Details

sample61.0ms

Algorithm

intervals

Results

14.0ms	540×	pre	80	true
11.0ms	145×	body	160	valid
10.0ms	284×	body	80	nan
5.0ms	44×	body	320	valid
3.0ms	67×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize12.0ms

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)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
36.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
50.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune203.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.2b	(- (- 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)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
186.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5003	2388

prune446.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

11.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series393.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
154.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify88.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	512	1105
1	3243	867
2	5001	860

prune258.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 156

Calls

4 calls:

5.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
10.0ms	(- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))
22.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))

series497.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(+ (* b b) (- 0 (* 4.0 (* a c))))
80.0ms	(- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c))))))) (* 2.0 a))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (+ (* b b) (- 0 (* 4.0 (* a c)))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	648	2882
1	3149	2592
2	5001	2578

prune389.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes142.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

354.0ms	4773×	body	160	valid
315.0ms	16539×	pre	80	true
302.0ms	8539×	body	80	nan
158.0ms	1436×	body	320	valid
67.0ms	1791×	body	80	valid