Details

sample43.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	198×	body	80	valid
6.0ms	103×	body	80	nan
4.0ms	22×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune2.0ms

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: 34.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `associate-/r*` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `pow1/2` `div-sub` `clear-num` `*-commutative` `div-inv`

Counts

4 → 19

Calls

4 calls:

7.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	269	246
1	985	235
2	3932	225
3	5002	224

prune94.0ms

Filtered

31 candidates to 27 candidates (87.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	24	7	31
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	7	32

Merged error: 6.1b

Counts

32 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`associate-/r*`
5×	`associate-*r/`
4×	`clear-num` `*-commutative`
3×	`frac-2neg`
2×	`flip3--` `sqrt-div` `associate-*l/` `un-div-inv` `flip--`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `pow1/2` `associate-r` `div-inv`

Counts

4 → 32

Calls

4 calls:

8.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
221.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	308	454
1	1355	434
2	5001	406

prune131.0ms

Filtered

44 candidates to 36 candidates (81.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 6.1b

Counts

51 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
0.2b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/l/`
2×	`neg-sub0` `associate-+l-` `flip3--` `frac-2neg` `flip3-+` `sqrt-div` `div-sub` `clear-num` `flip--` `flip-+` `div-inv`
1×	`+-commutative` `sub-neg` `pow1/2` `associate-/l*`

Counts

4 → 21

Calls

4 calls:

8.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
5.0ms	(- (* b b) (* (* 4.0 a) c))
5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) a)
44.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify130.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	277	245
1	991	233
2	4474	219
3	5002	219

prune86.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 6.1b

Counts

40 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ 1 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`frac-times`
11×	`clear-num`
10×	`frac-2neg`
8×	`associate-/l/`
5×	`flip3-+` `associate-*l/` `flip-+`
3×	`associate-*r/`
2×	`flip3--` `sqrt-div` `un-div-inv` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `pow1/2` `associate-r` `associate-l` `*-commutative`

Counts

4 → 39

Calls

4 calls:

9.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ 1 a))
5.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) 2.0) (/ 1 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	358	463
1	1504	432
2	5001	405

prune113.0ms

Filtered

51 candidates to 37 candidates (72.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	51	7	58

Merged error: 6.1b

Counts

58 → 7

regimes159.0ms

Accuracy

82.3% (5.0b remaining)

Error of 10.7b against oracle of 5.6b and baseline of 34.1b

bsearch104.0ms

Steps

Iters	Range		Point
9	6.997117448607536e-159	6.9825357345617866e-152	6.8956779722136e-152
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	32	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

255.0ms	1092×	body	2560	valid
228.0ms	5871×	body	80	valid
167.0ms	874×	body	1280	valid
106.0ms	2855×	body	80	nan
66.0ms	452×	body	640	valid
33.0ms	117×	body	5120	valid
24.0ms	224×	body	320	valid
8.0ms	115×	body	160	valid