Details

sample298.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
7.0ms	35×	body	2560	valid
6.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	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: 33.0b

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)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 17

Calls

4 calls:

6.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	234	195
1	769	185
2	2680	176
3	5001	175

prune99.0ms

Filtered

29 candidates to 25 candidates (86.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	7	30

Merged error: 5.8b

Counts

30 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 26

Calls

4 calls:

7.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
4.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
73.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
34.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	255	302
1	1030	285
2	4852	255
3	5003	255

prune110.0ms

Filtered

38 candidates to 29 candidates (76.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	37	8	45

Merged error: 5.8b

Counts

45 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(* (/ 1 a) (+ (* a c) 0))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`frac-times`
4×	`flip3-+` `flip-+`
3×	`flip3--` `frac-2neg` `associate-*l/` `clear-num` `flip--`
2×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `sqrt-div` `associate-*r/`
1×	`associate--l-` `neg-sub0` `pow1/2` `associate-l` `*-commutative` `div-inv`

Counts

4 → 29

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(* (/ 1 a) (+ (* a c) 0))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series178.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(* (/ 1 a) (+ (* a c) 0))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (112.0ms)

Iter	Nodes	Cost
0	298	202
1	1592	189
2	5001	178

prune110.0ms

Filtered

41 candidates to 30 candidates (73.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	39	2	41
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	43	6	49

Merged error: 5.7b

Counts

49 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 19

Calls

4 calls:

7.0ms	(/ (* 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (* 1 c) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	214	212
1	810	199
2	3870	189
3	5003	187

prune73.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	31	6	37

Merged error: 5.7b

Counts

37 → 6

regimes173.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.3b

bsearch165.0ms

Steps

Iters	Range	Point
8	1.31764557419022e+108	4.7801703725873666e+111	5.8672354253329364e+110
10	-3.3872652091741538e-211	-3.093295365731255e-225	-8.781062788627254e-225
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

1.31764557419022e+108

4.7801703725873666e+111

5.8672354253329364e+110

-3.3872652091741538e-211

-3.093295365731255e-225

-8.781062788627254e-225

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	44	22
2	44	22

end0.0ms

sample1.1s

Algorithm

intervals

Results

234.0ms	1105×	body	2560	valid
205.0ms	5783×	body	80	valid
157.0ms	898×	body	1280	valid
99.0ms	2921×	body	80	nan
61.0ms	460×	body	640	valid
27.0ms	105×	body	5120	valid
26.0ms	226×	body	320	valid
8.0ms	124×	body	160	valid