Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	110×	body	320	valid
10.0ms	534×	pre	80	true
9.0ms	278×	body	80	nan
6.0ms	90×	body	160	valid
3.0ms	20×	body	640	valid
1.0ms	36×	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: 51.8b

localize11.0ms

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))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
25.5b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite58.0ms

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

series310.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
51.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

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

prune185.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

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

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:

12.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
29.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series457.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
181.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
152.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify118.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	642	2665
1	3175	2400
2	5002	2388

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

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`
26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
16×	`rec-exp`
14×	`associate-/l*`
7×	`associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3--` `associate-l` `associate-/r/` `flip--` `div-inv`
4×	`frac-times` `associate-*r/`
3×	`sub-neg`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-neg-in` `diff-log` `pow-prod-down` `sqrt-prod` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 197

Calls

4 calls:

3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
38.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
68.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
154.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
89.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify51.0ms

Algorithm

egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1170	3195
1	5001	2443

prune319.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

100×	`times-frac`
96×	`add-exp-log`
88×	`add-cbrt-cube`
67×	`add-sqr-sqrt`
63×	`add-cube-cbrt` `*-un-lft-identity`
41×	`prod-exp` `cbrt-unprod`
29×	`div-exp`
26×	`associate-r`
21×	`cbrt-undiv`
14×	`distribute-lft-out` `associate-/l*`
10×	`associate-l`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-inv`
8×	`pow1` `sqrt-div` `associate-*l/` `distribute-neg-frac`
7×	`associate-/r/`
6×	`sqrt-prod`
5×	`1-exp` `frac-add` `associate-/r*`
4×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
2×	`neg-mul-1` `rec-exp` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `distribute-rgt-neg-out` `unswap-sqr`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

4 → 213

Calls

4 calls:

7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
50.0ms	(/ (/ 1 1) (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
47.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
28.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- b))

series353.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
188.0ms	(/ (/ 1 1) (+ (* (/ (* 2.0 a) (* 4.0 (* a c))) (- b)) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
127.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* (* 4.0 a) c)))))
26.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- b))

simplify67.0ms

Algorithm

egg-herbie

Counts

225 → 225

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1223	4087
1	5001	3547

prune477.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.4b 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	28	13
1	28	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

364.0ms	3656×	body	320	valid
296.0ms	16202×	pre	80	true
260.0ms	8202×	body	80	nan
195.0ms	2901×	body	160	valid
70.0ms	482×	body	640	valid
32.0ms	961×	body	80	valid