Details

sample53.0ms

Algorithm

intervals

Results

11.0ms	569×	pre	80	true
10.0ms	313×	body	80	nan
10.0ms	135×	body	160	valid
4.0ms	121×	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: 27.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
27.7b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite56.0ms

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)))
34.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
107.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

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

prune208.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

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:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
41.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series447.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
43.0ms	(- (* b b) (* (* 4.0 a) c))
182.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (92.0ms)

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

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.4b	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
63.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
66.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
86.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify40.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	819	2154
1	5002	1664

prune303.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
52×	`add-exp-log`
45×	`times-frac`
32×	`add-cbrt-cube`
28×	`add-cube-cbrt`
27×	`associate-r`
18×	`div-exp`
17×	`prod-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`cbrt-undiv`
9×	`cbrt-unprod`
8×	`associate-/r*`
7×	`pow1` `distribute-rgt-neg-in` `sqrt-prod`
6×	`associate-/l/` `add-log-exp`
4×	`frac-times` `rec-exp` `flip3-+` `1-exp` `associate-l/` `associate-/r/` `flip-+` `associate-/l`
3×	`flip3--` `associate-l` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `un-div-inv`
1×	`sub-neg` `pow-flip` `diff-log` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 150

Calls

4 calls:

21.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
18.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
52.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series482.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
146.0ms	(/ (* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
48.0ms	(- (* b b) (* (* 4.0 a) c))
183.0ms	(* (+ 0 (* 4.0 (* a c))) (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify195.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	727	2182
1	4787	1804
2	5001	1788

prune361.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes160.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13

end0.0ms

sample1.4s

Algorithm

intervals

Results

314.0ms	4460×	body	160	valid
303.0ms	16511×	pre	80	true
286.0ms	8511×	body	80	nan
126.0ms	3539×	body	80	valid
0.0ms	1×	body	320	valid