Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	183×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	99×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	5×	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: 33.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

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:

11.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
238.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (34.0ms)

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

prune246.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite48.0ms

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))
20.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
12.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series431.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
150.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
188.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	725	2899
1	3204	2743
2	5001	2723

prune462.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.0b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.1b	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
119×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
70×	`add-cube-cbrt`
32×	`add-exp-log`
25×	`associate-/r*`
24×	`difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp`
15×	`sqrt-prod`
12×	`distribute-lft-out--`
10×	`cbrt-undiv`
6×	`prod-exp` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `associate-/r/` `associate-/l/`

Counts

4 → 162

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
20.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
162.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
129.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	773	2158
1	3591	1999
2	5002	1976

prune388.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.1b	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
3.1b	(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

792×	`times-frac`
491×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
322×	`add-cube-cbrt`
101×	`add-exp-log`
84×	`difference-of-squares`
67×	`div-exp`
45×	`sqrt-prod`
42×	`distribute-lft-out--`
41×	`add-cbrt-cube` `div-inv`
29×	`associate-/r/`
25×	`associate-/l*`
22×	`cbrt-undiv`
18×	`prod-exp`
16×	`flip3--` `associate-/r*` `flip--`
15×	`1-exp`
6×	`rec-exp` `add-log-exp`
5×	`pow1` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/`

Counts

4 → 443

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
34.0ms	(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series386.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* b_2 b_2) (* a c))
161.0ms	(/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
126.0ms	(/ (* 1 (/ (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))) a)
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify99.0ms

Algorithm

egg-herbie

Counts

455 → 455

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	2091	8111
1	5001	7477

prune790.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.5b

regimes181.0ms

Accuracy

93.4% (1.7b remaining)

Error of 7.2b against oracle of 5.6b and baseline of 30.8b

bsearch134.0ms

Steps

Iters	Range		Point
9	1.846147638884188e+104	1.7844061428947563e+109	8.04930514182413e+105
7	8.864719785943747e-237	7.298514919297617e-235	1.839460229192161e-236
9	-2.1533965607457413e+86	-9.153817644976897e+80	-2.1532693658084115e+84

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	24
1	45	24
2	45	24

end0.0ms

sample997.0ms

Algorithm

intervals

Results

215.0ms	1089×	body	2560	valid
193.0ms	5824×	body	80	valid
135.0ms	845×	body	1280	valid
88.0ms	2971×	body	80	nan
58.0ms	453×	body	640	valid
29.0ms	113×	body	5120	valid
24.0ms	260×	body	320	valid
8.0ms	129×	body	160	valid