Details

sample293.0ms

Algorithm

intervals

Results

8.0ms	33×	body	2560	valid
6.0ms	38×	body	1280	valid
6.0ms	177×	body	80	valid
3.0ms	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

simplify12.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

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

rewrite70.0ms

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:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

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

prune249.0ms

Pruning

9 alts after pruning (9 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))
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)))

rewrite87.0ms

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))
47.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
25.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
160.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
190.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (80.0ms)

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

prune486.0ms

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 (* (/ 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)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-exp-log`
23×	`add-cbrt-cube`
16×	`div-exp`
13×	`prod-exp`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `cbrt-undiv`
6×	`times-frac` `associate-/l*` `add-log-exp`
5×	`associate-/r/` `cbrt-unprod`
4×	`rec-exp` `flip3--` `1-exp` `flip--`
3×	`sqrt-prod`
2×	`frac-times` `pow-flip` `frac-2neg` `sqrt-div` `associate-r/` `clear-num` `associate-/r` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `inv-pow`

Counts

4 → 89

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ 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)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
156.0ms	(/ 1 (* (/ a (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(/ a (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	459	756
1	2135	573
2	5001	556

prune204.0ms

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)))

rewrite48.0ms

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:

20.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
33.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify131.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	314	813
1	1002	760
2	3949	755
3	5001	755

prune187.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 6.0b

regimes121.0ms

Accuracy

95.4% (1.1b remaining)

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

bsearch137.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	21
1	36	21

end0.0ms

sample987.0ms

Algorithm

intervals

Results

209.0ms	1075×	body	2560	valid
189.0ms	5860×	body	80	valid
144.0ms	904×	body	1280	valid
90.0ms	2862×	body	80	nan
56.0ms	457×	body	640	valid
32.0ms	114×	body	5120	valid
19.0ms	211×	body	320	valid
7.0ms	120×	body	160	valid