Details

sample142.0ms

Algorithm

intervals

Results

12.0ms	43×	body	2560	valid
10.0ms	176×	body	80	valid
7.0ms	31×	body	1280	valid
4.0ms	106×	body	80	nan
3.0ms	19×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify28.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	10	13
1	14	13
2	22	12
3	25	12
4	27	12
5	29	12
done	29	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

153.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
17.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
56.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

96 → 96

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	154	1624
1	361	1526
2	927	1426
3	2327	1418
done	5000	1410

prune308.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.2b	(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
9.5b	(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod` `associate-/l/`
2×	`flip3--` `frac-2neg` `sub0-neg` `sqrt-div` `clear-num` `flip--`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 156

Calls

4 calls:

62.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
83.0ms	(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
95.0ms	(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series710.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
267.0ms	(/ (/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
255.0ms	(/ (- 0 (* c a)) (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

168 → 168

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	271	4493
1	680	4026
2	2152	3822
done	5000	3772

prune588.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
0.8b	(- (* b_2 b_2) (* a c))
1.2b	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 72

Calls

4 calls:

49.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
8.0ms	(- (* b_2 b_2) (* a c))
51.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series583.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ c (+ (sqrt (- (* b_2 b_2) (* a c))) b_2))
51.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(+ (sqrt (- (* b_2 b_2) (* a c))) b_2)
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.8s

Counts

84 → 84

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	128	1320
1	279	1222
2	712	1124
3	1701	1121
4	4372	1109
done	5000	1107

prune376.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune1.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.2b

Details

sample142.0ms

simplify28.0ms

prune8.0ms

localize12.0ms

rewrite300.0ms

series392.0ms

simplify2.3s

prune308.0ms

localize14.0ms

rewrite268.0ms

series710.0ms

simplify1.9s

prune588.0ms

localize21.0ms

rewrite119.0ms

series583.0ms

simplify3.8s

prune376.0ms

localize9.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune1.0ms

regimes204.0ms

bsearch3.0ms