Details

sample95.0ms

Algorithm

intervals

Results

33.0ms	66×	body	1280	valid
26.0ms	335×	body	80	valid
9.0ms	30×	body	640	valid
4.0ms	62×	body	80	overflowed
4.0ms	19×	body	320	valid
1.0ms	8×	body	160	valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (38.0ms)

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: 28.9b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b	(* (- 1.0 eps) x)
2.0b	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite62.0ms

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:

14.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
13.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
6.0ms	(* (- 1.0 eps) x)
17.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
50.0ms	(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
28.0ms	(* (- 1.0 eps) x)
193.0ms	(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify149.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (114.0ms)

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

prune409.0ms

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: 0.5b

Counts

186 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.6666666666666667 (pow x 3))
7.6b	(- (+ (* 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:

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

prune117.0ms

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: 0.5b

Counts

54 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 0.6666666666666667 x) x)
0.6b	(cbrt x)
0.7b	(pow (cbrt x) 3)
7.6b	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (* 0.6666666666666667 x) x)
1.0ms	(cbrt x)
3.0ms	(pow (cbrt x) 3)
11.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (* 0.6666666666666667 x) x)
176.0ms	(cbrt x)
232.0ms	(pow (cbrt x) 3)
55.0ms	(- (+ (* (* (* 0.6666666666666667 x) x) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))

simplify72.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	311	379
1	1784	317
2	5003	303

prune181.0ms

Filtered

85 candidates to 49 candidates (57.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0.5b

Counts

89 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

7.6b	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
36.2b	(cbrt (* (* 0.6666666666666667 x) x))
36.2b	(cbrt (* (* 0.6666666666666667 x) x))
36.2b	(cbrt (* (* 0.6666666666666667 x) x))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

16.0ms	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))
4.0ms	(cbrt (* (* 0.6666666666666667 x) x))

series728.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (+ (* (* (* (cbrt (* (* 0.6666666666666667 x) x)) (cbrt (* (* 0.6666666666666667 x) x))) (cbrt (* (* 0.6666666666666667 x) x))) (pow (cbrt x) 3)) 2.0) (* 1.0 (pow x 2)))
208.0ms	(cbrt (* (* 0.6666666666666667 x) x))
219.0ms	(cbrt (* (* 0.6666666666666667 x) x))
213.0ms	(cbrt (* (* 0.6666666666666667 x) x))

simplify191.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (185.0ms)

Iter	Nodes	Cost
0	145	548
1	596	474
2	4005	427
3	5001	391

prune158.0ms

Filtered

53 candidates to 39 candidates (73.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 0.5b

Counts

57 → 4

regimes83.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.4b

bsearch179.0ms

Steps

Iters	Range		Point
10	0.0031014677214056706	385601024814.3293	64.75935345485665

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	42
1	73	42
2	73	42

end0.0ms

sample2.6s

Algorithm

intervals

Results

892.0ms	1771×	body	1280	valid
693.0ms	10041×	body	80	valid
388.0ms	1250×	body	640	valid
138.0ms	1943×	body	80	overflowed
138.0ms	629×	body	320	valid
46.0ms	339×	body	160	valid