Details

sample84.0ms

Algorithm

intervals

Results

19.0ms	155×	body	160	valid
16.0ms	259×	body	80	nan
16.0ms	515×	pre	80	true
11.0ms	45×	body	320	valid
4.0ms	56×	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: 43.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(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)))) (* 2.0 a))
38.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite53.0ms

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:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
2.0ms	(- (* b b) (* (* 4.0 a) c))
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
11.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series290.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
43.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
78.0ms	(+ (- 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

prune183.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite87.0ms

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:

3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
27.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
40.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series433.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
172.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify117.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5002	2388

prune403.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

312×	`add-exp-log`
142×	`div-exp`
138×	`add-cbrt-cube`
137×	`prod-exp`
57×	`cbrt-unprod`
48×	`cbrt-undiv`
40×	`1-exp`
33×	`times-frac`
30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`rec-exp`
14×	`associate-/l*`
8×	`add-log-exp`
7×	`associate-r`
6×	`pow1`
5×	`flip3--` `associate-l` `associate-/r/` `flip--` `div-inv`
4×	`frac-times` `associate-*r/` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `frac-2neg` `distribute-lft-in` `diff-log` `associate-l/` `clear-num` `associate-/r` `sqrt-prod`
1×	`associate--l-` `neg-sub0` `pow-prod-down` `neg-log` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 203

Calls

4 calls:

11.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
63.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
35.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
81.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
144.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1148	3308
1	5001	2536

prune322.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

462×	`times-frac`
276×	`add-sqr-sqrt` `*-un-lft-identity`
160×	`add-cube-cbrt`
98×	`add-exp-log`
66×	`div-exp`
58×	`distribute-lft-out--` `difference-of-squares`
38×	`add-cbrt-cube` `div-inv`
30×	`associate-/l*`
29×	`distribute-rgt-neg-in` `sqrt-prod`
21×	`cbrt-undiv`
19×	`associate-/r/`
16×	`prod-exp`
15×	`1-exp`
14×	`associate-/r*`
11×	`flip3--` `flip--`
10×	`add-log-exp`
7×	`rec-exp`
5×	`pow1`
4×	`cbrt-unprod`
3×	`diff-log`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`associate--l-` `neg-sub0` `pow-flip` `neg-log` `associate-/l/` `inv-pow`

Counts

4 → 346

Calls

4 calls:

2.0ms	(- (* b b) (* (* 4.0 a) c))
23.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
42.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))

series335.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 4.0 a) c))
96.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
71.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
125.0ms	(/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ (* (/ 2.0 4.0) 1) c))

simplify86.0ms

Algorithm

egg-herbie

Counts

358 → 358

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1436	6912
1	5001	6327

prune614.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes130.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	25	13
1	27	12
2	29	12
3	29	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

601.0ms	4831×	body	160	valid
524.0ms	8260×	body	80	nan
488.0ms	16260×	pre	80	true
233.0ms	1314×	body	320	valid
132.0ms	1855×	body	80	valid