Details

sample51.0ms

Algorithm

intervals

Results

12.0ms	45×	body	2560	valid
9.0ms	196×	body	80	valid
7.0ms	23×	body	1280	valid
4.0ms	96×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

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: 35.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
85.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune183.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	65	7	72
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	8	73

Merged error: 13.9b

Counts

73 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
5.1b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.9b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
159.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
190.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune435.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	151	9	160
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	154	14	168

Merged error: 12.8b

Counts

168 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

14.0b	(cbrt (+ 0 (* 3.0 (* a c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (+ 0 (* 3.0 (* a c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
75.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
79.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	259	543
1	1000	516
2	5002	500

prune383.0ms

Filtered

70 candidates to 64 candidates (91.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	70	14	84

Merged error: 12.8b

Counts

84 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
5.0b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
8.9b	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 3.0 a) c))
158.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
188.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	682	1937
1	4416	1476
2	5002	1435

prune274.0ms

Filtered

122 candidates to 81 candidates (66.4%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	4	8	12
Picked	1	0	1
Done	0	1	1
Total	121	15	136

Merged error: 12.5b

Counts

136 → 15

regimes479.0ms

Accuracy

92.2% (1.7b remaining)

Error of 13.1b against oracle of 11.4b and baseline of 32.7b

bsearch258.0ms

Steps

Iters	Range	Point
9	4.136575721607635e+152	2.0850798451966124e+158	1.2300615712489121e+154
9	7.726796297099125e-115	1.9456244798947194e-105	8.71285355682513e-110
9	-3.1093417089968686e+156	-2.796615923212647e+151	-1.3570665871440235e+154

Iters

Range

Point

4.136575721607635e+152

2.0850798451966124e+158

1.2300615712489121e+154

7.726796297099125e-115

1.9456244798947194e-105

8.71285355682513e-110

-3.1093417089968686e+156

-2.796615923212647e+151

-1.3570665871440235e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	66
1	62	66
2	62	66

end0.0ms

sample1.6s

Algorithm

intervals

Results

411.0ms	913×	body	1280	valid
305.0ms	1122×	body	2560	valid
281.0ms	5735×	body	80	valid
135.0ms	2828×	body	80	nan
93.0ms	498×	body	640	valid
32.0ms	98×	body	5120	valid
29.0ms	222×	body	320	valid
10.0ms	116×	body	160	valid

Details

sample51.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite22.0ms

series231.0ms

simplify47.0ms

prune183.0ms

localize19.0ms

rewrite43.0ms

series470.0ms

simplify120.0ms

prune435.0ms

localize28.0ms

rewrite16.0ms

series335.0ms

simplify55.0ms

prune383.0ms

localize20.0ms

rewrite42.0ms

series467.0ms

simplify128.0ms

prune274.0ms

regimes479.0ms

bsearch258.0ms

simplify3.0ms

end0.0ms

sample1.6s

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