Details

sample313.0ms

Algorithm

intervals

Results

14.0ms	43×	body	2560	valid
14.0ms	181×	body	80	valid
11.0ms	40×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	12×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	320	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))))
0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

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:

12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series270.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
92.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune241.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
10.4b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
25.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
141.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
164.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

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

prune492.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

25.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
55.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
157.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify100.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1582	8735
1	5001	8087

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 c)))
0.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

149×	`add-exp-log`
132×	`add-sqr-sqrt`
131×	`times-frac`
89×	`*-un-lft-identity`
82×	`div-exp`
52×	`prod-exp`
51×	`add-cube-cbrt`
44×	`associate-r`
41×	`rec-exp` `1-exp`
27×	`associate-l`
25×	`add-cbrt-cube`
21×	`unswap-sqr`
10×	`add-log-exp`
9×	`pow1` `cbrt-undiv`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`sqrt-prod`
6×	`cbrt-unprod`
5×	`div-inv`
4×	`flip3--` `distribute-rgt-neg-in` `flip--`
3×	`diff-log` `pow-prod-down` `associate-/r/`
2×	`sub-neg` `pow-flip` `sqrt-div` `inv-pow`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `neg-log` `associate-l/` `un-div-inv` `*-commutative`

Counts

4 → 210

Calls

4 calls:

80.0ms	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 c)))
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)))

series272.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 (/ 1 c)))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	1126	2508
1	4463	2092
2	5001	1966

prune353.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.3b

regimes222.0ms

Accuracy

93.9% (1.5b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.5b

bsearch151.0ms

Steps

Iters	Range	Point
9	1.0966316111626227e+109	8.247031634266059e+117	1.6719249902234693e+111
6	-2.3998897035896985e-228	-5.442304884128225e-229	-5.498188913150987e-229
7	-1.347931383778874e+29	-1.5320971041566743e+27	-1.3279271689820989e+29

Iters

Range

Point

1.0966316111626227e+109

8.247031634266059e+117

1.6719249902234693e+111

-2.3998897035896985e-228

-5.442304884128225e-229

-5.498188913150987e-229

-1.347931383778874e+29

-1.5320971041566743e+27

-1.3279271689820989e+29

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	22
1	39	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

391.0ms	5823×	body	80	valid
363.0ms	1084×	body	2560	valid
243.0ms	904×	body	1280	valid
182.0ms	2979×	body	80	nan
98.0ms	455×	body	640	valid
47.0ms	113×	body	5120	valid
40.0ms	212×	body	320	valid
13.0ms	110×	body	160	valid