Details

sample41.0ms

Algorithm

intervals

Results

9.0ms	40×	body	2560	valid
7.0ms	187×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	86×	body	80	nan
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	5×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	45	16
3	87	16
4	106	16
5	114	16
done	114	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.3b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

33.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
52.0ms	(- (* b b) (* (* 4.0 a) c))
86.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
75.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify489.0ms

Counts

102 → 102

Iterations

Useful iterations: done (487.0ms)

Iter	Nodes	Cost
0	167	1697
1	449	1584
2	1576	1361
done	5000	1351

prune303.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0b	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
8.8b	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
124×	`*-un-lft-identity`
90×	`times-frac`
80×	`add-cube-cbrt`
60×	`prod-diff`
44×	`sqrt-prod`
32×	`distribute-rgt-neg-in`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`add-exp-log` `add-cbrt-cube`
10×	`fma-neg`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `neg-mul-1` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 232

Calls

4 calls:

15.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
53.0ms	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
37.0ms	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
151.0ms	(/ (/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
182.0ms	(/ (+ (* (* 4.0 a) c) (* b (- b b))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
72.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify924.0ms

Counts

244 → 244

Iterations

Useful iterations: done (914.0ms)

Iter	Nodes	Cost
0	337	10795
1	843	8234
2	2941	6675
done	5000	6673

prune580.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
0.8b	(- (pow b 2) (* 4.0 (* a c)))
1.3b	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
21.1b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`fma-neg` `prod-diff`
6×	`unpow-prod-down` `distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/` `unpow2` `sqr-pow`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 104

Calls

4 calls:

49.0ms	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
12.0ms	(- (pow b 2) (* 4.0 (* a c)))
17.0ms	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
10.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c))))) (* 2.0 a))
53.0ms	(- (pow b 2) (* 4.0 (* a c)))
87.0ms	(+ (- b) (sqrt (- (pow b 2) (* 4.0 (* a c)))))
77.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify118.0ms

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	182	1925
1	474	1793