Details

sample90.0ms

Algorithm

intervals

Results

19.0ms	43×	body	2560	valid
16.0ms	176×	body	80	valid
11.0ms	31×	body	1280	valid
8.0ms	106×	body	80	nan
5.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify174.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

155.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
18.0ms	(- (* b b) (* 4.0 (* a c)))
76.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 2.0 a))
94.0ms	(- (* b b) (* 4.0 (* a c)))
152.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
134.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	193	2476
1	481	2169
2	1419	1861
done	5000	1789

prune502.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize9.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify1.0ms

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
done	0	0

prune35.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.4b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.7b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

111.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
19.0ms	(- (* b b) (* 4.0 (* a c)))
70.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
23.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
61.0ms	(- (* b b) (* 4.0 (* a c)))
112.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
124.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify2.0s

Counts

164 → 164

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	259	4025
1	588	3484
2	1633	3082
done	5000	2938

prune386.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (/ c b) (/ b a))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

249×	`times-frac`
202×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
190×	`add-cube-cbrt`
169×	`prod-diff`
27×	`div-inv`
13×	`fma-neg`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 203

Calls

1 calls:

49.0ms

(- (/ c b) (/ b a))

series39.0ms

Counts

1 → 3

Calls

1 calls:

39.0ms

(- (/ c b) (/ b a))

simplify4.0s

Counts

206 → 206

Iterations

Useful iterations: 3 (2.3s)

Iter	Nodes	Cost
0	310	7860
1	681	6866
2	1473	4941
3	4664	3536
done	5000	3536

prune246.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.2b

Details

sample90.0ms

simplify174.0ms

prune11.0ms

localize39.0ms

rewrite277.0ms

series561.0ms

simplify1.5s

prune502.0ms

localize9.0ms

rewrite0.0ms

series0.0ms

simplify1.0ms

prune35.0ms

localize40.0ms

rewrite229.0ms

series498.0ms

simplify2.0s

prune386.0ms

localize7.0ms

rewrite82.0ms

series39.0ms

simplify4.0s

prune246.0ms

regimes408.0ms

bsearch4.0ms