Details

sample98.0ms

Algorithm

intervals

Results

32.0ms	30×	body	1280	valid
20.0ms	38×	body	2560	valid
17.0ms	189×	body	80	valid
8.0ms	87×	body	80	nan
5.0ms	15×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid

simplify158.0ms

Counts: 1 → 1

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize19.0ms

Local error

Found 3 expressions with local error:

22.6b	(sqrt (fma c (* -4 a) (* b b)))
0.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite34.0ms

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

20.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series327.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

115.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
110.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
102.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify754.0ms

Counts: 177 → 177

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 27.6b

localize24.0ms

Local error

Found 3 expressions with local error:

22.6b	(sqrt (fma c (* -4 a) (* b b)))
5.2b	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
0.1b	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)

rewrite308.0ms

Algorithm

rewrite-expression-head

Rules

10113×	`times-frac`
5325×	`add-sqr-sqrt`
5299×	`*-un-lft-identity`
5273×	`add-cube-cbrt`
3010×	`prod-diff`
1230×	`sqrt-prod`
469×	`div-inv`
70×	`fma-neg`
22×	`associate-/l*`
13×	`distribute-lft-out--`
12×	`difference-of-squares`
8×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`pow1` `distribute-rgt-out--`
3×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `div-exp` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `frac-sub` `flip--` `sub-div` `associate-/l/`

Counts

3 → 3251

Calls

3 calls:

Slowest

46.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
15.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series850.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

572.0ms	(- (/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a) (/ (/ b 2) a))
155.0ms	(/ (/ (sqrt (fma c (* -4 a) (* b b))) 2) a)
123.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify8.1s

Counts: 3260 → 3260

prune1.0m

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 27.6b

localize23.0ms

Local error

Found 3 expressions with local error:

22.6b	(sqrt (fma c (* a -4) (* b b)))
0.3b	(- (sqrt (fma c (* a -4) (* b b))) b)
0.2b	(* (- (sqrt (fma c (* a -4) (* 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

31.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
14.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series356.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

127.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
122.0ms	(sqrt (fma c (* a -4) (* b b)))
107.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))

simplify1.6s

Counts: 109 → 109

prune2.0s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 27.6b

localize34.0ms

Local error

Found 4 expressions with local error:

22.6b	(sqrt (fma c (* -4 a) (* b b)))
0.5b	(/ (sqrt 1/2) a)
0.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.3b	(* (sqrt 1/2) (- (sqrt (fma c (* -4 a) (* b b))) b))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
61×	`add-cube-cbrt`
54×	`prod-diff`
51×	`sqrt-prod`
20×	`distribute-rgt-in` `distribute-lft-in`
18×	`times-frac`
8×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-r` `associate-l` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`associate-/r*` `sub-neg`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 170

Calls

4 calls:

Slowest

27.0ms	(* (sqrt 1/2) (- (sqrt (fma c (* -4 a) (* b b))) b))
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
5.0ms	(/ (sqrt 1/2) a)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series508.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(* (sqrt 1/2) (- (sqrt (fma c (* -4 a) (* b b))) b))
118.0ms	(sqrt (fma c (* -4 a) (* b b)))
118.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
64.0ms	(/ (sqrt 1/2) a)

simplify1.3s

Counts: 182 → 182

prune2.2s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 27.6b

regimes811.0ms

Accuracy

91.5% (0.4b remaining)

Error of 28.7b against oracle of 28.2b and baseline of 33.0b

bsearch187.0ms

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.3s	5902×	body	80	valid
1.1s	1070×	body	2560	valid
792.0ms	864×	body	1280	valid
442.0ms	2867×	body	80	nan
304.0ms	458×	body	640	valid
131.0ms	102×	body	5120	valid
82.0ms	207×	body	320	valid
32.0ms	112×	body	160	valid