Details

sample271.0ms

Algorithm

intervals

Results

54.0ms	29×	body	1280	valid
23.0ms	36×	body	2560	valid
23.0ms	184×	body	80	valid
9.0ms	77×	body	80	nan
4.0ms	10×	body	640	valid
3.0ms	10×	body	320	valid
2.0ms	4×	body	5120	valid
1.0ms	4×	body	160	valid

simplify37.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite134.0ms

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--` `insert-posit16` `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 → 122

Calls

4 calls:

70.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
78.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
42.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

134 → 134

Iterations

Iter	Nodes
3	3562
2	1173
1	461
0	199

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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--` `insert-posit16` `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 → 122

Calls

4 calls:

95.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
47.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
11.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
109.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
51.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

134 → 134

Iterations

Iter	Nodes
3	3562
2	1173
1	461
0	199

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite200.0ms

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` `insert-posit16` `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 → 123

Calls

4 calls:

130.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms	(- (* b_2 b_2) (* a c))
75.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

135 → 135

Iterations

Iter	Nodes
3	4151
2	1399
1	527
0	219

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.1b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
23.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite165.0ms

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` `insert-posit16` `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 → 200

Calls

4 calls:

55.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
81.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
54.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.9s

Counts

212 → 212

Iterations

Iter	Nodes
3	5728
2	1838
1	711
0	303

prune2.3s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 4.4b

regimes306.0ms

Accuracy

84.2% (4.4b remaining)

Error of 10.0b against oracle of 5.6b and baseline of 33.3b

bsearch140.0ms

Steps

Iters	Range		Point
10	8.951341119180922e-71	6.02619389320856e-56	2.3930366094323856e-68
8	-5.520406447692031e+155	-8.116303404487084e+152	-4.82289647433212e+153

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	5821×	body	80	valid
861.0ms	1114×	body	2560	valid
634.0ms	912×	body	1280	valid
328.0ms	2904×	body	80	nan
175.0ms	416×	body	640	valid
80.0ms	110×	body	5120	valid
70.0ms	229×	body	320	valid
21.0ms	105×	body	160	valid