Details

sample117.0ms

Algorithm

intervals

Results

27.0ms	189×	body	80	valid
27.0ms	34×	body	2560	valid
16.0ms	23×	body	1280	valid
10.0ms	80×	body	80	nan
7.0ms	12×	body	640	valid
4.0ms	9×	body	320	valid
4.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify159.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.3b

localize26.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.9b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) 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

21.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
16.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series469.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

179.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
112.0ms	(sqrt (fma (* a c) -4 (* b b)))
103.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
74.0ms	(fma (* a c) -4 (* b b))

simplify707.0ms

Counts: 191 → 191

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.1b

localize40.0ms

Local error

Found 3 expressions with local error:

21.4b	(sqrt (fma a (* -4 c) (* b b)))
0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 168

Calls

3 calls:

Slowest

30.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
3.0ms	(sqrt (fma a (* -4 c) (* b b)))

series342.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

139.0ms	(/ (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2) a)
109.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
94.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify811.0ms

Counts: 177 → 177

prune2.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 28.1b

localize19.0ms

Local error

Found 3 expressions with local error:

21.4b	(sqrt (fma a (* -4 c) (* b b)))
0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
0.2b	(* (- (sqrt (fma a (* -4 c) (* b b))) b) (/ 1/2 a))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
10×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `fma-neg` `associate-l`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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` `div-inv`

Counts

3 → 100

Calls

3 calls:

Slowest

39.0ms	(* (- (sqrt (fma a (* -4 c) (* b b))) b) (/ 1/2 a))
8.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
1.0ms	(sqrt (fma a (* -4 c) (* b b)))

series393.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

181.0ms	(* (- (sqrt (fma a (* -4 c) (* b b))) b) (/ 1/2 a))
107.0ms	(sqrt (fma a (* -4 c) (* b b)))
106.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)

simplify1.7s

Counts: 109 → 109

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 28.1b

localize43.0ms

Local error

Found 4 expressions with local error:

21.4b	(sqrt (fma a (* -4 c) (* b b)))
0.9b	(- (sqrt (fma a (* -4 c) (* b b))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2)))
0.1b	(/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
563×	`add-sqr-sqrt`
464×	`*-un-lft-identity`
366×	`add-cube-cbrt`
98×	`difference-of-squares`
93×	`associate-/r*`
64×	`sqrt-prod`
49×	`distribute-lft-out--`
30×	`add-exp-log`
22×	`div-inv`
18×	`add-cbrt-cube` `div-exp` `prod-diff`
9×	`cbrt-undiv`
6×	`pow1` `fma-neg` `associate-/r/` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-flip` `flip--` `inv-pow`

Counts

4 → 482

Calls

4 calls:

Slowest

23.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
19.0ms	(/ 1 (/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2)))
12.0ms	(/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2))
2.0ms	(sqrt (fma a (* -4 c) (* b b)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

320.0ms	(/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2))
187.0ms	(/ 1 (/ a (/ (- (sqrt (fma a (* -4 c) (* b b))) b) 2)))
142.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
100.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify1.1s

Counts: 494 → 494

prune7.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.8b

regimes442.0ms

Accuracy

79.5% (4.3b remaining)

Error of 16.7b against oracle of 12.4b and baseline of 33.4b

bsearch126.0ms

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.2s	860×	body	1280	valid
1.1s	5796×	body	80	valid
1.1s	1094×	body	2560	valid
369.0ms	2811×	body	80	nan
281.0ms	481×	body	640	valid
128.0ms	251×	body	320	valid
102.0ms	103×	body	5120	valid
35.0ms	130×	body	160	valid