Details

sample119.0ms

Algorithm

intervals

Results

45.0ms	191×	body	80	valid
20.0ms	29×	body	2560	valid
12.0ms	22×	body	1280	valid
8.0ms	77×	body	80	nan
4.0ms	11×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify173.0ms

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize20.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma b b (* c (* -4 a))))
1.8b	(fma b b (* c (* -4 a)))
1.3b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.1b	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
135×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
82×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
22×	`associate-/l*`
18×	`prod-diff`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/r*` `div-exp`
2×	`div-sub`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `flip--` `associate-/l/`

Counts

4 → 179

Calls

4 calls:

Slowest

26.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
13.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
1.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

133.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
97.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
83.0ms	(sqrt (fma b b (* c (* -4 a))))
48.0ms	(fma b b (* c (* -4 a)))

simplify837.0ms

Counts: 191 → 191

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.7b

localize39.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma b b (* c (* -4 a))))
1.8b	(fma b b (* c (* -4 a)))
1.3b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.1b	(/ (- (sqrt (fma b b (* c (* -4 a)))) b) (/ a 1/2))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

143×	`add-sqr-sqrt`
141×	`times-frac`
112×	`*-un-lft-identity`
82×	`add-cube-cbrt`
30×	`sqrt-prod` `difference-of-squares`
18×	`prod-diff`
15×	`distribute-lft-out--`
13×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`div-inv`
6×	`fma-neg` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/` `fma-udef`

Counts

4 → 187

Calls

4 calls:

Slowest

35.0ms	(/ (- (sqrt (fma b b (* c (* -4 a)))) b) (/ a 1/2))
25.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
2.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
144.0ms	(/ (- (sqrt (fma b b (* c (* -4 a)))) b) (/ a 1/2))
94.0ms	(sqrt (fma b b (* c (* -4 a))))
55.0ms	(fma b b (* c (* -4 a)))

simplify1.1s

Counts: 199 → 199

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize52.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma b b (* c (* -4 a))))
1.8b	(fma b b (* c (* -4 a)))
1.3b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac`
452×	`add-sqr-sqrt`
377×	`*-un-lft-identity`
303×	`add-cube-cbrt`
74×	`difference-of-squares`
71×	`associate-/r*`
52×	`sqrt-prod`
37×	`distribute-lft-out--`
25×	`add-exp-log`
18×	`prod-diff`
17×	`div-inv`
15×	`div-exp`
13×	`add-cbrt-cube`
6×	`pow1` `cbrt-undiv` `fma-neg` `add-log-exp`
5×	`associate-/r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `associate-/l*`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `fma-udef` `pow-flip` `flip--` `inv-pow`

Counts

4 → 384

Calls

4 calls:

Slowest

30.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
14.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
2.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
134.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
102.0ms	(sqrt (fma b b (* c (* -4 a))))
82.0ms	(fma b b (* c (* -4 a)))

simplify1.4s

Counts: 396 → 396

prune5.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.7b

localize29.0ms

Local error

Found 4 expressions with local error:

21.6b	(sqrt (fma b b (* c (* -4 a))))
21.6b	(sqrt (fma b b (* c (* -4 a))))
1.8b	(fma b b (* c (* -4 a)))
1.8b	(fma b b (* c (* -4 a)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

Slowest

1.0ms	(sqrt (fma b b (* c (* -4 a))))
1.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))
0.0ms	(fma b b (* c (* -4 a)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

132.0ms	(sqrt (fma b b (* c (* -4 a))))
96.0ms	(sqrt (fma b b (* c (* -4 a))))
67.0ms	(fma b b (* c (* -4 a)))
49.0ms	(fma b b (* c (* -4 a)))

simplify875.0ms

Counts: 66 → 66

prune1.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.7b

regimes323.0ms

Accuracy

81.9% (4.9b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 33.0b

bsearch189.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.6s	5845×	body	80	valid
866.0ms	1114×	body	2560	valid
616.0ms	847×	body	1280	valid
458.0ms	2891×	body	80	nan
306.0ms	415×	body	640	valid
141.0ms	123×	body	5120	valid
86.0ms	246×	body	320	valid
33.0ms	137×	body	160	valid