Details

sample162.0ms

Algorithm

intervals

Results

14.0ms	39×	body	2560	valid
10.0ms	177×	body	80	valid
5.0ms	104×	body	80	nan
5.0ms	23×	body	1280	valid
4.0ms	16×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify55.0ms

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: 33.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.4b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite221.0ms

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:

107.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
48.0ms	(- (* b_2 b_2) (* a c))
112.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
120.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.3s

Counts

130 → 130

Iterations

Iter	Nodes
done	5007
2	1420
1	491
0	195

prune752.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite246.0ms

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:

139.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
12.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series391.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
55.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.6s

Counts

131 → 131

Iterations

Iter	Nodes
done	5000
2	1633
1	557
0	215

prune682.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.4b	(- (* b_2 b_2) (* a c))
1.5b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

68.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
6.0ms	(- (* b_2 b_2) (* a c))
49.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
45.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
78.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.7s

Counts

208 → 208

Iterations

Iter	Nodes
done	5001
2	2167
1	741
0	299

prune733.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.4b	(- (* b_2 b_2) (* a c))
7.9b	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
21.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite191.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
287×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
23×	`fma-neg`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--` `distribute-lft-out--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-exp` `frac-sub` `sub-div`

Counts

4 → 411

Calls

4 calls:

26.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
13.0ms	(- (* b_2 b_2) (* a c))
98.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
64.0ms	(- (* b_2 b_2) (* a c))
125.0ms	(- (/ (sqrt (- (* b_2 b_2) (* a c))) a) (/ b_2 a))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

423 → 423

Iterations

Iter	Nodes
done	5000
2	2652
1	1134
0	499

prune2.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.1b

regimes522.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 34.0b

bsearch147.0ms

Steps

Iters	Range		Point
10	2.044647849876085e-45	1.359053137570048e-33	6.407662420749315e-35
10	-8.897020078895062e+156	-1.101416214509623e+146	-8.035809894237901e+152

simplify8.0ms

Iterations

Iter	Nodes
done	27
1	27
0	24

end0.0ms

sample2.7s

Algorithm

intervals

Results

682.0ms	2884×	body	80	nan
510.0ms	5806×	body	80	valid
479.0ms	1030×	body	2560	valid
308.0ms	885×	body	1280	valid
206.0ms	507×	body	640	valid
54.0ms	118×	body	5120	valid
38.0ms	215×	body	320	valid
14.0ms	123×	body	160	valid