Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	43×	body	2560	valid
7.0ms	171×	body	80	valid
7.0ms	38×	body	1280	valid
7.0ms	103×	body	80	nan
3.0ms	21×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 37.2b

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)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

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))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
42.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify110.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	274	267
1	960	259
2	3423	248
3	5001	247

prune294.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	26	7	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	7	34

Merged error: 5.9b

Counts

34 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.5b	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
165.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
199.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	356	497
1	1279	459
2	5001	441

prune147.0ms

Filtered

49 candidates to 45 candidates (91.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Merged error: 5.8b

Counts

56 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.9b	(/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
5.2b	(/ (/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c)) (* 2.0 a))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
20×	`associate-/r/`
15×	`*-commutative` `div-inv`
14×	`associate-/l/`
12×	`associate-/l*`
7×	`frac-2neg` `clear-num`
6×	`flip3--` `flip--`
4×	`associate-/r*`
2×	`sqrt-div`
1×	`sub-neg` `pow1/2`

Counts

4 → 55

Calls

4 calls:

6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
9.0ms	(/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
13.0ms	(/ (/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c)) (* 2.0 a))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series471.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
179.0ms	(/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c))
142.0ms	(/ (/ (* 4.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c)) (* 2.0 a))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	451	635
1	1593	574
2	5002	564

prune192.0ms

Filtered

67 candidates to 58 candidates (86.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Merged error: 5.8b

Counts

74 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.5b	(/ 1 (* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c) (/ 2.0 4.0)))
1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/r/`
15×	`frac-times`
12×	`clear-num`
11×	`frac-2neg`
8×	`associate-/l/`
7×	`flip3--` `flip--`
5×	`associate-*l/`
4×	`associate-/r*`
3×	`associate-*r/` `div-inv`
2×	`sub-neg` `sqrt-div`
1×	`pow1/2` `associate-r` `associate-l` `un-div-inv` `*-commutative` `inv-pow`

Counts

4 → 43

Calls

4 calls:

5.0ms	(- (* b b) (* 4.0 (* a c)))
12.0ms	(/ 1 (* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c) (/ 2.0 4.0)))
6.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series307.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(/ 1 (* (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) c) (/ 2.0 4.0)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	349	436
1	1437	401
2	5001	393

prune143.0ms

Filtered

55 candidates to 45 candidates (81.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	55	0	55
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	55	7	62

Merged error: 5.8b

Counts

62 → 7

regimes178.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.8b

bsearch137.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	1.703504653326294e+111
5	5.655525127217964e-251	1.9763919052369517e-250	5.949382726835493e-251
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3298367139250566e+153

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

1.703504653326294e+111

5.655525127217964e-251

1.9763919052369517e-250

5.949382726835493e-251

-2.083222696695489e+156

-8.927571262924557e+151

-1.3298367139250566e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

250.0ms	1094×	body	2560	valid
226.0ms	5866×	body	80	valid
170.0ms	878×	body	1280	valid
105.0ms	2855×	body	80	nan
72.0ms	481×	body	640	valid
30.0ms	106×	body	5120	valid
21.0ms	197×	body	320	valid
9.0ms	117×	body	160	valid