Details

sample48.0ms

Algorithm

intervals

Results

10.0ms	43×	body	2560	valid
7.0ms	38×	body	1280	valid
7.0ms	171×	body	80	valid
7.0ms	21×	body	640	valid
4.0ms	103×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	9
1	65	9
2	121	9
3	151	9
4	160	9
5	164	9
6	164	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: 37.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

8.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
5.0ms	(- (* b b) (* 4.0 (* a c)))
5.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series282.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
43.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify132.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	325	356
1	1145	329
2	4433	316
3	5001	314

prune120.0ms

Filtered

44 candidates to 31 candidates (70.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	7	45

Merged error: 5.9b

Counts

45 → 7

localize193.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.2b	(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.5b	(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 29

Calls

4 calls:

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

series603.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
238.0ms	(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
214.0ms	(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	330	431
1	1057	398
2	5001	364

prune140.0ms

Filtered

41 candidates to 37 candidates (90.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	40	8	48

Merged error: 5.8b

Counts

48 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
15.1b	(/ (fma a (* 4.0 c) 0) a)
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 24

Calls

4 calls:

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
41.0ms	(/ (fma a (* 4.0 c) 0) a)
68.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify92.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	213	237
1	714	224
2	2955	216
3	5001	216

prune88.0ms

Filtered

36 candidates to 20 candidates (55.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	37	7	44

Merged error: 5.8b

Counts

44 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.2b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
9×	`associate-*r/`
8×	`prod-diff`
5×	`associate-r` `associate-/l/`
4×	`flip3--` `clear-num` `un-div-inv` `flip--` `associate-/l*`
3×	`div-inv`
2×	`sub-neg` `frac-2neg` `fma-neg` `sqrt-div` `associate-l` `associate-/r/`
1×	`pow1/2`

Counts

4 → 38

Calls

4 calls:

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

series381.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
46.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	285	312
1	1032	290
2	5001	279

prune97.0ms

Filtered

50 candidates to 31 candidates (62.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	49	8	57

Merged error: 5.8b

Counts

57 → 8

regimes197.0ms

Accuracy

96% (1.0b remaining)

Error of 6.5b against oracle of 5.6b and baseline of 29.7b

bsearch142.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	1.703504653326294e+111
5	5.655525127217964e-251	1.9763919052369517e-250	5.949382726835493e-251
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3298367139250566e+153

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

1.703504653326294e+111

5.655525127217964e-251

1.9763919052369517e-250

5.949382726835493e-251

-2.083222696695489e+156

-8.927571262924557e+151

-1.3298367139250566e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	26
1	47	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

255.0ms	1094×	body	2560	valid
228.0ms	5866×	body	80	valid
162.0ms	878×	body	1280	valid
105.0ms	2855×	body	80	nan
69.0ms	481×	body	640	valid
29.0ms	106×	body	5120	valid
21.0ms	197×	body	320	valid
9.0ms	117×	body	160	valid