Details

sample35.0ms

Algorithm

intervals

Results

6.0ms	33×	body	2560	valid
6.0ms	38×	body	1280	valid
6.0ms	177×	body	80	valid
2.0ms	21×	body	640	valid
2.0ms	79×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	7×	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: 37.7b

localize11.0ms

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))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite53.0ms

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:

32.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune240.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.5b	(/ (/ (+ 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))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite81.0ms

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:

3.0ms	(- (* b_2 b_2) (* a c))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
24.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
154.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
192.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (76.0ms)

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

prune478.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
0.5b	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.7b	(/ a (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-exp-log`
60×	`div-exp`
41×	`add-cbrt-cube`
34×	`times-frac`
29×	`prod-exp`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`1-exp`
18×	`cbrt-undiv`
16×	`associate-/l*`
9×	`cbrt-unprod`
8×	`rec-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
4×	`flip3--` `flip--` `div-inv`
3×	`sqrt-prod`
2×	`frac-times` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `associate-/r`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*l/` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* b_2 b_2) (* a c))
157.0ms	(/ (/ 1 1) (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(/ a (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	720	1231
1	3818	888
2	5001	826

prune227.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.2b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.4b	(- (* b_2 b_2) (* a c))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

19.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify134.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	314	812
1	1008	760
2	3967	755
3	5001	755

prune200.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

regimes118.0ms

Accuracy

95.4% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.6b

bsearch130.0ms

Steps

Iters	Range	Point
8	1.5276508475467709e+44	4.1560730947117816e+46	9.965676396086742e+45
8	-3.876848940398081e-247	-7.459891070112096e-252	-7.593271511213179e-252
9	-1.829086240692416e+154	-8.160318760930525e+144	-6.968524887173992e+152

Iters

Range

Point

1.5276508475467709e+44

4.1560730947117816e+46

9.965676396086742e+45

-3.876848940398081e-247

-7.459891070112096e-252

-7.593271511213179e-252

-1.829086240692416e+154

-8.160318760930525e+144

-6.968524887173992e+152

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample992.0ms

Algorithm

intervals

Results

211.0ms	1075×	body	2560	valid
189.0ms	5860×	body	80	valid
142.0ms	904×	body	1280	valid
89.0ms	2862×	body	80	nan
58.0ms	457×	body	640	valid
26.0ms	114×	body	5120	valid
19.0ms	211×	body	320	valid
7.0ms	120×	body	160	valid