Details

sample101.0ms

Algorithm

intervals

Results

41.0ms	41×	body	2560	valid
12.0ms	186×	body	80	valid
10.0ms	28×	body	1280	valid
7.0ms	108×	body	80	nan
5.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	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)))

rewrite642.0ms

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:

515.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
18.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
60.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.4s

Counts

183 → 183

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1408	3549
done	5000	3001

prune513.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize31.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
5.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
10.3b	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
24.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
6×	`flip3--` `fma-neg` `flip--` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 217

Calls

4 calls:

12.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
68.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
75.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
3.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series724.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
233.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)) a)
272.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
118.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.4s

Counts

229 → 229

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	329	6395
1	757	5450
2	2207	5130
done	5002	5015

prune905.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0b	(fma b_2 b_2 (- (* c a)))
1.4b	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
24.0b	(sqrt (fma b_2 b_2 (- (* c a))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-exp-log` `fma-neg` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/l*`
2×	`flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

31.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
1.0ms	(fma b_2 b_2 (- (* c a)))
23.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
4.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

series652.0ms

Counts

4 → 12

Calls

4 calls:

371.0ms	(/ c (- (sqrt (fma b_2 b_2 (- (* c a)))) b_2))
56.0ms	(fma b_2 b_2 (- (* c a)))
110.0ms	(- (sqrt (fma b_2 b_2 (- (* c a)))) b_2)
115.0ms	(sqrt (fma b_2 b_2 (- (* c a))))

simplify2.3s

Counts

121 → 121

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	167	2224
1	334	1950
2	702	1731
3	1968	1653
done	5000	1598

prune452.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

localize8.0ms

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

sample101.0ms

simplify49.0ms

prune5.0ms

localize24.0ms

rewrite642.0ms

series418.0ms

simplify1.4s

prune513.0ms

localize31.0ms

rewrite172.0ms

series724.0ms

simplify2.4s

prune905.0ms

localize35.0ms

rewrite66.0ms

series652.0ms

simplify2.3s

prune452.0ms

localize8.0ms

rewrite0.0ms

series0.0ms

simplify0.0ms

prune0.0ms

regimes274.0ms

bsearch3.0ms