Details

sample282.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
7.0ms	198×	body	80	valid
5.0ms	23×	body	1280	valid
3.0ms	103×	body	80	nan
2.0ms	16×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	320	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	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: 34.2b

Counts

2 → 1

localize12.0ms

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))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

Calls

4 calls:

6.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
81.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify86.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	258	227
1	862	209
2	3117	196
3	5001	182

prune103.0ms

Filtered

36 candidates to 28 candidates (77.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Merged error: 6.1b

Counts

37 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b	(- (* b_2 b_2) (* a c))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 33

Calls

4 calls:

7.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify37.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	279	358
1	1113	309
2	5001	280

prune111.0ms

Filtered

45 candidates to 32 candidates (71.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	46	7	53

Merged error: 6.1b

Counts

53 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.5b	(* (/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
10.2b	(/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(* (/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
8.0ms	(/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms	(* (/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
166.0ms	(/ (+ 0 (* 1 (* a c))) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	434	489
1	2244	426
2	5003	423

prune154.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	57	8	65

Merged error: 6.0b

Counts

65 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.5b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (/ a 1))
23.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-/r/`
13×	`div-inv`
10×	`associate-/l/`
7×	`frac-2neg` `clear-num`
6×	`times-frac` `associate-/l*`
5×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sqrt-div`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `sub-neg` `pow1/2` `fma-neg`

Counts

4 → 41

Calls

4 calls:

5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
9.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (/ a 1))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
177.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
149.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) (/ a 1))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	385	426
1	1566	372
2	5001	357

prune128.0ms

Filtered

53 candidates to 46 candidates (86.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	3	4
Picked	0	1	1
Done	0	3	3
Total	53	8	61

Merged error: 6.0b

Counts

61 → 8

regimes222.0ms

Accuracy

90.4% (2.7b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 34.0b

bsearch88.0ms

Steps

Iters	Range	Point
4	2.3845199923604579e-23	4.11746385148662e-23	4.055107544394889e-23
5	-7.993878766881022e-170	-2.689985920497121e-170	-2.8947243902888692e-170
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

Iters

Range

Point

2.3845199923604579e-23

4.11746385148662e-23

4.055107544394889e-23

-7.993878766881022e-170

-2.689985920497121e-170

-2.8947243902888692e-170

-2.083222696695489e+156

-8.927571262924557e+151

-1.3324370156406744e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	43	24
2	43	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

225.0ms	1094×	body	2560	valid
203.0ms	5873×	body	80	valid
140.0ms	877×	body	1280	valid
90.0ms	2851×	body	80	nan
66.0ms	453×	body	640	valid
31.0ms	117×	body	5120	valid
21.0ms	221×	body	320	valid
7.0ms	113×	body	160	valid