Details

sample344.0ms

Algorithm

intervals

Results

167.0ms	23×	body	1280	valid
54.0ms	189×	body	80	valid
27.0ms	34×	body	2560	valid
10.0ms	80×	body	80	nan
6.0ms	12×	body	640	valid
5.0ms	3×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify101.0ms

Counts: 1 → 1

prune118.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize53.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)

rewrite215.0ms

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:

Slowest

106.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
67.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(- (* b_2 b_2) (* a c))

series302.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

96.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))
79.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
39.0ms	(- (* b_2 b_2) (* a c))

simplify1.2s

Counts: 134 → 134

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize20.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))

rewrite156.0ms

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:

Slowest

65.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
53.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(- (* b_2 b_2) (* a c))

series428.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

154.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
120.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))
65.0ms	(- (* b_2 b_2) (* a c))

simplify985.0ms

Counts: 212 → 212

prune2.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.2b	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))

rewrite277.0ms

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` `insert-posit16` `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 → 162

Calls

4 calls:

Slowest

185.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
65.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(* (/ 1 a) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
100.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(- (* b_2 b_2) (* a c))

simplify1.7s

Counts: 174 → 174

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
21.4b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (* b_2 b_2) (* a c))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 70

Calls

4 calls:

Slowest

12.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series330.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(sqrt (- (* b_2 b_2) (* a c)))
105.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(- (* b_2 b_2) (* a c))

simplify1.6s

Counts: 82 → 82

prune940.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

regimes338.0ms

Accuracy

83.4% (4.7b remaining)

Error of 10.0b against oracle of 5.3b and baseline of 33.5b

bsearch182.0ms

end0.0ms

sample3.8s

Algorithm

intervals

Results

888.0ms	1095×	body	2560	valid
832.0ms	2810×	body	80	nan
778.0ms	5798×	body	80	valid
493.0ms	860×	body	1280	valid
241.0ms	485×	body	640	valid
127.0ms	106×	body	5120	valid
116.0ms	247×	body	320	valid
27.0ms	129×	body	160	valid