Details

sample69.0ms

Algorithm

intervals

Results

14.0ms	143×	body	160	valid
12.0ms	253×	body	80	nan
12.0ms	509×	pre	80	true
6.0ms	113×	body	80	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
27.4b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite162.0ms

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:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
77.0ms	(- (* b b) (* (* 4.0 a) c))
174.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
98.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	167	1697
1	452	1588
2	2118	1361
done	5001	1352

prune369.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite285.0ms

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:

15.0ms	(- (* b b) (* (* 4.0 a) c))
44.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
111.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
95.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series584.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 4.0 a) c))
101.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
235.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
198.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify447.0ms

Counts

243 → 243

Iterations

Useful iterations: done (431.0ms)

Iter	Nodes	Cost
0	339	10026
1	861	7622
done	5000	6606

prune852.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite337.0ms

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:

171.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms	(/ (* (* 4.0 a) c) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
49.0ms	(- (* b b) (* (* 4.0 a) c))
95.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
204.0ms	(/ (* (* 4.0 a) c) (* a (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify607.0ms

Counts

297 → 297

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	363	16959
1	914	11277
done	5000	8818

prune788.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite171.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 170

Calls

4 calls:

13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
66.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(- (* b b) (* (* 4.0 a) c))
68.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series599.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
289.0ms	(/ c (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
60.0ms	(- (* b b) (* (* 4.0 a) c))
132.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify2.0s

Counts

182 → 182

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	239	6987
1	556	5006
2	2201	4086
done	5004	3438

prune684.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes140.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	26
1	31	24
2	43	24
3	47	24
done	47	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	4385×	body	160	valid
856.0ms	8610×	body	80	nan
706.0ms	16610×	pre	80	true
353.0ms	3615×	body	80	valid