Details

sample65.0ms

Algorithm

intervals

Results

18.0ms	196×	body	80	valid
13.0ms	29×	body	2560	valid
10.0ms	28×	body	1280	valid
7.0ms	99×	body	80	nan
4.0ms	13×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify58.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize17.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 175

Calls

4 calls:

Slowest

61.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
45.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

126.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
123.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
90.0ms	(sqrt (- (* b_2 b_2) (* a c)))
51.0ms	(- (* b_2 b_2) (* a c))

simplify304.0ms

Counts: 280 → 187

prune1.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.5b

localize21.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
0.9b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

Slowest

28.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
24.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

160.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
46.0ms	(- (* b_2 b_2) (* a c))

simplify550.0ms

Counts: 424 → 273

prune3.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.5b

localize20.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
6.1b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
0.6b	(- (* b_2 b_2) (* a c))
0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 893

Calls

4 calls:

Slowest

56.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
27.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
15.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

157.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
152.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(- (* b_2 b_2) (* a c))

simplify2.0s

Counts: 1687 → 905

prune12.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.5b

localize52.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (- (* b_2 b_2) (* a c)))
15.8b	(- (* b_2 b_2) (- (* b_2 b_2) (* a c)))
7.3b	(/ (- (* b_2 b_2) (- (* b_2 b_2) (* a c))) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.6b	(- (* b_2 b_2) (* a c))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
20×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-log-exp`
10×	`distribute-lft-out`
7×	`difference-of-squares`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*` `distribute-rgt-neg-in` `prod-diff`
4×	`expm1-log1p-u` `flip3--` `diff-log` `insert-posit16` `log1p-expm1-u` `flip--` `associate-/l*`
3×	`sub-neg` `sqrt-prod` `associate--r+`
2×	`fma-neg` `sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `flip-+` `div-inv` `associate--r-`

Counts

4 → 109

Calls

4 calls:

Slowest

130.0ms	(/ (- (* b_2 b_2) (- (* b_2 b_2) (* a c))) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
35.0ms	(- (* b_2 b_2) (- (* b_2 b_2) (* a c)))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(- (* b_2 b_2) (* a c))

series380.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(/ (- (* b_2 b_2) (- (* b_2 b_2) (* a c))) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))
42.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (* b_2 b_2) (- (* b_2 b_2) (* a c)))

simplify549.0ms

Counts: 155 → 121

prune1.2s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.5b

regimes289.0ms

Accuracy

82.9% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 32.9b

bsearch186.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

772.0ms	5900×	body	80	valid
739.0ms	1055×	body	2560	valid
639.0ms	885×	body	1280	valid
509.0ms	228×	body	320	valid
399.0ms	2923×	body	80	nan
171.0ms	420×	body	640	valid
92.0ms	116×	body	5120	valid
48.0ms	118×	body	160	valid