Details

sample141.0ms

Algorithm

intervals

Results

35.0ms	34×	body	2560	valid
34.0ms	189×	body	80	valid
19.0ms	23×	body	1280	valid
13.0ms	80×	body	80	nan
8.0ms	12×	body	640	valid
4.0ms	9×	body	320	valid
4.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify182.0ms

Counts: 1 → 1

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.3b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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

16.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
10.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series276.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

101.0ms	(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
93.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
81.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify756.0ms

Counts: 177 → 177

prune2.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 28.1b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite59.0ms

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 c (* a -4) (* b b))) b) (/ 1/2 a))
16.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series347.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

117.0ms	(* (- (sqrt (fma c (* a -4) (* b b))) b) (/ 1/2 a))
116.0ms	(sqrt (fma c (* a -4) (* b b)))
114.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)

simplify1.8s

Counts: 109 → 109

prune1.4s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 28.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

Slowest

47.0ms	(/ (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2) a)
15.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series350.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

121.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
121.0ms	(sqrt (fma c (* a -4) (* b b)))
108.0ms	(/ (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2) a)

simplify1.5s

Counts: 93 → 93

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 28.1b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
42×	`times-frac`
41×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`add-exp-log`
18×	`add-cbrt-cube` `prod-diff`
16×	`sqrt-prod`
14×	`div-exp`
11×	`associate-/r/`
10×	`associate-/r` `associate-l/`
7×	`cbrt-undiv`
6×	`pow1` `flip3--` `fma-neg` `div-inv` `flip--` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 151

Calls

4 calls:

Slowest

40.0ms	(/ 1 (/ a (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2)))
23.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
12.0ms	(/ a (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2))
3.0ms	(sqrt (fma c (* a -4) (* b b)))

series670.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

267.0ms	(/ a (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2))
175.0ms	(/ 1 (/ a (* (- (sqrt (fma c (* a -4) (* b b))) b) 1/2)))
122.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
106.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify2.4s

Counts: 163 → 163

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 11.7b

regimes355.0ms

Accuracy

75.7% (4.5b remaining)

Error of 16.7b against oracle of 12.2b and baseline of 30.6b

bsearch177.0ms

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1094×	body	2560	valid
844.0ms	5796×	body	80	valid
712.0ms	860×	body	1280	valid
684.0ms	481×	body	640	valid
465.0ms	2811×	body	80	nan
165.0ms	251×	body	320	valid
107.0ms	103×	body	5120	valid
33.0ms	130×	body	160	valid