Details

sample39.0ms

Algorithm

intervals

Results

6.0ms	35×	body	2560	valid
6.0ms	191×	body	80	valid
5.0ms	35×	body	1280	valid
3.0ms	115×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	4×	body	5120	valid
0.0ms	5×	body	160	valid
0.0ms	3×	body	320	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

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))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

59.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
29.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
54.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune228.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 187

Calls

4 calls:

40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
138.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
166.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
51.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune457.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.5b	(/ a (* a c))
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`flip3--` `times-frac` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `distribute-lft-out--`

Counts

4 → 63

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(/ a (* a c))
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series156.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(/ a (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	277	415
1	944	374
2	4178	369
3	5002	368

prune160.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 1) (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.7b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

104×	`add-exp-log`
69×	`div-exp`
32×	`1-exp`
31×	`times-frac`
28×	`prod-exp`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`rec-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
8×	`add-log-exp`
5×	`pow1` `flip3--` `associate-/r/` `flip--`
4×	`sqrt-prod` `cbrt-unprod`
3×	`div-inv`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `associate-*r/` `difference-of-squares`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `clear-num` `associate-/r` `associate-/l/` `distribute-lft-out--`

Counts

4 → 126

Calls

4 calls:

51.0ms	(/ (/ 1 1) (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
7.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (/ 1 1) (* (/ 1 c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
33.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	709	1194
1	3396	971
2	5002	933

prune188.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes114.0ms

Accuracy

81.5% (4.5b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 30.0b

bsearch83.0ms

Steps

Iters	Range		Point
9	3.3226137104618393e-109	3.6384927546515274e-103	1.5134930447811e-103
8	-1.0016636615098116e+114	-3.260864156300871e+111	-8.723712166727036e+113

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	15
1	35	15

end0.0ms

sample1.1s

Algorithm

intervals

Results

200.0ms	5904×	body	80	valid
198.0ms	1063×	body	2560	valid
138.0ms	915×	body	1280	valid
88.0ms	2946×	body	80	nan
54.0ms	465×	body	640	valid
24.0ms	97×	body	5120	valid
17.0ms	192×	body	320	valid
7.0ms	122×	body	160	valid