Details

sample186.0ms

Algorithm

intervals

Results

21.0ms	43×	body	2560	valid
16.0ms	164×	body	80	valid
13.0ms	32×	body	1280	valid
7.0ms	80×	body	80	nan
5.0ms	16×	body	640	valid
5.0ms	8×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify95.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite277.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

12.0ms	(- (* b_2 b_2) (* a c))
143.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
93.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (* b_2 b_2) (* a c))
145.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
122.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1980
1	491
0	195

prune812.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.6b

localize7.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune45.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 119

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
174.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
62.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series350.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
97.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	3279
1	560
0	215

prune819.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b_2 b_2) (* a c))
0.4b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
55×	`prod-diff`
51×	`add-cube-cbrt`
35×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-l` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `prod-exp` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `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 → 158

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
124.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b_2 b_2) (* a c))
199.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
106.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
86.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	3556
1	679
0	239

prune648.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

regimes418.0ms

Accuracy

87.8% (4.2b remaining)

Error of 9.4b against oracle of 5.2b and baseline of 39.5b

bsearch54.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-3.450829996567048e+138

simplify4.0ms

Iterations

Iter	Nodes
done	26
1	26
0	23

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.0s	5788×	body	80	valid
558.0ms	1095×	body	2560	valid
446.0ms	885×	body	1280	valid
239.0ms	2874×	body	80	nan
166.0ms	470×	body	640	valid
52.0ms	110×	body	5120	valid
47.0ms	244×	body	320	valid
13.0ms	116×	body	160	valid