Details

sample105.0ms

Algorithm

intervals

Results

63.0ms	283×	body	80	valid
19.0ms	96×	body	80	nan

simplify305.0ms

Counts: 1 → 1

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize141.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))
1.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.8b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite48.0ms

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

22.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
16.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

113.0ms	(sqrt (fma (* -4 a) c (* b b)))
112.0ms	(sqrt (fma (* -4 a) c (* b b)))
82.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
79.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify1.1s

Counts: 177 → 177

prune3.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.5b

localize185.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))
15.2b	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

3.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
0.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

series721.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

410.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
120.0ms	(sqrt (fma (* -4 a) c (* b b)))
98.0ms	(sqrt (fma (* -4 a) c (* b b)))
92.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify873.0ms

Counts: 71 → 71

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.2b

localize157.0ms

Local error

Found 4 expressions with local error:

21.5b	(sqrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))
10.3b	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 86

Calls

4 calls:

Slowest

19.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

120.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
103.0ms	(sqrt (fma (* -4 a) c (* b b)))
97.0ms	(sqrt (fma (* -4 a) c (* b b)))
95.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.9s

Counts: 98 → 98

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.2b

localize200.0ms

Local error

Found 4 expressions with local error:

22.2b	(cbrt (fma (* -4 a) c (* b b)))
22.2b	(cbrt (fma (* -4 a) c (* b b)))
22.2b	(cbrt (fma (* -4 a) c (* b b)))
21.5b	(sqrt (fma (* -4 a) c (* b b)))

rewrite11.0ms

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

8.0ms	(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)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

294.0ms	(cbrt (fma (* -4 a) c (* b b)))
272.0ms	(cbrt (fma (* -4 a) c (* b b)))
251.0ms	(cbrt (fma (* -4 a) c (* b b)))
116.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts: 70 → 70

prune1.5s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.2b

regimes345.0ms

Accuracy

85.3% (1.1b remaining)

Error of 13.3b against oracle of 12.3b and baseline of 19.5b

bsearch133.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8750×	body	80	valid
531.0ms	2935×	body	80	nan