Details

sample90.0ms

Algorithm

intervals

Results

36.0ms	36×	body	2560	valid
14.0ms	190×	body	80	valid
8.0ms	28×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite233.0ms

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:

120.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
15.0ms	(- (* b b) (* (* 4.0 a) c))
75.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
78.0ms	(- (* b b) (* (* 4.0 a) c))
146.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
103.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.4s

Counts

84 → 84

Iterations

Useful iterations: 3 (1.8s)

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

prune336.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite209.0ms

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:

97.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
17.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
25.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series530.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
82.0ms	(- (* b b) (* (* 4.0 a) c))
129.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

130 → 130

Iterations

Useful iterations: done (1.3s)

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

prune432.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

71×	`times-frac`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
43×	`associate-l`
41×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`div-exp` `associate-r`
5×	`flip3--` `prod-exp` `sqrt-prod` `flip--`
4×	`sub-neg` `div-inv` `difference-of-squares` `unswap-sqr`
3×	`cbrt-undiv` `cbrt-unprod`
2×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `sqrt-div` `diff-log` `associate-*r/` `distribute-lft-out--`
1×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 121

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
215.0ms	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
83.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* (* 4.0 a) c))
194.0ms	(* (/ (/ 1 a) 2.0) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
124.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
108.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.2s

Counts

133 → 133

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	246	2733
1	621	2575
2	1830	2263
done	5000	2227

prune463.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

45.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
79.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
112.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	81	1248
1	190	1104
2	570	1036
3	1885	1028
done	5000	1016

prune292.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes260.0ms

Accuracy

84.2% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 34.2b

bsearch276.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.5501620157466267e+150

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample3.2s

Algorithm

intervals

Results

854.0ms	1076×	body	2560	valid
589.0ms	468×	body	640	valid
569.0ms	5882×	body	80	valid
394.0ms	848×	body	1280	valid
304.0ms	2915×	body	80	nan
55.0ms	107×	body	5120	valid
43.0ms	212×	body	320	valid
17.0ms	122×	body	160	valid