Details

sample62.0ms

Algorithm

intervals

Results

12.0ms	129×	body	320	valid
9.0ms	546×	pre	80	true
9.0ms	290×	body	80	nan
5.0ms	80×	body	160	valid
2.0ms	13×	body	640	valid
1.0ms	34×	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: 52.1b

localize15.0ms

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))
23.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite104.0ms

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)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
62.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series324.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
51.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (39.0ms)

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

prune242.0ms

Pruning

4 alts after pruning (4 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))

rewrite178.0ms

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))
53.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
79.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series486.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
47.0ms	(- (* b b) (* (* 4.0 a) c))
198.0ms	(/ (+ 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))

simplify142.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (110.0ms)

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

prune567.0ms

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) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

181×	`prod-diff`
133×	`add-sqr-sqrt`
131×	`*-un-lft-identity`
123×	`add-cube-cbrt`
92×	`sqrt-prod`
62×	`distribute-rgt-in` `distribute-lft-in`
59×	`distribute-rgt-neg-in`
57×	`distribute-lft-neg-in`
27×	`add-exp-log` `add-cbrt-cube`
19×	`neg-mul-1`
11×	`fma-neg`
10×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `associate-*r/` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `associate-l`
2×	`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 → 285

Calls

4 calls:

28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
91.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
38.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
115.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
52.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify152.0ms

Counts

297 → 297

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	797	8337
1	4394	5185
2	5001	5161
done	5001	5161

prune453.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0b	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.1b	(- (* b b) (* (* 4.0 a) c))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
73×	`times-frac`
70×	`add-cube-cbrt`
61×	`prod-diff`
42×	`sqrt-prod`
30×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
13×	`add-cbrt-cube`
11×	`fma-neg`
10×	`add-log-exp`
9×	`div-exp` `div-inv`
7×	`neg-mul-1` `associate-/r` `associate-/l`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div` `1-exp` `prod-exp` `associate-/r/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 209

Calls

4 calls:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))

series399.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
189.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
48.0ms	(- (* b b) (* (* 4.0 a) c))

simplify94.0ms

Counts

221 → 221

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	757	4277
1	3241	3087
2	5001	3006
done	5001	3006

prune420.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes88.0ms

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	24	12
1	24	12
done	24	12

end0.0ms

sample1.7s

Algorithm

intervals

Results

372.0ms	3691×	body	320	valid
277.0ms	16155×	pre	80	true
258.0ms	8155×	body	80	nan
193.0ms	2902×	body	160	valid
75.0ms	547×	body	640	valid
29.0ms	860×	body	80	valid