Details

sample289.0ms

Algorithm

intervals

Results

10.0ms	37×	body	2560	valid
7.0ms	180×	body	80	valid
6.0ms	35×	body	1280	valid
4.0ms	110×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

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: 33.7b

Counts

2 → 1

localize12.0ms

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))
1.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

30.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
16.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
30.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
78.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	397	996
1	1372	933
2	5002	912

prune199.0ms

Filtered

120 candidates to 77 candidates (35.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	8	120
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	9	121

Merged error: 5.0b

Counts

121 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

2.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.5b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.6b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

383×	`*-un-lft-identity`
298×	`times-frac`
253×	`add-sqr-sqrt`
115×	`add-cube-cbrt`
74×	`distribute-lft-out`
66×	`difference-of-squares`
60×	`distribute-lft-out--`
51×	`associate-/l*`
45×	`sqrt-prod`
41×	`associate-l`
28×	`distribute-rgt-neg-in`
21×	`associate-/l/`
17×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--` `unswap-sqr`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`frac-2neg` `clear-num`
2×	`flip3-+` `sqrt-div` `diff-log` `swap-sqr` `*-commutative` `flip-+`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 308

Calls

4 calls:

24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
33.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
145.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
181.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify137.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	801	4888
1	3544	4626
2	5002	4600

prune422.0ms

Filtered

320 candidates to 160 candidates (50.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	318	2	320
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	320	9	329

Merged error: 5.0b

Counts

329 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
144×	`times-frac`
117×	`*-un-lft-identity`
72×	`add-cube-cbrt`
48×	`difference-of-squares`
31×	`sqrt-prod`
30×	`associate-/r*`
22×	`distribute-lft-out--`
20×	`associate-/r/`
15×	`add-exp-log`
14×	`unswap-sqr`
9×	`add-cbrt-cube`
8×	`associate-l` `add-log-exp`
7×	`flip3--` `div-exp` `flip--` `associate-/l*`
6×	`pow1`
5×	`div-inv`
4×	`swap-sqr` `*-commutative`
3×	`cbrt-undiv` `clear-num`
2×	`sub-neg` `rec-exp` `frac-2neg` `sqrt-div` `diff-log` `1-exp` `remove-double-div`
1×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `inv-pow`

Counts

4 → 203

Calls

4 calls:

28.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
15.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
38.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify82.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	619	2357
1	2825	2149
2	5001	2019

prune237.0ms

Filtered

215 candidates to 99 candidates (54.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	215	9	224

Merged error: 5.0b

Counts

224 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
22.4b	(sqrt (- (* b_2 b_2) (* a c)))
22.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
36×	`sqrt-prod`
26×	`*-un-lft-identity`
24×	`difference-of-squares`
14×	`unswap-sqr`
10×	`distribute-lft-out--`
8×	`associate-l` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `swap-sqr` `*-commutative` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 88

Calls

4 calls:

21.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
75.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	223	746
1	677	720
2	2082	714
3	5001	700

prune206.0ms

Filtered

100 candidates to 66 candidates (34.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	100	9	109

Merged error: 5.0b

Counts

109 → 9

regimes187.0ms

Accuracy

83.8% (4.4b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 32.7b

bsearch104.0ms

Steps

Iters	Range		Point
9	2.9593950748212843e-63	2.4702945119117623e-58	3.075714862027618e-63
10	-5.223066032138611e+59	-9.249404424269967e+45	-1.8583482015417066e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	14
1	32	14

end0.0ms

sample1.0s

Algorithm

intervals

Results

228.0ms	1098×	body	2560	valid
201.0ms	5798×	body	80	valid
143.0ms	885×	body	1280	valid
90.0ms	2778×	body	80	nan
61.0ms	464×	body	640	valid
29.0ms	116×	body	5120	valid
24.0ms	249×	body	320	valid
9.0ms	117×	body	160	valid