Details

sample62.0ms

Algorithm

intervals

Results

13.0ms	117×	body	320	valid
12.0ms	257×	body	80	nan
10.0ms	513×	pre	80	true
6.0ms	82×	body	160	valid
2.0ms	12×	body	640	valid
2.0ms	45×	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: 49.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
24.4b	(+ (- 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))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
102.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
45.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify138.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (133.0ms)

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

prune86.0ms

Filtered

42 candidates to 30 candidates (71.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	3	43

Merged error: 0.1b

Counts

43 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* 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	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite30.0ms

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))))
6.0ms	(- (* 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))
9.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
175.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (34.0ms)

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

prune152.0ms

Filtered

54 candidates to 37 candidates (68.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	47	7	54
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	48	9	57

Merged error: 0.0b

Counts

57 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma b b (- (* (* a c) 4.0))))
0.1b	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
0.2b	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) (* 2.0 a))
0.2b	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 29

Calls

4 calls:

1.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))
3.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
5.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) (* 2.0 a))
3.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))

series534.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(sqrt (fma b b (- (* (* a c) 4.0))))
83.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
183.0ms	(/ (/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) (* 2.0 a))
189.0ms	(/ (fma (* 4.0 c) a 0) (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))

simplify95.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	284	458
1	846	410
2	4314	355
3	5001	354

prune147.0ms

Filtered

41 candidates to 36 candidates (87.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	42	8	50

Merged error: 0.0b

Counts

50 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (fma (* 4.0 c) a 0) a)
0.1b	(/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
0.1b	(- (- 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`
22×	`clear-num`
20×	`frac-2neg`
14×	`associate-/l/`
13×	`associate-/l*`
10×	`associate-/r/`
9×	`associate-*r/` `div-inv`
6×	`flip3--` `flip--`
4×	`un-div-inv`
3×	`associate-*l/`
1×	`associate--l-` `neg-sub0` `neg-mul-1` `sub-neg` `fma-neg` `associate-r` `associate-l` `*-commutative` `inv-pow`

Counts

4 → 61

Calls

4 calls:

2.0ms	(/ (fma (* 4.0 c) a 0) a)
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))

series409.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (fma (* 4.0 c) a 0) a)
110.0ms	(/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0))))))
84.0ms	(- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))
181.0ms	(* (/ (fma (* 4.0 c) a 0) a) (/ (/ 1 (- (- b) (sqrt (fma b b (- (* (* a c) 4.0)))))) 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	396	737
1	1505	661
2	5001	656

prune191.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	73	8	81

Merged error: 0.0b

Counts

81 → 8

regimes145.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	12
1	33	12
2	33	12

end0.0ms

sample1.6s

Algorithm

intervals

Results

396.0ms	3612×	body	320	valid
305.0ms	16024×	pre	80	true
275.0ms	8024×	body	80	nan
209.0ms	2923×	body	160	valid
70.0ms	493×	body	640	valid
35.0ms	972×	body	80	valid