Details

sample169.0ms

Algorithm

intervals

Results

20.0ms	43×	body	2560	valid
15.0ms	176×	body	80	valid
12.0ms	31×	body	1280	valid
8.0ms	106×	body	80	nan
6.0ms	19×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	10	13
1	15	13
2	23	12
3	30	12
4	32	12
5	34	12
done	34	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize28.0ms

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))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

112.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series424.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
65.0ms	(- (* b_2 b_2) (* a c))
122.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.9s

Counts

112 → 112

Iterations

Useful iterations: done (3.9s)

Iter	Nodes	Cost
0	164	1638
1	385	1535
2	1103	1355
3	3179	1340
done	5000	1332

prune464.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

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

prune16.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.3b

localize13.0ms

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))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite251.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
13×	`add-exp-log` `associate-r`
11×	`times-frac`
10×	`fma-def` `add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`distribute-rgt-neg-in` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out`
3×	`distribute-lft-neg-in` `flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `associate-r/` `prod-diff` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 104

Calls

4 calls:

151.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
18.0ms	(- (* b_2 b_2) (* a c))
60.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms	(- (* b_2 b_2) (* a c))
103.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
96.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.3s

Counts

116 → 116

Iterations

Useful iterations: 3 (2.7s)

Iter	Nodes	Cost
0	188	1751
1	468	1536
2	1429	1313
3	4575	1286
done	5000	1286

prune505.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(/ (+ 0 (* c a)) a)
24.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 154

Calls

4 calls:

18.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(/ (+ 0 (* c a)) a)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b_2 b_2) (* a c))
81.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(/ (+ 0 (* c a)) a)
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

166 → 166

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	235	5314
1	509	3555
2	1470	2844
done	5000	2249

prune528.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 5.2b

Details

sample169.0ms

simplify32.0ms

prune9.0ms

localize28.0ms

rewrite208.0ms

series424.0ms

simplify3.9s

prune464.0ms

localize5.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune16.0ms

localize13.0ms

rewrite251.0ms

series354.0ms

simplify4.3s

prune505.0ms

localize15.0ms

rewrite100.0ms

series246.0ms

simplify2.5s

prune528.0ms

regimes198.0ms

bsearch2.0ms