Details

sample132.0ms

Algorithm

intervals

Results

31.0ms	195×	body	80	valid
23.0ms	30×	body	1280	valid
23.0ms	24×	body	2560	valid
15.0ms	100×	body	80	nan
8.0ms	14×	body	640	valid
5.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid
1.0ms	2×	body	160	valid

simplify152.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize22.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.1b	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)

rewrite53.0ms

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

36.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
8.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
2.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

165.0ms	(/ (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2) a)
125.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
118.0ms	(sqrt (fma b b (* c (* -4 a))))
82.0ms	(fma b b (* c (* -4 a)))

simplify416.0ms

Counts: 282 → 191

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.2b	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `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` `fma-udef` `div-inv`

Counts

4 → 111

Calls

4 calls:

Slowest

32.0ms	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))
7.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
1.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

134.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
133.0ms	(* (- (sqrt (fma b b (* c (* -4 a)))) b) (/ 1/2 a))
111.0ms	(sqrt (fma b b (* c (* -4 a))))
66.0ms	(fma b b (* c (* -4 a)))

simplify1000.0ms

Counts: 149 → 123

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.1b

localize26.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.4b	(- (sqrt (fma b b (* c (* -4 a)))) b)
0.2b	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))

rewrite72.0ms

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

29.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
22.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
2.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

204.0ms	(/ 1 (/ a (/ (- (sqrt (fma b b (* c (* -4 a)))) b) 2)))
129.0ms	(- (sqrt (fma b b (* c (* -4 a)))) b)
88.0ms	(sqrt (fma b b (* c (* -4 a))))
50.0ms	(fma b b (* c (* -4 a)))

simplify1.3s

Counts: 632 → 396

prune5.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.1b

localize38.0ms

Local error

Found 4 expressions with local error:

21.9b	(sqrt (fma b b (* c (* -4 a))))
21.9b	(sqrt (fma b b (* c (* -4 a))))
0.8b	(fma b b (* c (* -4 a)))
0.8b	(fma b b (* c (* -4 a)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

Slowest

1.0ms	(sqrt (fma b b (* c (* -4 a))))
1.0ms	(sqrt (fma b b (* c (* -4 a))))
0.0ms	(fma b b (* c (* -4 a)))
0.0ms	(fma b b (* c (* -4 a)))

series342.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

109.0ms	(sqrt (fma b b (* c (* -4 a))))
98.0ms	(sqrt (fma b b (* c (* -4 a))))
77.0ms	(fma b b (* c (* -4 a)))
58.0ms	(fma b b (* c (* -4 a)))

simplify996.0ms

Counts: 68 → 66

prune1.1s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 7.1b

regimes362.0ms

Accuracy

82.4% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.4b

bsearch291.0ms

end0.0ms

sample4.3s

Algorithm

intervals

Results

992.0ms	1049×	body	2560	valid
872.0ms	5843×	body	80	valid
738.0ms	889×	body	1280	valid
564.0ms	107×	body	5120	valid
422.0ms	2926×	body	80	nan
295.0ms	490×	body	640	valid
85.0ms	223×	body	320	valid
26.0ms	114×	body	160	valid