Details

sample285.0ms

Algorithm

intervals

Results

7.0ms	183×	body	80	valid
7.0ms	39×	body	2560	valid
4.0ms	24×	body	1280	valid
3.0ms	84×	body	80	nan
2.0ms	15×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify24.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	45	13
4	47	13
done	47	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite90.0ms

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-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

44.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
28.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify689.0ms

Counts

183 → 183

Iterations

Useful iterations: done (683.0ms)

Iter	Nodes	Cost
0	242	5993
1	566	4363
2	1610	3549
done	5001	3540

prune348.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

55.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
17.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify934.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (223.0ms)

Iter	Nodes	Cost
0	261	5917
1	631	4195
2	1994	3313
done	5001	3313

prune338.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 257

Calls

4 calls:

28.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
3.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

269 → 269

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	351	8660
1	796	6655
2	2464	5553
done	5001	5545

prune382.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.0b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
21.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity`
36×	`times-frac`
32×	`add-sqr-sqrt`
31×	`add-cube-cbrt`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`associate-/l*`
9×	`distribute-lft-out`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `log1p-expm1-u`
3×	`fma-def` `associate-/r*` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `flip--` `flip-+` `associate-/l/` `distribute-neg-frac`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `distribute-frac-neg` `div-exp` `prod-diff` `clear-num` `sum-log` `div-inv`

Counts

4 → 119

Calls

4 calls:

46.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
33.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify407.0ms

Iterations

Useful iterations: 2 (121.0ms)

Iter	Nodes	Cost
0	197	2260
1	442	2136
2	1330	2031