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify106.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	171	690
1	611	636
2	3106	618
3	5003	616

prune193.0ms

Filtered

70 candidates to 52 candidates (74.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	70	5	75

Merged error: 0.6b

Counts

75 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
8.0b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
11.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
11.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `diff-log` `add-cbrt-cube` `flip--`
2×	`sub-neg` `pow1/3` `associate--l+` `sum-log`

Counts

4 → 54

Calls

4 calls:

8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
8.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
7.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
38.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
147.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
148.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify133.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	252	862
1	905	800
2	4257	736
3	5002	736

prune257.0ms

Filtered

66 candidates to 54 candidates (81.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	66	5	71

Merged error: 0.6b

Counts

71 → 5

regimes85.0ms

Accuracy

96.4% (0.6b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.0b

bsearch127.0ms

Steps

Iters	Range		Point
8	1.3894494120209264	554.8082141746271	192.56282467869

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	25
1	58	25
2	58	25

end0.0ms

sample2.6s

Algorithm

intervals

Results

888.0ms	1722×	body	1280	valid
710.0ms	10009×	body	80	valid
414.0ms	1310×	body	640	valid
142.0ms	649×	body	320	valid
136.0ms	1910×	body	80	overflowed
44.0ms	316×	body	160	valid

Details

sample90.0ms

simplify37.0ms

prune6.0ms

localize17.0ms

rewrite64.0ms

series310.0ms

simplify150.0ms

prune404.0ms

localize14.0ms

rewrite15.0ms

series78.0ms

simplify36.0ms

prune94.0ms

localize12.0ms

rewrite33.0ms

series186.0ms

simplify106.0ms

prune193.0ms

localize17.0ms

rewrite30.0ms

series374.0ms

simplify133.0ms

prune257.0ms

regimes85.0ms

bsearch127.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling