Details

sample47.0ms

Algorithm

intervals

Results

9.0ms	33×	body	2560	valid
8.0ms	185×	body	80	valid
5.0ms	25×	body	1280	valid
4.0ms	97×	body	80	nan
3.0ms	4×	body	160	valid
3.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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

localize12.0ms

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))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 21

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

series305.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
47.0ms	(- (* b b) (* 4.0 (* a c)))
81.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify102.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	274	267
1	960	259
2	3423	248
3	5001	247

prune114.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	25	8	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	8	34

Merged error: 5.8b

Counts

34 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 37

Calls

4 calls:

5.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series505.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* 4.0 (* a c)))
174.0ms	(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
213.0ms	(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
71.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	340	495
1	1236	457
2	5001	440

prune159.0ms

Filtered

49 candidates to 43 candidates (87.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	4	49
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 5.7b

Counts

57 → 7

localize15.0ms

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)))
6.0b	(* (* 2.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 21

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
5.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(* (* 2.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
46.0ms	(- (* b b) (* 4.0 (* a c)))
93.0ms	(* (* 2.0 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify105.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	209	221
1	751	215
2	3673	210
3	5001	208

prune102.0ms

Filtered

33 candidates to 26 candidates (78.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 5.7b

Counts

40 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.8b	(/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
3.3b	(/ (/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)) (* 2.0 a))
23.9b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
20×	`associate-/r/`
15×	`*-commutative` `div-inv`
14×	`associate-/l/`
12×	`associate-/l*`
7×	`frac-2neg` `clear-num`
6×	`flip3--` `flip--`
4×	`associate-/r*`
2×	`sqrt-div`
1×	`sub-neg` `pow1/2`

Counts

4 → 55

Calls

4 calls:

6.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
12.0ms	(/ (/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)) (* 2.0 a))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* 4.0 (* a c)))
177.0ms	(/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a))
198.0ms	(/ (/ (* 4.0 c) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) a)) (* 2.0 a))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	425	624
1	1521	545
2	5001	539

prune182.0ms

Filtered

67 candidates to 55 candidates (82.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	67	7	74

Merged error: 5.7b

Counts

74 → 7

regimes171.0ms

Accuracy

93.9% (1.5b remaining)

Error of 7.0b against oracle of 5.5b and baseline of 30.7b

bsearch234.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.6809283377365093e+101
11	1.8145151230270015e-269	9.272403512084269e-250	8.40594418978702e-269
10	-1.2131416731721854e+50	-2.1643807627199687e+37	-2.186349513120992e+48

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.6809283377365093e+101

1.8145151230270015e-269

9.272403512084269e-250

8.40594418978702e-269

-1.2131416731721854e+50

-2.1643807627199687e+37

-2.186349513120992e+48

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	27
1	47	27

end0.0ms

sample1.2s

Algorithm

intervals

Results

278.0ms	1054×	body	2560	valid
250.0ms	5924×	body	80	valid
189.0ms	898×	body	1280	valid
119.0ms	2939×	body	80	nan
73.0ms	438×	body	640	valid
37.0ms	113×	body	5120	valid
24.0ms	199×	body	320	valid
11.0ms	131×	body	160	valid