Details

sample33.0ms

Algorithm

intervals

Results

6.0ms	203×	body	80	valid
5.0ms	31×	body	1280	valid
4.0ms	23×	body	2560	valid
2.0ms	79×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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

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: 32.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

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:

17.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (43.0ms)

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

prune339.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	172	11	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	11	184

Merged error: 6.3b

Counts

184 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(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))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
38.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (84.0ms)

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

prune359.0ms

Filtered

269 candidates to 111 candidates (41.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	265	4	269
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	271	9	280

Merged error: 6.3b

Counts

280 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

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:

14.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (43.0ms)

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

prune312.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	183	9	192

Merged error: 6.3b

Counts

192 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

309×	`times-frac`
268×	`add-sqr-sqrt`
267×	`*-un-lft-identity`
179×	`add-cube-cbrt`
139×	`sqrt-prod`
61×	`prod-diff`
44×	`distribute-lft-out--` `difference-of-squares`
43×	`distribute-rgt-neg-in`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
15×	`associate-/r/`
11×	`fma-neg`
10×	`flip3--` `flip--` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
7×	`neg-mul-1`
6×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `div-exp`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num`

Counts

4 → 335

Calls

4 calls:

17.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (sqrt 1) (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
37.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

347 → 347

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	885	6487
1	3878	4990
2	5001	4588

prune389.0ms

Filtered

347 candidates to 111 candidates (32.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	347	9	356

Merged error: 6.3b

Counts

356 → 9

regimes207.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.7b

bsearch93.0ms

Steps

Iters	Range		Point
9	4.546949039871578e+116	7.0067478635952275e+121	2.12330831537073e+121
10	-1.0320842654441656e-69	-6.354733239957269e-82	-8.480118384731098e-73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	32	12
2	32	12

end0.0ms

sample959.0ms

Algorithm

intervals

Results

197.0ms	1063×	body	2560	valid
191.0ms	5848×	body	80	valid
130.0ms	850×	body	1280	valid
87.0ms	2860×	body	80	nan
57.0ms	465×	body	640	valid
24.0ms	105×	body	5120	valid
21.0ms	234×	body	320	valid
7.0ms	120×	body	160	valid