Details

sample57.0ms

Algorithm

intervals

Results

10.0ms	157×	body	160	valid
9.0ms	288×	body	80	nan
9.0ms	544×	pre	80	true
4.0ms	44×	body	320	valid
2.0ms	55×	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: 44.8b

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))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
39.0b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite112.0ms

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:

11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
64.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
26.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series311.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
48.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
83.0ms	(+ (- 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

prune231.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (- 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))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite190.0ms

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:

9.0ms	(- (* b b) (* (* 4.0 a) c))
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
82.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
58.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series483.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
194.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify148.0ms

Counts

243 → 243

Iterations

Useful iterations: 2 (114.0ms)

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

prune542.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite192.0ms

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:

8.0ms	(- (* b b) (* (* 4.0 a) c))
92.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
29.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
43.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
83.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
155.0ms	(/ (* 4.0 (* a c)) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify149.0ms

Counts

297 → 297

Iterations

Useful iterations: 2 (100.0ms)

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

prune428.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

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

rewrite107.0ms

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)))
8.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
28.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series395.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
50.0ms	(- (* b b) (* (* 4.0 a) c))
185.0ms	(/ (/ (* c 4.0) 1) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
85.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify94.0ms

Counts

221 → 221

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	757	4277
1	3239	3087
2	5001	3006
done	5001	3006

prune381.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	20
1	28	20
done	28	20

end0.0ms

sample1.5s

Algorithm

intervals

Results

323.0ms	4880×	body	160	valid
282.0ms	16304×	pre	80	true
267.0ms	8304×	body	80	nan
135.0ms	1364×	body	320	valid
58.0ms	1756×	body	80	valid