Details

sample102.0ms

Algorithm

intervals

Results

24.0ms	176×	body	80	valid
23.0ms	43×	body	2560	valid
13.0ms	31×	body	1280	valid
9.0ms	106×	body	80	nan
6.0ms	18×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify142.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite207.0ms

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:

106.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
19.0ms	(- (* b b) (* (* 4.0 a) c))
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
33.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
87.0ms	(- (* b b) (* (* 4.0 a) c))
99.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
96.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

102 → 102

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	167	1697
1	433	1584
2	1488	1361
done	5000	1347

prune458.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize22.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.1b	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.7b	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite304.0ms

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:

46.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
93.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
242.0ms	(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
249.0ms	(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

244 → 244

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	338	10067
1	811	7605
2	3063	6508
done	5000	6422

prune864.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.7b	(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
152×	`times-frac`
150×	`*-un-lft-identity`
109×	`add-cube-cbrt`
94×	`add-exp-log`
85×	`associate-r`
61×	`prod-diff`
58×	`add-cbrt-cube`
43×	`sqrt-prod`
39×	`div-exp`
35×	`prod-exp`
31×	`distribute-rgt-neg-in`
21×	`cbrt-undiv` `distribute-lft-neg-in` `cbrt-unprod`
20×	`distribute-lft-out--` `difference-of-squares`
11×	`fma-neg`
10×	`add-log-exp`
7×	`pow1` `neg-mul-1` `associate-l`
6×	`flip3--` `associate-/r/` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `unswap-sqr`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `*-commutative`

Counts

4 → 265

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
217.0ms	(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
244.0ms	(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts

277 → 277

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	442	10420
1	1225	7945
2	4180	6391
done	5000	6342

prune916.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 4.0 a) c))
1.2b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.8b	(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
24.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite264.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

13.0ms	(- (* b b) (* (* 4.0 a) c))
58.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
162.0ms	(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
24.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(- (* b b) (* (* 4.0 a) c))
123.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
276.0ms	(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
101.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

164 → 164

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	267	6876
1	648	4772
2	2958	3777
done	5000	3692

prune643.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

Details

sample102.0ms

simplify142.0ms

prune6.0ms

localize16.0ms

rewrite207.0ms

series438.0ms

simplify1.4s

prune458.0ms

localize22.0ms

rewrite304.0ms

series715.0ms

simplify1.9s

prune864.0ms

localize29.0ms

rewrite315.0ms

series551.0ms

simplify2.4s

prune916.0ms

localize42.0ms

rewrite264.0ms

series590.0ms

simplify2.3s

prune643.0ms

regimes272.0ms

bsearch1.0ms