Details

sample156.0ms

Algorithm

intervals

Results

52.0ms	191×	body	80	valid
38.0ms	41×	body	2560	valid
21.0ms	28×	body	1280	valid
14.0ms	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

simplify208.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.5b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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

17.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series441.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

153.0ms	(/ (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2) a)
114.0ms	(sqrt (fma (* a c) -4 (* b b)))
112.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
63.0ms	(fma (* a c) -4 (* b b))

simplify826.0ms

Counts: 191 → 191

prune2.4s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 28.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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

30.0ms	(* (- (sqrt (fma a (* -4 c) (* b b))) b) (/ 1/2 a))
20.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
2.0ms	(sqrt (fma a (* -4 c) (* b b)))

series384.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

168.0ms	(* (- (sqrt (fma a (* -4 c) (* b b))) b) (/ 1/2 a))
113.0ms	(- (sqrt (fma a (* -4 c) (* b b))) b)
103.0ms	(sqrt (fma a (* -4 c) (* b b)))

simplify1.6s

Counts: 109 → 109

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 28.0b

localize37.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.8b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))

rewrite74.0ms

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

28.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
16.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
10.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series511.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

192.0ms	(/ 1 (/ a (/ (- (sqrt (fma (* a c) -4 (* b b))) b) 2)))
120.0ms	(sqrt (fma (* a c) -4 (* b b)))
120.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
78.0ms	(fma (* a c) -4 (* b b))

simplify752.0ms

Counts: 396 → 396

prune4.9s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 28.0b

localize42.0ms

Local error

Found 4 expressions with local error:

23.1b	(sqrt (fma (* a c) -4 (* b b)))
1.0b	(fma (* a c) -4 (* b b))
0.8b	(- (sqrt (fma (* a c) -4 (* b b))) b)
0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) (/ a (/ 1 2)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
494×	`add-sqr-sqrt`
401×	`*-un-lft-identity`
309×	`add-cube-cbrt`
92×	`difference-of-squares`
61×	`sqrt-prod`
46×	`distribute-lft-out--`
44×	`associate-/r*`
29×	`div-inv`
19×	`add-exp-log`
18×	`prod-diff`
13×	`add-cbrt-cube`
11×	`div-exp`
8×	`associate-/r/`
6×	`cbrt-undiv` `fma-neg` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `rec-exp` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `div-sub` `fma-udef`

Counts

4 → 408

Calls

4 calls:

Slowest

33.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) (/ a (/ 1 2)))
12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
0.0ms	(fma (* a c) -4 (* b b))

series410.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) (/ a (/ 1 2)))
113.0ms	(sqrt (fma (* a c) -4 (* b b)))
92.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
70.0ms	(fma (* a c) -4 (* b b))

simplify870.0ms

Counts: 420 → 420

prune5.8s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 28.0b

regimes345.0ms

Accuracy

90.6% (0.4b remaining)

Error of 29.4b against oracle of 28.9b and baseline of 33.7b

bsearch144.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.6s	1143×	body	2560	valid
1.0s	5839×	body	80	valid
747.0ms	888×	body	1280	valid
491.0ms	2933×	body	80	nan
274.0ms	450×	body	640	valid
148.0ms	115×	body	5120	valid
105.0ms	203×	body	320	valid
29.0ms	108×	body	160	valid