Details

sample107.0ms

Algorithm

intervals

Results

60.0ms	276×	body	80	valid
22.0ms	99×	body	80	nan

simplify354.0ms

Counts: 1 → 1

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize160.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
0.9b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.4b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite42.0ms

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))))
12.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

124.0ms	(sqrt (fma (* -4 a) c (* b b)))
99.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
93.0ms	(sqrt (fma (* -4 a) c (* b b)))
91.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify505.0ms

Counts: 265 → 177

prune2.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 11.1b

localize167.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
15.5b	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))

rewrite4.0ms

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

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

series743.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

390.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- b))
133.0ms	(sqrt (fma (* -4 a) c (* b b)))
131.0ms	(sqrt (fma (* -4 a) c (* b b)))
89.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify908.0ms

Counts: 74 → 71

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 10.9b

localize168.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
9.2b	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite14.0ms

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

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

series442.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

131.0ms	(sqrt (fma (* -4 a) c (* b b)))
109.0ms	(sqrt (fma (* -4 a) c (* b b)))
108.0ms	(sqrt (fma (* -4 a) c (* b b)))
94.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

simplify603.0ms

Counts: 114 → 98

prune1.9s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.9b

localize196.0ms

Local error

Found 4 expressions with local error:

21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))
21.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

Slowest

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

series560.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

172.0ms	(sqrt (fma (* -4 a) c (* b b)))
148.0ms	(sqrt (fma (* -4 a) c (* b b)))
134.0ms	(sqrt (fma (* -4 a) c (* b b)))
106.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.0s

Counts: 80 → 76

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 10.9b

regimes289.0ms

Accuracy

87.3% (0.9b remaining)

Error of 12.8b against oracle of 11.9b and baseline of 18.9b

bsearch120.0ms

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.2s	8723×	body	80	valid
450.0ms	2927×	body	80	nan