Details

sample56.0ms

Algorithm

intervals

Results

12.0ms	168×	body	160	valid
10.0ms	555×	pre	80	true
10.0ms	299×	body	80	nan
4.0ms	39×	body	320	valid
2.0ms	49×	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: 45.7b

localize16.0ms

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))
0.2b	(- (* b b) (* (* 4.0 a) c))
40.0b	(+ (- 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)))
36.0ms	(/ (+ (- 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))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
48.0ms	(- (* 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

prune191.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

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))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
31.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms	(/ (+ 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

prune434.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

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:

43.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
151.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (80.0ms)

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

prune251.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

7.0ms	(/ (* 4.0 (* a c)) a)
32.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
13.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))

series282.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* 4.0 (* a c)) a)
150.0ms	(/ (/ (* 4.0 (* a c)) a) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
73.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))

simplify87.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	635	2032
1	3308	1822
2	5002	1796

prune346.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	21
1	32	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

340.0ms	4825×	body	160	valid
295.0ms	16432×	pre	80	true
279.0ms	8432×	body	80	nan
147.0ms	1388×	body	320	valid
63.0ms	1787×	body	80	valid