Details

sample283.0ms

Algorithm

intervals

Results

8.0ms	44×	body	2560	valid
7.0ms	172×	body	80	valid
6.0ms	37×	body	1280	valid
3.0ms	103×	body	80	nan
3.0ms	21×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

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: 37.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`flip3--` `prod-diff` `flip--`
3×	`fma-neg`
2×	`associate--l-` `neg-sub0` `sub-neg` `sqrt-div` `div-sub` `associate-/l/`
1×	`neg-mul-1` `frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 26

Calls

4 calls:

7.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	246	245
1	802	232
2	2674	218
3	5001	204

prune107.0ms

Filtered

38 candidates to 29 candidates (76.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	30	8	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	8	39

Merged error: 6.1b

Counts

39 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.2b	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.5b	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 21

Calls

4 calls:

5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
203.0ms	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
198.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify97.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	274	231
1	855	221
2	3674	200
3	5001	200

prune102.0ms

Filtered

33 candidates to 29 candidates (87.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	28	5	33
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	32	9	41

Merged error: 6.0b

Counts

41 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.3b	(* (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
10.5b	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 34

Calls

4 calls:

5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(* (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
6.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
199.0ms	(* (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
198.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	328	300
1	1209	279
2	5001	272

prune120.0ms

Filtered

46 candidates to 35 candidates (76.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	4	46
Fresh	3	4	7
Picked	1	0	1
Done	1	0	1
Total	47	8	55

Merged error: 6.0b

Counts

55 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.1b	(/ (fma c a 0) a)
23.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`prod-diff`
3×	`flip3--` `flip--`
2×	`sub-neg` `fma-neg` `sqrt-div`
1×	`frac-2neg` `pow1/2` `clear-num` `div-inv`

Counts

4 → 20

Calls

4 calls:

5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(/ (fma c a 0) a)
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series191.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
28.0ms	(/ (fma c a 0) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify57.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	179	159
1	555	154
2	1941	146
3	5001	132

prune62.0ms

Filtered

32 candidates to 20 candidates (62.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	32	8	40

Merged error: 6.0b

Counts

40 → 8

regimes192.0ms

Accuracy

96.4% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.5b

bsearch103.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	1.703504653326294e+111
5	5.655525127217964e-251	1.9763919052369517e-250	6.3411928596588654e-251
8	-2.083222696695489e+156	-8.927571262924557e+151	-8.764892488422707e+153

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

1.703504653326294e+111

5.655525127217964e-251

1.9763919052369517e-250

6.3411928596588654e-251

-2.083222696695489e+156

-8.927571262924557e+151

-8.764892488422707e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	21
1	39	21

end0.0ms

sample993.0ms

Algorithm

intervals

Results

213.0ms	1098×	body	2560	valid
191.0ms	5864×	body	80	valid
138.0ms	877×	body	1280	valid
89.0ms	2851×	body	80	nan
58.0ms	480×	body	640	valid
25.0ms	106×	body	5120	valid
18.0ms	198×	body	320	valid
8.0ms	122×	body	160	valid