Details

sample39.0ms

Algorithm

intervals

Results

19.0ms	285×	body	80	valid
5.0ms	103×	body	80	nan

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	18

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: 20.2b

Counts

2 → 1

localize111.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqrt-div`
3×	`flip3--` `flip--`
2×	`neg-sub0` `neg-mul-1` `pow1/2`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `fma-def` `flip3-+` `fma-neg` `flip-+`

Counts

4 → 17

Calls

4 calls:

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

series288.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	190	252
1	754	228
2	3077	213
3	5001	210

prune132.0ms

Filtered

29 candidates to 28 candidates (96.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	4	30

Merged error: 7.4b

Counts

30 → 4

localize115.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(/ (* a c) b)
4.6b	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 22

Calls

4 calls:

6.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (* a c) b)
9.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* a c) b)
78.0ms	(/ (- (* 2.0 (/ (* a c) b)) (* 2 b)) (* 2.0 a))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify35.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	288	221
1	1124	206
2	5001	198

prune128.0ms

Filtered

34 candidates to 28 candidates (82.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	34	4	38

Merged error: 6.6b

Counts

38 → 4

localize111.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

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

series352.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (* 2.0 c) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
42.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	277	339
1	953	308
2	3782	295
3	5001	293

prune144.0ms

Filtered

42 candidates to 29 candidates (69.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	38	4	42
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	39	7	46

Merged error: 6.5b

Counts

46 → 7

localize117.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(/ (* a c) b)
4.8b	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
23.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/l*`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `associate-/r/` `*-commutative` `flip--` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `fma-def` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 20

Calls

4 calls:

5.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(/ (* a c) b)
9.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
18.0ms	(/ (* a c) b)
97.0ms	(/ (* 2.0 c) (- (* 2.0 (/ (* a c) b)) (* 2 b)))
68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	246	186
1	974	173
2	4457	166
3	5001	163

prune108.0ms

Filtered

32 candidates to 27 candidates (84.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	30	2	32
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	32	7	39

Merged error: 6.1b

Counts

39 → 7

regimes197.0ms

Accuracy

94.9% (0.8b remaining)

Error of 6.4b against oracle of 5.6b and baseline of 21.3b

bsearch203.0ms

Steps

Iters	Range	Point
6	2.066422626357648e+110	1.9801395410105552e+111	5.814135232525877e+110
5	-9.356784633994376e-254	-2.6224388913309515e-254	-2.6712931574782514e-254
8	-2.083222696695489e+156	-8.927571262924557e+151	-1.3324370156406744e+154

Iters

Range

Point

2.066422626357648e+110

1.9801395410105552e+111

5.814135232525877e+110

-9.356784633994376e-254

-2.6224388913309515e-254

-2.6712931574782514e-254

-2.083222696695489e+156

-8.927571262924557e+151

-1.3324370156406744e+154

simplify17.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	92
1	88	92
2	90	92
3	119	92
4	153	92
5	164	92
6	185	92
7	207	92
8	217	92
9	226	92
10	230	92
11	237	92
12	250	92
13	260	92
14	274	92
15	324	92
16	351	92
17	371	92
18	392	92
19	426	92
20	433	92
21	433	92

end0.0ms

sample826.0ms

Algorithm

intervals

Results

447.0ms	8745×	body	80	valid
133.0ms	2855×	body	80	nan

Iter	Nodes	Cost
0	80	92
1	88	92
2	90	92
3	119	92
4	153	92
5	164	92
6	185	92
7	207	92
8	217	92
9	226	92
10	230	92
11	237	92
12	250	92
13	260	92
14	274	92
15	324	92
16	351	92
17	371	92
18	392	92
19	426	92
20	433	92
21	433	92

Iter	Nodes	Cost
0	80	92
1	88	92
2	90	92
3	119	92
4	153	92
5	164	92
6	185	92
7	207	92
8	217	92
9	226	92
10	230	92
11	237	92
12	250	92
13	260	92
14	274	92
15	324	92
16	351	92
17	371	92
18	392	92
19	426	92
20	433	92
21	433	92

Iter	Nodes	Cost
0	80	92
1	88	92
2	90	92
3	119	92
4	153	92
5	164	92
6	185	92
7	207	92
8	217	92
9	226	92
10	230	92
11	237	92
12	250	92
13	260	92
14	274	92
15	324	92
16	351	92
17	371	92
18	392	92
19	426	92
20	433	92
21	433	92