Details

sample127.0ms

Algorithm

intervals

Results

66.0ms	277×	body	80	valid
17.0ms	80×	body	80	nan

simplify334.0ms

Counts: 1 → 1

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.9b

localize146.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (fma (* -4 a) c (* b b)))
20.9b	(sqrt (fma (* -4 a) c (* b b)))
0.9b	(- (sqrt (fma (* -4 a) c (* b b))) b)
0.3b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 165

Calls

4 calls:

Slowest

21.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
16.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
5.0ms	(sqrt (fma (* -4 a) c (* b b)))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series525.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

158.0ms	(sqrt (fma (* -4 a) c (* b b)))
128.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
120.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
119.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts: 177 → 177

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.4b

localize153.0ms

Local error

Found 4 expressions with local error:

20.9b	(sqrt (fma (* -4 a) c (* b b)))
20.9b	(sqrt (fma (* -4 a) c (* b b)))
20.9b	(sqrt (fma (* -4 a) c (* b b)))
0.9b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

Slowest

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

series452.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

140.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
121.0ms	(sqrt (fma (* -4 a) c (* b b)))
108.0ms	(sqrt (fma (* -4 a) c (* b b)))
82.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify3.0s

Counts: 102 → 102

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

localize161.0ms

Local error

Found 4 expressions with local error:

21.6b	(cbrt (fma (* -4 a) c (* b b)))
21.6b	(cbrt (fma (* -4 a) c (* b b)))
21.6b	(cbrt (fma (* -4 a) c (* b b)))
20.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))
1.0ms	(cbrt (fma (* -4 a) c (* b b)))

series811.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

247.0ms	(cbrt (fma (* -4 a) c (* b b)))
237.0ms	(cbrt (fma (* -4 a) c (* b b)))
230.0ms	(cbrt (fma (* -4 a) c (* b b)))
96.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify967.0ms

Counts: 70 → 70

prune1.5s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.4b

localize162.0ms

Local error

Found 4 expressions with local error:

21.6b	(cbrt (fma (* -4 a) c (* b b)))
21.6b	(cbrt (fma (* -4 a) c (* b b)))
21.6b	(cbrt (fma (* -4 a) c (* b b)))
20.9b	(sqrt (fma (* -4 a) c (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

Slowest

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

series929.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

280.0ms	(cbrt (fma (* -4 a) c (* b b)))
269.0ms	(cbrt (fma (* -4 a) c (* b b)))
263.0ms	(cbrt (fma (* -4 a) c (* b b)))
117.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts: 70 → 70

prune1.4s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.4b

regimes447.0ms

Accuracy

91.6% (0.6b remaining)

Error of 12.6b against oracle of 12.1b and baseline of 19.0b

bsearch173.0ms

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.0s	8696×	body	80	valid
476.0ms	2806×	body	80	nan