Details

sample99.0ms

Algorithm

intervals

Results

25.0ms	147×	body	160	valid
23.0ms	271×	body	80	nan
22.0ms	527×	pre	80	true
10.0ms	109×	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: 29.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.0b	(+ (- 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)))
3.0ms	(- (* b b) (* (* 4.0 a) c))
35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
13.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
47.0ms	(- (* b b) (* (* 4.0 a) c))
105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

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

prune190.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(- (- 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))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite94.0ms

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))))
42.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series451.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
76.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
180.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify116.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (94.0ms)

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

prune417.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
65.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
66.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series320.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
147.0ms	(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
85.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify120.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	773	2238
1	4633	1689
2	5001	1671

prune296.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

20548×	`times-frac`
9815×	`add-sqr-sqrt` `*-un-lft-identity`
7499×	`add-cube-cbrt`
1158×	`distribute-lft-out--` `difference-of-squares`
879×	`div-inv`
621×	`associate-/l*`
579×	`distribute-rgt-neg-in` `sqrt-prod`
200×	`add-exp-log`
169×	`div-exp`
129×	`associate-/r/`
54×	`add-cbrt-cube`
37×	`cbrt-undiv`
30×	`rec-exp` `1-exp`
20×	`associate-/r*`
10×	`add-log-exp`
4×	`pow1`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `frac-2neg` `clear-num` `associate-/l/`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 5377

Calls

4 calls:

27.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
215.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ (/ 1 (/ 2.0 4.0)) (/ 1 c))
170.0ms	(/ (/ (/ 1 (/ 2.0 4.0)) (/ 1 c)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.4s

Algorithm

egg-herbie

Counts

5389 → 5389

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5489	147385

prune15.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.3b 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	22	12
1	22	12

end0.0ms

sample2.8s

Algorithm

intervals

Results

765.0ms	8768×	body	80	nan
735.0ms	4402×	body	160	valid
610.0ms	16768×	pre	80	true
339.0ms	3598×	body	80	valid