Details

sample134.0ms

Algorithm

intervals

Results

30.0ms	30×	body	1280	valid
30.0ms	195×	body	80	valid
23.0ms	24×	body	2560	valid
14.0ms	100×	body	80	nan
8.0ms	14×	body	640	valid
4.0ms	10×	body	320	valid
4.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify163.0ms

Counts: 1 → 1

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize43.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.1b	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)

rewrite58.0ms

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

33.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
16.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
3.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

137.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
116.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
103.0ms	(sqrt (fma b b (* c (* -4 a))))
71.0ms	(fma b b (* c (* -4 a)))

simplify439.0ms

Counts: 282 → 191

prune2.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize23.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.2b	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--`
2×	`frac-times` `associate-*l/` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 111

Calls

4 calls:

Slowest

50.0ms	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))
15.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
3.0ms	(sqrt (fma b b (* c (* -4 a))))
1.0ms	(fma b b (* c (* -4 a)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

147.0ms	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))
132.0ms	(sqrt (fma b b (* c (* -4 a))))
100.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
67.0ms	(fma b b (* c (* -4 a)))

simplify577.0ms

Counts: 149 → 123

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize35.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))

rewrite78.0ms

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

40.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
15.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
3.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
120.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
120.0ms	(sqrt (fma b b (* c (* -4 a))))
59.0ms	(fma b b (* c (* -4 a)))

simplify1.4s

Counts: 632 → 396

prune4.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize33.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.8b	(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)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(sqrt (fma b b (* c (* -4 a))))
112.0ms	(sqrt (fma b b (* c (* -4 a))))
83.0ms	(fma b b (* c (* -4 a)))
49.0ms	(fma b b (* c (* -4 a)))

simplify801.0ms

Counts: 68 → 66

prune871.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.1b

regimes298.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.4b

bsearch195.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	1049×	body	2560	valid
790.0ms	5843×	body	80	valid
699.0ms	889×	body	1280	valid
445.0ms	2926×	body	80	nan
270.0ms	490×	body	640	valid
93.0ms	107×	body	5120	valid
78.0ms	223×	body	320	valid
26.0ms	114×	body	160	valid