Details

sample40.0ms

Algorithm

intervals

Results

9.0ms	196×	body	80	valid
6.0ms	31×	body	2560	valid
5.0ms	32×	body	1280	valid
4.0ms	113×	body	80	nan
1.0ms	11×	body	320	valid
1.0ms	4×	body	5120	valid
1.0ms	7×	body	640	valid
0.0ms	1×	body	160	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: 36.9b

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) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

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:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune254.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
3.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
146.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
178.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune479.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.0b

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.7b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.7b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
22.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
161.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
127.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify89.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.6b	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
3.7b	(/ (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c)) a)
25.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

4788×	`times-frac`
2627×	`add-sqr-sqrt`
2230×	`*-un-lft-identity`
1834×	`add-cube-cbrt`
396×	`difference-of-squares`
341×	`associate-/l*`
201×	`sqrt-prod`
198×	`distribute-lft-out--`
193×	`div-inv`
137×	`associate-/r/`
68×	`flip3--` `flip--`
58×	`add-exp-log`
41×	`div-exp`
34×	`add-cbrt-cube`
21×	`cbrt-undiv`
16×	`associate-/r*`
6×	`add-log-exp`
5×	`pow1`
4×	`rec-exp` `1-exp`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1696

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
73.0ms	(/ (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
166.0ms	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
131.0ms	(/ (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c)) a)
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify320.0ms

Algorithm

egg-herbie

Counts

1708 → 1708

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5001	35439

prune4.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.0b

regimes298.0ms

Accuracy

87.7% (3.2b remaining)

Error of 8.9b against oracle of 5.6b and baseline of 32.0b

bsearch116.0ms

Steps

Iters	Range		Point
6	389373804.8346531	2491217878.346211	2445759453.473797
9	1.147231796899814e-295	2.5496030178102582e-290	6.634941373388381e-295
6	-7.692731713148582e+22	-5.509752788368676e+21	-9.346214526832347e+21

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample1.0s

Algorithm

intervals

Results

230.0ms	1087×	body	2560	valid
199.0ms	5897×	body	80	valid
135.0ms	842×	body	1280	valid
92.0ms	2915×	body	80	nan
57.0ms	434×	body	640	valid
30.0ms	122×	body	5120	valid
22.0ms	228×	body	320	valid
7.0ms	116×	body	160	valid