Details

sample275.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	189×	body	80	valid
4.0ms	27×	body	1280	valid
4.0ms	17×	body	640	valid
3.0ms	101×	body	80	nan
0.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
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 → 80

Calls

4 calls:

44.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune231.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
158×	`add-sqr-sqrt`
157×	`*-un-lft-identity`
89×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 206

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
27.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
142.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
169.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune489.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.8b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1831×	`add-sqr-sqrt`
1830×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
242×	`distribute-lft-out--` `difference-of-squares`
124×	`sqrt-prod`
121×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 1148

Calls

4 calls:

16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
110.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
91.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
109.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify260.0ms

Algorithm

egg-herbie

Counts

1160 → 1160

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	4287	24836
1	5001	24170

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.3b	(/ (/ 1 (/ (/ 1 a) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

1710×	`times-frac`
741×	`add-sqr-sqrt`
740×	`*-un-lft-identity`
736×	`add-cube-cbrt`
134×	`associate-/l*`
56×	`add-exp-log`
53×	`div-inv`
44×	`div-exp`
18×	`add-cbrt-cube`
10×	`cbrt-undiv` `add-log-exp`
8×	`rec-exp` `1-exp`
5×	`pow1`
4×	`sqrt-prod` `associate-/r/`
3×	`flip3--` `diff-log` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 615

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
48.0ms	(/ (/ 1 (/ (/ 1 a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(/ (/ 1 (/ (/ 1 a) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify120.0ms

Algorithm

egg-herbie

Counts

627 → 627

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	3254	7594
1	5001	6429

prune1.4s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

regimes190.0ms

Accuracy

88.8% (3.0b remaining)

Error of 8.7b against oracle of 5.8b and baseline of 32.1b

bsearch139.0ms

Steps

Iters	Range		Point
8	1.239611320374306e+48	5.283842533261271e+50	1.7889848425355323e+48
9	-2.26016353878232e-246	-2.0825697103975006e-253	-8.141064449292044e-250
8	-6.30521239297407e+53	-2.0681333037085905e+50	-4.837192574744688e+53

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	41	24

end0.0ms

sample975.0ms

Algorithm

intervals

Results

202.0ms	1042×	body	2560	valid
189.0ms	5874×	body	80	valid
139.0ms	910×	body	1280	valid
91.0ms	2868×	body	80	nan
55.0ms	461×	body	640	valid
29.0ms	112×	body	5120	valid
20.0ms	230×	body	320	valid
6.0ms	104×	body	160	valid