Details

sample90.0ms

Algorithm

intervals

Results

31.0ms	53×	body	1280	valid
22.0ms	309×	body	80	valid
9.0ms	31×	body	640	valid
4.0ms	58×	body	80	overflowed
4.0ms	20×	body	320	valid
2.0ms	12×	body	160	valid

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (34.0ms)

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: 26.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 eps) x)
0.0b	(exp (- (* (+ 1.0 eps) x)))
0.0b	(exp (- (* (- 1.0 eps) x)))
1.7b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

81×	`frac-sub`
74×	`exp-neg`
72×	`frac-times`
56×	`neg-sub0` `exp-diff`
38×	`associate-*l/`
36×	`associate-*r/`
29×	`flip3--` `flip--`
27×	`flip3-+` `flip-+`
18×	`un-div-inv`
12×	`add-sqr-sqrt` `exp-prod`
10×	`*-un-lft-identity` `add-log-exp`
8×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-l`
4×	`rem-exp-log`
3×	`associate-r`
2×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `neg-log`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

6.0ms	(* (- 1.0 eps) x)
3.0ms	(exp (- (* (+ 1.0 eps) x)))
3.0ms	(exp (- (* (- 1.0 eps) x)))
16.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- 1.0 eps) x)
26.0ms	(exp (- (* (+ 1.0 eps) x)))
26.0ms	(exp (- (* (- 1.0 eps) x)))
232.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify135.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	1175	3668
1	4323	3407
2	5001	3396

prune348.0ms

Filtered

161 candidates to 82 candidates (50.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Merged error: 0.3b

Counts

162 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

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)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(* 0.6666666666666667 (pow x 3))
39.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	207	270
1	894	242
2	5002	238

prune97.0ms

Filtered

51 candidates to 31 candidates (60.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.3b

Counts

54 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
0.5b	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
7.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
12.4b	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

6.0ms	(* 0.6666666666666667 (pow x 3))
8.0ms	(exp (log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))))
7.0ms	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 0.6666666666666667 (pow x 3))
40.0ms	(exp (log (- (+ (* 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)))
87.0ms	(log (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	330	694
1	1352	629
2	5002	603

prune209.0ms

Filtered

88 candidates to 58 candidates (65.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	87	5	92

Merged error: 0.3b

Counts

92 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

7.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
7.8b	(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))
12.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
12.7b	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

rewrite29.0ms

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:

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

series379.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (+ (* 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)))
149.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))
150.0ms	(cbrt (- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2))))

simplify128.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (23.0ms)

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

prune240.0ms

Filtered

66 candidates to 54 candidates (81.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	66	5	71

Merged error: 0.2b

Counts

71 → 5

regimes122.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.3b

bsearch137.0ms

Steps

Iters	Range		Point
9	3.220789993380391	25340457.240933813	173.79350790004767

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	60
1	62	60
2	62	60

end0.0ms

sample2.7s

Algorithm

intervals

Results

908.0ms	1763×	body	1280	valid
738.0ms	10034×	body	80	valid
411.0ms	1284×	body	640	valid
139.0ms	626×	body	320	valid
132.0ms	1874×	body	80	overflowed
43.0ms	303×	body	160	valid