Details

sample62.0ms

Algorithm

intervals

Results

14.0ms	292×	body	80	nan
10.0ms	134×	body	160	valid
10.0ms	548×	pre	80	true
4.0ms	122×	body	80	valid

simplify12.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize11.0ms

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))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

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:

12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* 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))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
89.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify48.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

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

prune264.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite183.0ms

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))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
80.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms	(- (* b b) (* (* 4.0 a) c))
158.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
192.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify150.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (117.0ms)

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

prune563.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
70×	`add-cube-cbrt`
61×	`prod-diff`
51×	`add-exp-log`
46×	`times-frac`
38×	`sqrt-prod`
29×	`distribute-rgt-neg-in`
27×	`associate-l` `add-cbrt-cube`
21×	`distribute-lft-neg-in`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`neg-mul-1` `associate-r` `associate-/r*`
6×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`diff-log` `div-inv` `associate-/l*`
2×	`sub-neg` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 226

Calls

4 calls:

27.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
110.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
55.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series472.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
46.0ms	(- (* b b) (* (* 4.0 a) c))
156.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
188.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify174.0ms

Counts

238 → 238

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	924	4825
1	4731	3436
2	5001	3436
done	5001	3436

prune532.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt` `*-un-lft-identity`
61×	`prod-diff`
59×	`add-cube-cbrt`
54×	`add-exp-log` `add-cbrt-cube`
44×	`times-frac`
37×	`sqrt-prod`
28×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
19×	`cbrt-undiv` `div-exp`
18×	`prod-exp` `cbrt-unprod`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`div-inv` `add-log-exp`
8×	`associate-/r*`
7×	`neg-mul-1`
6×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
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 → 209

Calls

4 calls:

22.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
59.0ms	(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
14.0ms	(- (* b b) (* (* 4.0 a) c))

series320.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/ (* 4.0 (* a c)) (* 2.0 a))
90.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
169.0ms	(/ (/ (* 4.0 (* a c)) (* 2.0 a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms	(- (* b b) (* (* 4.0 a) c))

simplify145.0ms

Counts

221 → 221

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	851	4438
1	4856	3131
2	5001	3129
done	5001	3129

prune470.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes130.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12
done	26	12

end0.0ms

sample1.5s

Algorithm

intervals

Results

322.0ms	4496×	body	160	valid
299.0ms	8759×	body	80	nan
291.0ms	16759×	pre	80	true
129.0ms	3504×	body	80	valid