Details

sample57.0ms

Algorithm

intervals

Results

15.0ms	151×	body	160	valid
11.0ms	297×	body	80	nan
10.0ms	553×	pre	80	true
4.0ms	105×	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: 30.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
30.1b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite59.0ms

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)))
38.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (- 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	5002	674

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

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:

47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
28.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
44.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
187.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify118.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (96.0ms)

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

prune466.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite84.0ms

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:

47.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series390.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
150.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (83.0ms)

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

prune269.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
29.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series354.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
150.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify90.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	639	2039
1	3262	1879
2	5003	1879

prune365.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	12
1	26	12
2	26	12

end0.0ms

sample1.4s

Algorithm

intervals

Results

339.0ms	4516×	body	160	valid
311.0ms	8602×	body	80	nan
297.0ms	16602×	pre	80	true
131.0ms	3484×	body	80	valid