Details

sample130.0ms

Algorithm

intervals

Results

49.0ms	43×	body	2560	valid
16.0ms	176×	body	80	valid
13.0ms	31×	body	1280	valid
9.0ms	106×	body	80	nan
6.0ms	18×	body	640	valid
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	14	17
1	24	17
2	44	16
3	78	16
4	91	16
5	99	16
done	99	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize14.0ms

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)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
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 → 72

Calls

4 calls:

117.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
48.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
65.0ms	(- (* b b) (* (* 4.0 a) c))
94.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
90.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	154	1592
1	386	1488
2	1233	1332
3	4648	1324
done	5002	1324

prune322.0ms

Pruning

8 alts after pruning (8 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

prune32.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize16.0ms

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)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

60×	`times-frac`
47×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod` `add-log-exp`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
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 → 118

Calls

4 calls:

84.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
9.0ms	(- (* b b) (* (* 4.0 a) c))
78.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
56.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
113.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

130 → 130

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	220	3137
1	497	2801
2	1461	2561
done	5000	2481

prune359.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
7×	`*-un-lft-identity`
6×	`times-frac`
4×	`difference-of-squares`
3×	`add-log-exp`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `frac-sub` `add-cbrt-cube` `flip--`

Counts

1 → 19

Calls

1 calls:

45.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify3.6s

Counts

22 → 22

Iterations

Useful iterations: 5 (1.9s)

Iter	Nodes	Cost
0	47	278
1	105	273
2	230	259
3	528	259
4	1400	259
5	4344	257
done	5000	257

prune59.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

regimes602.0ms

Accuracy

82.2% (6.0b remaining)

Error of 11.9b against oracle of 5.9b and baseline of 39.8b

bsearch109.0ms

Steps

Iters	Range		Point
6	1.6855676195581707e-170	7.565529323099765e-170	7.455592343308264e-170
7	-1.8340745317516165e+50	-1.0728429653156412e+49	-1.5476666036365373e+50

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.3s

Algorithm

intervals

Results

987.0ms	5876×	body	80	valid
591.0ms	1074×	body	2560	valid
486.0ms	885×	body	1280	valid
342.0ms	3010×	body	80	nan
176.0ms	492×	body	640	valid
97.0ms	218×	body	320	valid
83.0ms	107×	body	5120	valid
13.0ms	92×	body	160	valid