Details

sample54.0ms

Algorithm

intervals

Results

10.0ms	154×	body	160	valid
9.0ms	520×	pre	80	true
8.0ms	264×	body	80	nan
4.0ms	42×	body	320	valid
2.0ms	60×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
61.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
94.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
73.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5001	674

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite173.0ms

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:

8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
79.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
165.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	651	2692
1	3141	2439
2	5001	2426

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
10×	`prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`cbrt-undiv` `div-exp`
5×	`sqrt-prod`
4×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `associate-l`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `diff-log` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `times-frac` `pow1/2` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

73.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
40.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series361.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
70.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	520	1133
1	3223	904
2	5002	896

prune257.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 (* a c)) a)
0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`sqrt-prod`
3×	`cbrt-undiv` `flip3--` `times-frac` `diff-log` `div-exp` `prod-exp` `associate-/r*` `flip--` `cbrt-unprod`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

21.0ms	(/ (* 4.0 (* a c)) a)
8.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (* 4.0 (* a c)) a)
42.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
68.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	377	574
1	1787	514
2	5002	497

prune208.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes89.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	11
1	23	11

end0.0ms

sample1.5s

Algorithm

intervals

Results

324.0ms	4849×	body	160	valid
265.0ms	8347×	body	80	nan
263.0ms	16347×	pre	80	true
131.0ms	1336×	body	320	valid
63.0ms	1815×	body	80	valid