Details

sample56.0ms

Algorithm

intervals

Results

13.0ms	300×	body	80	nan
10.0ms	556×	pre	80	true
10.0ms	140×	body	160	valid
4.0ms	116×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	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: 27.1b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
4×	`associate-l`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `fma-neg` `sqrt-div` `associate-/r*` `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 → 30

Calls

4 calls:

6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms	(- (* b b) (* (* 4.0 a) c))
106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify142.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	322	329
1	1151	301
2	4760	289
3	5001	287

prune94.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	4	43

Merged error: 0.4b

Counts

43 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.4b	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 42

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
7.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series502.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
193.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	360	567
1	1240	510
2	5001	474

prune180.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	41	13	54
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	45	13	58

Merged error: 0.0b

Counts

58 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

27×	`frac-times`
21×	`clear-num`
19×	`frac-2neg`
14×	`associate-/l/`
13×	`associate-/l*`
10×	`associate-/r/` `*-commutative`
9×	`associate-*r/`
8×	`prod-diff` `div-inv`
7×	`flip3--` `flip--`
5×	`associate-l`
4×	`un-div-inv`
3×	`fma-neg` `associate-*l/`
2×	`sub-neg`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `associate-r` `inv-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

series415.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) 2.0))

simplify63.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	487	850
1	1970	763
2	5002	755

prune246.0ms

Filtered

84 candidates to 52 candidates (61.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	86	11	97

Merged error: 0.0b

Counts

97 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (fma b b (- (* (* a c) 4.0))))
0.2b	(/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
0.3b	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
0.3b	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) 2.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

27×	`frac-times`
21×	`clear-num`
19×	`frac-2neg`
14×	`associate-/l/`
13×	`associate-/l*`
10×	`associate-/r/`
9×	`associate-*r/`
8×	`div-inv`
6×	`flip3--` `flip--`
4×	`un-div-inv`
3×	`associate-*l/`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `sub-neg` `pow1/2` `fma-neg` `associate-r` `associate-l` `*-commutative` `inv-pow`

Counts

4 → 59

Calls

4 calls:

1.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))
3.0ms	(/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
3.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
8.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) 2.0))

series474.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))
108.0ms	(/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
87.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
196.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	411	741
1	1548	664
2	5001	658

prune197.0ms

Filtered

71 candidates to 51 candidates (71.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	70	12	82

Merged error: 0.0b

Counts

82 → 12

regimes195.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	13
1	37	13
2	37	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

316.0ms	4497×	body	160	valid
302.0ms	16342×	pre	80	true
283.0ms	8342×	body	80	nan
124.0ms	3503×	body	80	valid