Details

sample133.0ms

Algorithm

intervals

Results

33.0ms	41×	body	2560	valid
33.0ms	191×	body	80	valid
17.0ms	28×	body	1280	valid
12.0ms	93×	body	80	nan
7.0ms	12×	body	640	valid
5.0ms	4×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify181.0ms

Counts: 1 → 1

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.5b

localize26.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (- (* b b) (* (* 4 a) c)))
1.0b	(- (* b b) (* (* 4 a) c))
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

Slowest

58.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
19.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
10.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
9.0ms	(- (* b b) (* (* 4 a) c))

series495.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

156.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4 a) c))))
118.0ms	(sqrt (- (* b b) (* (* 4 a) c)))
95.0ms	(- (* b b) (* (* 4 a) c))

simplify2.3s

Counts: 106 → 106

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize23.0ms

Local error

Found 3 expressions with local error:

23.1b	(sqrt (fma c (* -4 a) (* b b)))
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite40.0ms

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

19.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series297.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

120.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
92.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
86.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify623.0ms

Counts: 177 → 177

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.6b

localize25.0ms

Local error

Found 3 expressions with local error:

23.1b	(sqrt (fma c (* a -4) (* b b)))
0.8b	(- (sqrt (fma c (* a -4) (* b b))) b)
0.2b	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))

rewrite35.0ms

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

24.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
8.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
1.0ms	(sqrt (fma c (* a -4) (* b b)))

series272.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

93.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
91.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
89.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.2s

Counts: 109 → 109

prune916.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

localize36.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma c (* -4 a) (* b b)))
23.1b	(sqrt (fma c (* -4 a) (* b b)))
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)
0.8b	(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

Slowest

8.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
7.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series362.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

93.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
91.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
89.0ms	(sqrt (fma c (* -4 a) (* b b)))
88.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify2.0s

Counts: 128 → 128

prune1.4s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.6b

regimes297.0ms

Accuracy

84.5% (4.3b remaining)

Error of 9.9b against oracle of 5.5b and baseline of 33.7b

bsearch135.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

835.0ms	888×	body	1280	valid
773.0ms	1143×	body	2560	valid
727.0ms	5839×	body	80	valid
351.0ms	203×	body	320	valid
347.0ms	2933×	body	80	nan
181.0ms	450×	body	640	valid
99.0ms	115×	body	5120	valid
20.0ms	108×	body	160	valid