Details

sample192.0ms

Algorithm

intervals

Results

24.0ms	192×	body	80	valid
20.0ms	31×	body	2560	valid
14.0ms	25×	body	1280	valid
11.0ms	99×	body	80	nan
5.0ms	12×	body	640	valid
4.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify69.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	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: 32.6b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite179.0ms

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:

93.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
54.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
114.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
40.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
3	3562
2	1173
1	461
0	199

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite211.0ms

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:

89.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
84.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
16.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
117.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
53.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

134 → 134

Iterations

Iter	Nodes
3	3562
2	1173
1	461
0	199

prune1.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
0.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.6b	(- (* b_2 b_2) (* a c))
24.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite152.0ms

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:

59.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
10.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
113.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
71.0ms	(- (* b_2 b_2) (* a c))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.5s

Counts

212 → 212

Iterations

Iter	Nodes
3	5728
2	1838
1	711
0	303

prune2.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.9b

localize10.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

17.0ms

(* -1/2 (/ c b_2))

series31.0ms

Counts

1 → 3

Calls

1 calls:

31.0ms

(* -1/2 (/ c b_2))

simplify4.7s

Counts

38 → 38

Iterations

Iter	Nodes
4	3577
3	1105
2	448
1	169
0	71

prune285.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.9b

regimes406.0ms

Accuracy

83% (4.7b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.2b

bsearch153.0ms

Steps

Iters	Range		Point
6	3.7222086374392734e-21	4.963951531010332e-20	3.821014310434392e-21
10	-3.568388406125044e+108	-3.585760457965514e+97	-5.571206846913461e+106

simplify4.0ms

Iterations

Iter	Nodes
2	26
1	26
0	23

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	1029×	body	2560	valid
865.0ms	5858×	body	80	valid
703.0ms	890×	body	1280	valid
342.0ms	2857×	body	80	nan
216.0ms	469×	body	640	valid
88.0ms	107×	body	5120	valid
67.0ms	201×	body	320	valid
32.0ms	140×	body	160	valid