Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	200×	body	80	valid
4.0ms	21×	body	2560	valid
3.0ms	23×	body	1280	valid
3.0ms	87×	body	80	nan
2.0ms	20×	body	640	valid
1.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune2.0ms

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: 34.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 91

Calls

4 calls:

13.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune222.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 8.1b

Counts

104 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
2.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
170.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune420.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	191	5	196
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	196	10	206

Merged error: 8.0b

Counts

206 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.8b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
2.0b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
26.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
162.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
131.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune886.0ms

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	448	1	449
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	451	8	459

Merged error: 8.0b

Counts

459 → 8

localize13.0ms

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))
1.1b	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
210×	`add-sqr-sqrt`
165×	`*-un-lft-identity`
121×	`add-cube-cbrt`
69×	`cbrt-prod`
44×	`difference-of-squares`
25×	`sqrt-prod`
22×	`associate-/r*` `distribute-lft-out--`
9×	`add-exp-log`
8×	`div-inv` `add-log-exp`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`pow1`
3×	`cbrt-undiv` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/`

Counts

4 → 217

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(- (* b_2 b_2) (* a c))
359.0ms	(/ (cbrt a) (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify142.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	805	3467
1	3276	3391
2	5002	3357

prune503.0ms

Filtered

229 candidates to 148 candidates (64.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	228	9	237

Merged error: 8.0b

Counts

237 → 9

regimes323.0ms

Accuracy

91.7% (2.0b remaining)

Error of 7.8b against oracle of 5.8b and baseline of 29.9b

bsearch152.0ms

Steps

Iters	Range	Point
7	6.184155830638016e+27	1.3306260697673677e+30	6.0917574507436946e+29
10	1.4094399726781053e-281	7.168010826183247e-271	5.200108364883736e-277
8	-3.739307379384431e+110	-1.120612400025049e+108	-2.0526834997616308e+109

Iters

Range

Point

6.184155830638016e+27

1.3306260697673677e+30

6.0917574507436946e+29

1.4094399726781053e-281

7.168010826183247e-271

5.200108364883736e-277

-3.739307379384431e+110

-1.120612400025049e+108

-2.0526834997616308e+109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	46	26
2	46	26

end0.0ms

sample1.1s

Algorithm

intervals

Results

220.0ms	5867×	body	80	valid
209.0ms	1040×	body	2560	valid
151.0ms	899×	body	1280	valid
93.0ms	2906×	body	80	nan
61.0ms	436×	body	640	valid
32.0ms	115×	body	5120	valid
26.0ms	258×	body	320	valid
9.0ms	128×	body	160	valid