Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
9.0ms	183×	body	80	valid
8.0ms	35×	body	1280	valid
4.0ms	79×	body	80	nan
3.0ms	16×	body	640	valid
1.0ms	2×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	2×	body	320	valid

simplify105.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	111
5	111
4	102
3	78
2	44
1	24
0	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
0.2b	(- (* b b) (* (* c a) 4.0))
1.3b	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
24.2b	(sqrt (- (* b b) (* (* c a) 4.0)))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/l*`
16×	`sqrt-prod`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
5×	`pow1` `div-inv`
3×	`cbrt-undiv` `associate-/r*` `flip3--` `div-exp` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `div-sub`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 149

Calls

4 calls:

113.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
12.0ms	(- (* b b) (* (* c a) 4.0))
63.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
18.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (/ (- (sqrt (- (* b b) (* (* c a) 4.0))) b) 2.0) a)
84.0ms	(- (* b b) (* (* c a) 4.0))
109.0ms	(- (sqrt (- (* b b) (* (* c a) 4.0))) b)
121.0ms	(sqrt (- (* b b) (* (* c a) 4.0)))

simplify1.6s

Counts

161 → 161

Iterations

Iter	Nodes
done	5002
2	3070
1	692
0	280

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
1.3b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
40×	`div-exp`
31×	`times-frac`
25×	`add-cbrt-cube`
24×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`1-exp`
14×	`prod-exp`
13×	`associate-/l*`
11×	`cbrt-undiv`
8×	`add-log-exp`
6×	`rec-exp`
5×	`pow1`
4×	`sqrt-prod` `cbrt-unprod`
3×	`flip3--` `div-inv` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/r/` `distribute-lft-out--` `associate-/l/`

Counts

4 → 108

Calls

4 calls:

14.0ms	(- (* b b) (* 4.0 (* a c)))
66.0ms	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
66.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series539.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b b) (* 4.0 (* a c)))
229.0ms	(/ (/ 1 1) (* (/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) 2.0))
140.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
115.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2984
1	679
0	224

prune551.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* a (* c 4.0)))
0.2b	(* (/ 1 a) (- (sqrt (- (* b b) (* a (* c 4.0)))) b))
1.3b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
24.2b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

13.0ms	(- (* b b) (* a (* c 4.0)))
113.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* a (* c 4.0)))) b))
62.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
14.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (* b b) (* a (* c 4.0)))
208.0ms	(* (/ 1 a) (- (sqrt (- (* b b) (* a (* c 4.0)))) b))
139.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
82.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	2487
1	451
0	166

prune565.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.7b

localize40.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.3b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
24.2b	(sqrt (- (* b b) (* a (* c 4.0))))
24.2b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite571.0ms

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×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

498.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
43.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
7.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
20.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
145.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
98.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
141.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify3.0s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	4465
2	793
1	199
0	81

prune415.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.7b

regimes340.0ms

Accuracy

83.1% (4.9b remaining)

Error of 10.3b against oracle of 5.4b and baseline of 34.7b

bsearch113.0ms

Steps

Iters	Range		Point
7	1.726360512453143e-63	2.3465896586148578e-61	1.3696631973385881e-61
5	-4.0529501114613944e+21	-1.3554105129294137e+21	-3.9950858563514354e+21

simplify7.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample2.8s

Algorithm

intervals

Results

857.0ms	1094×	body	2560	valid
477.0ms	5779×	body	80	valid
441.0ms	931×	body	1280	valid
293.0ms	2886×	body	80	nan
103.0ms	448×	body	640	valid
91.0ms	93×	body	5120	valid
40.0ms	226×	body	320	valid
14.0ms	125×	body	160	valid