Details

sample99.0ms

Algorithm

intervals

Results

25.0ms	5×	body	5120	valid
19.0ms	41×	body	2560	valid
13.0ms	186×	body	80	valid
9.0ms	28×	body	1280	valid
7.0ms	108×	body	80	nan
4.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify42.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	18	13
2	32	13
3	41	13
4	44	13
done	44	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize24.0ms

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))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite201.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
8×	`sqrt-prod`
7×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
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 → 91

Calls

4 calls:

92.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series358.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
54.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

103 → 103

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	156	1821
1	366	1727
2	1005	1611
3	2773	1595
done	5001	1593

prune449.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize27.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
5.1b	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.3b	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-/l*`
10×	`sqrt-prod` `associate-/r/`
9×	`associate-/r*`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 127

Calls

4 calls:

50.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
155.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
76.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series796.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
332.0ms	(/ (/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
256.0ms	(/ (* c a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

139 → 139

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	239	3118
1	593	2899
2	1941	2569
done	5000	2563

prune513.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize13.0ms

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))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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

Counts

4 → 83

Calls

4 calls:

56.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
17.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
40.0ms	(- (* b_2 b_2) (* a c))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
91.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

95 → 95

Iterations

Useful iterations: 4 (2.5s)

Iter	Nodes	Cost
0	147	1588
1	311	1491
2	773	1393
3	1814	1389
4	4582	1375
done	5000	1375

prune333.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize5.0ms

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

prune0.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.1b

Details

sample99.0ms

simplify42.0ms

prune5.0ms

localize24.0ms

rewrite201.0ms

series358.0ms

simplify2.8s

prune449.0ms

localize27.0ms

rewrite305.0ms

series796.0ms

simplify1.9s

prune513.0ms

localize13.0ms

rewrite166.0ms

series501.0ms

simplify4.3s

prune333.0ms

localize5.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune0.0ms

regimes197.0ms

bsearch1.0ms