Details

sample59.0ms

Algorithm

intervals

Results

13.0ms	98×	body	320	valid
8.0ms	499×	pre	80	true
8.0ms	243×	body	80	nan
7.0ms	99×	body	160	valid
3.0ms	20×	body	640	valid
1.0ms	39×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	9
1	46	9
2	86	9
3	113	9
4	121	9
5	121	9
done	121	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 50.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(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))
26.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-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` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

10.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
111.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	438	854
1	1702	750
2	5002	735
done	5002	735

prune235.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

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))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

123×	`add-sqr-sqrt` `*-un-lft-identity`
90×	`times-frac`
79×	`add-cube-cbrt`
61×	`prod-diff`
41×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `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 → 231

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
84.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series492.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
50.0ms	(- (* b b) (* (* 4.0 a) c))
192.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
159.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify156.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	832	5099
1	3967	3830
2	5001	3828
done	5001	3828

prune573.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize20.0ms

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)))))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

312×	`add-exp-log`
142×	`div-exp`
138×	`add-cbrt-cube`
137×	`prod-exp`
121×	`prod-diff`
102×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
96×	`add-cube-cbrt`
62×	`distribute-rgt-in` `distribute-lft-in`
61×	`sqrt-prod`
57×	`cbrt-unprod`
48×	`cbrt-undiv`
40×	`1-exp`
37×	`distribute-rgt-neg-in`
36×	`distribute-lft-neg-in`
33×	`times-frac`
16×	`rec-exp`
14×	`associate-/l*`
12×	`neg-mul-1`
7×	`associate-r`
6×	`pow1` `add-log-exp`
5×	`flip3--` `associate-l` `associate-/r/` `flip--` `div-inv`
4×	`expm1-log1p-u` `frac-times` `associate-*r/` `log1p-expm1-u`
3×	`sub-neg`
2×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `distribute-lft-out--` `difference-of-squares`
1×	`fma-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 327

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
21.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
75.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
146.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
164.0ms	(/ (/ 1 1) (* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
97.0ms	(* (/ (* 2.0 a) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify93.0ms

Counts

339 → 339

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1655	9053
1	5001	6430
done	5001	6430

prune434.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

183×	`add-exp-log`
102×	`prod-exp`
87×	`add-cbrt-cube`
61×	`add-sqr-sqrt` `*-un-lft-identity` `prod-diff`
49×	`add-cube-cbrt`
46×	`div-exp`
42×	`cbrt-unprod`
33×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
22×	`cbrt-undiv`
21×	`distribute-lft-neg-in`
13×	`pow1`
12×	`rec-exp` `1-exp`
11×	`fma-neg`
10×	`times-frac` `add-log-exp`
7×	`neg-mul-1` `associate-l` `associate-/r*`
6×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`sub-neg` `associate-*l/` `associate-/r/` `div-inv`
1×	`associate--l-` `neg-sub0` `frac-2neg` `associate-r` `neg-log` `clear-num` `-commutative` `associate-/l/` `associate-/l`

Counts

4 → 220

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
99.0ms	(/ (* (/ 1 (* 2.0 a)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(* (/ 1 (* 2.0 a)) (* 4.0 (* a c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
160.0ms	(/ (* (/ 1 (* 2.0 a)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(* (/ 1 (* 2.0 a)) (* 4.0 (* a c)))

simplify60.0ms

Counts

232 → 232

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	964	4285
1	5001	2793
done	5001	2793

prune352.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes116.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	17	9
done	17	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

354.0ms	3641×	body	320	valid
269.0ms	16291×	pre	80	true
267.0ms	8291×	body	80	nan
196.0ms	2924×	body	160	valid
63.0ms	491×	body	640	valid
31.0ms	944×	body	80	valid