Details

sample47.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	185×	body	80	valid
6.0ms	17×	body	640	valid
5.0ms	25×	body	1280	valid
4.0ms	97×	body	80	nan
2.0ms	7×	body	5120	valid
1.0ms	7×	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: 34.8b

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))
1.0b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.9b	(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)))
6.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
46.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify121.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (115.0ms)

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

prune132.0ms

Filtered

44 candidates to 31 candidates (70.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	36	8	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	8	45

Merged error: 5.8b

Counts

45 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
3.3b	(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
10.2b	(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 39

Calls

4 calls:

6.0ms	(- (* b b) (* 4.0 (* a c)))
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))))

series611.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* 4.0 (* a c)))
255.0ms	(/ (/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
230.0ms	(/ (fma a (* 4.0 c) 0) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify38.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	349	505
1	1124	464
2	5001	434

prune330.0ms

Filtered

51 candidates to 37 candidates (72.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	5	51
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	51	8	59

Merged error: 5.7b

Counts

59 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
15.3b	(/ (fma a (* 4.0 c) 0) a)
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

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:

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

series236.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
45.0ms	(- (* b b) (* 4.0 (* a c)))
42.0ms	(/ (fma a (* 4.0 c) 0) a)
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify91.0ms

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

prune97.0ms

Filtered

36 candidates to 20 candidates (55.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

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

Merged error: 5.7b

Counts

44 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
0.8b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
1.0b	(- (* b b) (* 4.0 (* a c)))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (* 4.0 c) (/ (/ 1 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
78.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
48.0ms	(- (* b b) (* 4.0 (* a c)))
73.0ms	(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

prune106.0ms

Filtered

50 candidates to 31 candidates (62.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	49	1	50
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	50	7	57

Merged error: 5.7b

Counts

57 → 7

regimes167.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.5b

bsearch187.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.0673291895585486e+103
11	1.8145151230270015e-269	9.272403512084269e-250	2.4192404254399383e-264
6	-1.2994787762702041e+157	-3.0529494422842112e+156	-3.0812943354752785e+156

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.0673291895585486e+103

1.8145151230270015e-269

9.272403512084269e-250

2.4192404254399383e-264

-1.2994787762702041e+157

-3.0529494422842112e+156

-3.0812943354752785e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	24
1	45	24

end0.0ms

sample1.2s

Algorithm

intervals

Results

253.0ms	1054×	body	2560	valid
243.0ms	5924×	body	80	valid
179.0ms	898×	body	1280	valid
111.0ms	2939×	body	80	nan
66.0ms	438×	body	640	valid
33.0ms	113×	body	5120	valid
23.0ms	199×	body	320	valid
10.0ms	131×	body	160	valid