Details

sample177.0ms

Algorithm

intervals

Results

48.0ms	18×	body	640	valid
20.0ms	191×	body	80	valid
18.0ms	29×	body	2560	valid
13.0ms	26×	body	1280	valid
8.0ms	80×	body	80	nan
5.0ms	8×	body	320	valid
4.0ms	3×	body	5120	valid
0.0ms	2×	body	160	valid

simplify99.0ms

Counts: 1 → 1

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize31.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)

rewrite154.0ms

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

96.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))

series404.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(sqrt (- (* b_2 b_2) (* a c)))
129.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
57.0ms	(- (* b_2 b_2) (* a c))

simplify729.0ms

Counts: 187 → 187

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))

rewrite99.0ms

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

35.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
29.0ms	(- (- 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)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

135.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
107.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))
46.0ms	(- (* b_2 b_2) (* a c))

simplify1.0s

Counts: 273 → 273

prune3.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize47.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (- (* b_2 b_2) (* a c)))
1.0b	(- (* b_2 b_2) (* a c))
0.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.3b	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
569×	`add-sqr-sqrt`
568×	`*-un-lft-identity`
396×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
76×	`sqrt-prod`
64×	`distribute-rgt-neg-in`
61×	`prod-diff`
44×	`add-exp-log`
43×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
21×	`distribute-lft-neg-in`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
11×	`fma-neg`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`neg-mul-1`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 552

Calls

4 calls:

Slowest

32.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(- (* b_2 b_2) (* a c))

series377.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
111.0ms	(/ (/ 1 a) (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))
54.0ms	(- (* b_2 b_2) (* a c))

simplify1.6s

Counts: 564 → 564

prune6.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize39.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (- (* b_2 b_2) (* a c)))
4.8b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
1.0b	(- (* b_2 b_2) (* a c))
0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)

rewrite132.0ms

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

42.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
29.0ms	(/ (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)))

series355.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

119.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
99.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))
41.0ms	(- (* b_2 b_2) (* a c))

simplify1.7s

Counts: 905 → 905

prune13.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.6b

regimes315.0ms

Accuracy

83.9% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 32.7b

bsearch209.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.4s	1081×	body	2560	valid
702.0ms	5875×	body	80	valid
435.0ms	844×	body	1280	valid
390.0ms	2799×	body	80	nan
230.0ms	458×	body	640	valid
118.0ms	222×	body	320	valid
116.0ms	113×	body	5120	valid
20.0ms	103×	body	160	valid