Details

sample38.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
7.0ms	190×	body	80	valid
5.0ms	27×	body	1280	valid
3.0ms	101×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.7b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

9.0ms	(* (* 3.0 a) c)
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
2.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (* 3.0 a) c)
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms	(- (* b b) (* (* 3.0 a) c))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	307	469
1	1303	428
2	5001	417

prune187.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.7b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
25.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
146.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
175.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	647	2692
1	3114	2439
2	5001	2426

prune463.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.8b

localize20.0ms

Local error

Found 4 expressions with local error:

12.5b	(/ (* 3.0 a) (* 3.0 (* a c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`prod-exp` `sqrt-prod` `cbrt-unprod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `sqrt-div` `div-exp`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

7.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	322	591
1	2070	492
2	5003	460

prune323.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `neg-log`

Counts

4 → 63

Calls

4 calls:

15.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
3.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	208	609
1	767	588
2	3140	577
3	5001	573

prune277.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.3b

regimes568.0ms

Accuracy

93.3% (1.4b remaining)

Error of 11.0b against oracle of 9.6b and baseline of 30.1b

bsearch185.0ms

Steps

Iters	Range		Point
8	5.462432632406119e+143	7.490608477860844e+146	7.408859534684435e+146
8	8.629846534349985e-166	8.868461722977577e-162	8.771921641277499e-166
7	-1.391381036556559e+59	-2.75227652547193e+57	-1.36928751418849e+59

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	72
1	60	72
2	60	72

end0.0ms

sample1.1s

Algorithm

intervals

Results

226.0ms	1039×	body	2560	valid
218.0ms	5881×	body	80	valid
160.0ms	911×	body	1280	valid
99.0ms	2871×	body	80	nan
63.0ms	461×	body	640	valid
29.0ms	112×	body	5120	valid
23.0ms	229×	body	320	valid
7.0ms	101×	body	160	valid