Details

sample287.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
7.0ms	36×	body	1280	valid
7.0ms	29×	body	2560	valid
4.0ms	95×	body	80	nan
2.0ms	11×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	5120	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 34.3b

Counts

2 → 1

localize13.0ms

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))
2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
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 → 171

Calls

4 calls:

15.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune326.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	175	8	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	176	8	184

Merged error: 5.3b

Counts

184 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.0b	(- (* b_2 b_2) (* a c))
2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

17.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
35.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	770	4550
1	3215	3424
2	5002	3236

prune325.0ms

Filtered

269 candidates to 112 candidates (41.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	267	2	269
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	268	9	277

Merged error: 5.2b

Counts

277 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(- (* b_2 b_2) (* a c))
2.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

15.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify79.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940

prune278.0ms

Filtered

181 candidates to 96 candidates (53.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	181	9	190

Merged error: 5.2b

Counts

190 → 9

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

7.0ms

(* -1/2 (/ c b_2))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* -1/2 (/ c b_2))

simplify66.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	166	134
1	729	124
2	2966	124
3	5001	124

prune56.0ms

Filtered

37 candidates to 26 candidates (70.3%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	32	5	37
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	33	13	46

Merged error: 5.2b

Counts

46 → 13

regimes270.0ms

Accuracy

81.9% (5.2b remaining)

Error of 10.7b against oracle of 5.5b and baseline of 34.1b

bsearch88.0ms

Steps

Iters	Range		Point
7	4.4312058130773924e+95	1.951780157010812e+97	6.012732101308388e+96
9	-1.4785651790829535e-130	-1.909704137735967e-139	-1.3486756060694896e-130

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

end0.0ms

sample1.2s

Algorithm

intervals

Results

260.0ms	1039×	body	2560	valid
256.0ms	5929×	body	80	valid
177.0ms	883×	body	1280	valid
120.0ms	2975×	body	80	nan
78.0ms	480×	body	640	valid
41.0ms	122×	body	5120	valid
26.0ms	222×	body	320	valid
9.0ms	112×	body	160	valid