Details

sample286.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
7.0ms	185×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	97×	body	80	nan
2.0ms	17×	body	640	valid
2.0ms	7×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

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_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 26

Calls

4 calls:

6.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	246	245
1	802	232
2	2674	218
3	5001	204

prune115.0ms

Filtered

38 candidates to 29 candidates (76.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	30	8	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	8	39

Merged error: 5.8b

Counts

39 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.2b	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 27

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
210.0ms	(/ (/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
206.0ms	(/ (fma c a 0) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	267	249
1	825	239
2	3538	219
3	5001	219

prune115.0ms

Filtered

39 candidates to 29 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	38	9	47

Merged error: 5.7b

Counts

47 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.3b	(/ (* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
10.2b	(* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 35

Calls

4 calls:

5.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(/ (* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
7.0ms	(* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series513.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
205.0ms	(/ (* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
204.0ms	(* (fma c a 0) (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify36.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	282	254
1	955	236
2	5001	222

prune119.0ms

Filtered

47 candidates to 30 candidates (63.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	47	9	56

Merged error: 5.7b

Counts

56 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
15.4b	(/ a (fma c a 0))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 20

Calls

4 calls:

6.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.0ms	(- (* b_2 b_2) (* a c))
2.0ms	(/ a (fma c a 0))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
36.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(/ a (fma c a 0))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	180	163
1	558	158
2	1959	150
3	5002	135

prune71.0ms

Filtered

32 candidates to 20 candidates (62.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	33	8	41

Merged error: 5.7b

Counts

41 → 8

regimes176.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 29.5b

bsearch157.0ms

Steps

Iters	Range	Point
8	4.088553977120381e+100	8.044751807128501e+103	1.7707226313517787e+102
11	1.8145151230270015e-269	9.272403512084269e-250	3.0003811195914403e-269
8	-6.305756997180833e+135	-5.1661869031349895e+132	-1.2750799850289763e+133

Iters

Range

Point

4.088553977120381e+100

8.044751807128501e+103

1.7707226313517787e+102

1.8145151230270015e-269

9.272403512084269e-250

3.0003811195914403e-269

-6.305756997180833e+135

-5.1661869031349895e+132

-1.2750799850289763e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.1s

Algorithm

intervals

Results

230.0ms	1052×	body	2560	valid
211.0ms	5925×	body	80	valid
154.0ms	900×	body	1280	valid
104.0ms	2937×	body	80	nan
64.0ms	438×	body	640	valid
30.0ms	115×	body	5120	valid
20.0ms	197×	body	320	valid
9.0ms	130×	body	160	valid