Details

sample51.0ms

Algorithm

intervals

Results

10.0ms	139×	body	160	valid
10.0ms	529×	pre	80	true
9.0ms	273×	body	80	nan
4.0ms	117×	body	80	valid

simplify11.0ms

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: 27.7b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
27.7b	(+ (- 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)))
8.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
6.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify140.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (134.0ms)

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

prune92.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	3	43

Merged error: 0.3b

Counts

43 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (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) (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))
6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series507.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (- 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))
44.0ms	(- (* b b) (* (* 4.0 a) c))
195.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (34.0ms)

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

prune168.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	44	10	54
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.0b

Counts

57 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 38

Calls

4 calls:

5.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(/ (- (fma (* 4.0 c) a 0)) (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ b (sqrt (- (* b b) (* (* 4.0 a) c))))
92.0ms	(* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
191.0ms	(/ (- (fma (* 4.0 c) a 0)) (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))

simplify39.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	341	422
1	1164	387
2	5001	372

prune159.0ms

Filtered

50 candidates to 37 candidates (74.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	52	8	60

Merged error: 0.0b

Counts

60 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
0.4b	(* (/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) (/ (fma (* 4.0 c) a 0) 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-commutative`
15×	`frac-times`
12×	`clear-num`
11×	`frac-2neg` `associate-*l/`
10×	`associate-/r*`
8×	`prod-diff`
7×	`associate-l`
4×	`associate-/r/`
3×	`flip3-+` `associate-*r/` `flip-+` `div-inv`
2×	`fma-neg`
1×	`sub-neg` `flip3--` `associate-r` `un-div-inv` `flip--`

Counts

4 → 53

Calls

4 calls:

6.0ms	(* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
10.0ms	(* (/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) (/ (fma (* 4.0 c) a 0) 2.0))

series395.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)
49.0ms	(- (* b b) (* (* 4.0 a) c))
118.0ms	(/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a))
141.0ms	(* (/ -1 (* (+ b (sqrt (- (* b b) (* (* 4.0 a) c)))) a)) (/ (fma (* 4.0 c) a 0) 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	471	544
1	1915	498
2	5001	492

prune177.0ms

Filtered

65 candidates to 50 candidates (76.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	65	8	73

Merged error: 0.0b

Counts

73 → 8

regimes122.0ms

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	25	12
1	29	12
2	34	12
3	34	12

end0.0ms

sample1.4s

Algorithm

intervals

Results

334.0ms	4450×	body	160	valid
315.0ms	8870×	body	80	nan
309.0ms	16870×	pre	80	true
137.0ms	3550×	body	80	valid