Details

sample47.0ms

Algorithm

intervals

Results

10.0ms	41×	body	2560	valid
9.0ms	34×	body	1280	valid
7.0ms	172×	body	80	valid
4.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	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	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: 32.3b

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)
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

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:

20.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
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)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (47.0ms)

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

prune318.0ms

Filtered

183 candidates to 97 candidates (53.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	173	10	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	10	184

Merged error: 3.4b

Counts

184 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

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:

20.0ms	(/ 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)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify123.0ms

Algorithm

egg-herbie

Counts

269 → 269

Iterations

Useful iterations: 2 (72.0ms)

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

prune322.0ms

Filtered

269 candidates to 112 candidates (41.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	265	4	269
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	269	10	279

Merged error: 3.3b

Counts

279 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 548

Calls

4 calls:

28.0ms	(/ (/ 1 a) (/ 1 (- (- 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)))

series273.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

560 → 560

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1887	10995
1	5001	9278

prune647.0ms

Filtered

560 candidates to 199 candidates (35.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	560	0	560
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	560	10	570

Merged error: 3.3b

Counts

570 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))
18.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

60×	`prod-diff`
55×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`add-cube-cbrt`
40×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
8×	`add-log-exp`
7×	`pow1` `neg-mul-1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 141

Calls

4 calls:

11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	369	2603
1	1203	1735
2	5001	1648

prune309.0ms

Filtered

153 candidates to 83 candidates (54.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	153	10	163

Merged error: 3.3b

Counts

163 → 10

regimes277.0ms

Accuracy

84.6% (4.4b remaining)

Error of 10.2b against oracle of 5.8b and baseline of 34.2b

bsearch100.0ms

Steps

Iters	Range		Point
9	1.537663903506608e+146	1.524085477896404e+154	1.5636109501278876e+146
9	-3.8236705409407114e-69	-3.0658855651502382e-74	-7.650980145198802e-70

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	15
1	33	15

end0.0ms

sample1.2s

Algorithm

intervals

Results

253.0ms	5855×	body	80	valid
244.0ms	1019×	body	2560	valid
186.0ms	896×	body	1280	valid
124.0ms	2933×	body	80	nan
70.0ms	451×	body	640	valid
35.0ms	119×	body	5120	valid
29.0ms	253×	body	320	valid
10.0ms	130×	body	160	valid