Details

sample101.0ms

Algorithm

intervals

Results

58.0ms	283×	body	80	valid
17.0ms	79×	body	80	nan

simplify276.0ms

Counts: 1 → 1

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.4b

localize178.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))
1.7b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
1.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite39.0ms

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

18.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
8.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
6.0ms	(sqrt (fma (* -4 a) c (* b b)))
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
124.0ms	(sqrt (fma (* -4 a) c (* b b)))
121.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
98.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.0s

Counts: 177 → 177

prune3.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.3b

localize180.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))
11.5b	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))

rewrite15.0ms

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)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

116.0ms	(sqrt (fma (* -4 a) c (* b b)))
105.0ms	(- (- b) (* (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b))))))
99.0ms	(sqrt (fma (* -4 a) c (* b b)))
96.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.9s

Counts: 98 → 98

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.3b

localize175.0ms

Local error

Found 4 expressions with local error:

21.4b	(cbrt (fma (* -4 a) c (* b b)))
21.4b	(cbrt (fma (* -4 a) c (* b b)))
21.4b	(cbrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))

rewrite7.0ms

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)))
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)))

series895.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

275.0ms	(cbrt (fma (* -4 a) c (* b b)))
261.0ms	(cbrt (fma (* -4 a) c (* b b)))
232.0ms	(cbrt (fma (* -4 a) c (* b b)))
127.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify889.0ms

Counts: 70 → 70

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.3b

localize230.0ms

Local error

Found 4 expressions with local error:

20.7b	(sqrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))
20.7b	(sqrt (fma (* -4 a) c (* b b)))
13.8b	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt 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)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

series698.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

386.0ms	(fma (sqrt (sqrt (fma (* -4 a) c (* b b)))) (sqrt (sqrt (fma (* -4 a) c (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
119.0ms	(sqrt (fma (* -4 a) c (* b b)))
104.0ms	(sqrt (fma (* -4 a) c (* b b)))
88.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.1s

Counts: 71 → 71

prune1.5s

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 12.0b

regimes410.0ms

Accuracy

88.1% (0.8b remaining)

Error of 12.8b against oracle of 12.0b and baseline of 19.1b

bsearch140.0ms

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.0s	8780×	body	80	valid
577.0ms	2903×	body	80	nan