Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	33×	body	2560	valid
6.0ms	192×	body	80	valid
4.0ms	26×	body	1280	valid
3.0ms	113×	body	80	nan
1.0ms	10×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	7×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 34.4b

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))
2.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

29.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- 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))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	1177
1	1358	1122
2	5002	1109

prune206.0ms

Filtered

132 candidates to 81 candidates (38.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	9	132
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	124	9	133

Merged error: 5.0b

Counts

133 → 9

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))
2.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

186×	`add-sqr-sqrt`
165×	`times-frac`
152×	`*-un-lft-identity`
79×	`add-cube-cbrt`
48×	`difference-of-squares`
36×	`distribute-lft-out--`
34×	`associate-/r*`
31×	`sqrt-prod`
21×	`associate-/r/`
15×	`add-exp-log`
14×	`distribute-rgt-neg-in` `unswap-sqr`
10×	`add-log-exp`
9×	`add-cbrt-cube`
8×	`associate-l`
7×	`flip3--` `div-exp` `flip--` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`swap-sqr` `*-commutative`
3×	`cbrt-undiv` `diff-log` `clear-num`
2×	`sub-neg` `rec-exp` `frac-2neg` `sqrt-div` `1-exp` `remove-double-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 219

Calls

4 calls:

35.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
14.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series269.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	642	2721
1	2977	2481
2	5001	2332

prune245.0ms

Filtered

231 candidates to 100 candidates (56.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	226	5	231
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	232	8	240

Merged error: 5.0b

Counts

240 → 8

localize10.0ms

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))
2.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

27.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
15.0ms	(- (* b_2 b_2) (* a c))
26.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms	(- (* 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)))

simplify49.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	409	1177
1	1358	1122
2	5002	1109

prune204.0ms

Filtered

132 candidates to 81 candidates (38.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	132	8	140

Merged error: 5.0b

Counts

140 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
258×	`times-frac`
243×	`add-sqr-sqrt`
105×	`add-cube-cbrt`
66×	`difference-of-squares`
64×	`distribute-lft-out`
46×	`associate-/l*`
45×	`sqrt-prod`
36×	`associate-l`
32×	`distribute-lft-out--`
20×	`associate-/l/`
15×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`flip3--` `flip--` `unswap-sqr`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `sqrt-div` `swap-sqr` `*-commutative` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 278

Calls

4 calls:

20.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
38.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
28.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
159.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
195.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify126.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	789	4143
1	3434	3915
2	5002	3895

prune407.0ms

Filtered

290 candidates to 161 candidates (44.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	289	9	298

Merged error: 5.0b

Counts

298 → 9

regimes472.0ms

Accuracy

90.5% (2.8b remaining)

Error of 8.2b against oracle of 5.4b and baseline of 34.3b

bsearch96.0ms

Steps

Iters	Range	Point
0	1.3836563058951246e+50	1.390978468581987e+50	1.3873173872385558e+50
8	-2.0030864347859544e-273	-1.6635287532714566e-276	-1.681581702221106e-276
8	-0.00048729477041016116	-1.019144331981781e-06	-8.958236979672504e-05

Iters

Range

Point

1.3836563058951246e+50

1.390978468581987e+50

1.3873173872385558e+50

-2.0030864347859544e-273

-1.6635287532714566e-276

-1.681581702221106e-276

-0.00048729477041016116

-1.019144331981781e-06

-8.958236979672504e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	25
1	51	25
2	51	25

end0.0ms

sample974.0ms

Algorithm

intervals

Results

210.0ms	1103×	body	2560	valid
196.0ms	5871×	body	80	valid
141.0ms	888×	body	1280	valid
84.0ms	2794×	body	80	nan
55.0ms	454×	body	640	valid
24.0ms	104×	body	5120	valid
21.0ms	232×	body	320	valid
7.0ms	115×	body	160	valid