Details

sample97.0ms

Algorithm

intervals

Results

48.0ms	287×	body	80	valid
14.0ms	93×	body	80	nan

simplify248.0ms

Counts: 1 → 1

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize147.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (fma (* -4 a) c (* b b)))
24.8b	(sqrt (fma (* -4 a) c (* b b)))
1.0b	(- (sqrt (fma (* -4 a) c (* b b))) b)
0.4b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

rewrite32.0ms

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

15.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
7.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms	(sqrt (fma (* -4 a) c (* b b)))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

136.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
130.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
126.0ms	(sqrt (fma (* -4 a) c (* b b)))
124.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.3s

Counts: 177 → 177

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.6b

localize188.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (fma (* -4 a) c (* b b)))
7.1b	(/ a (/ b c))
4.3b	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
1.0b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
66×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
21×	`add-cbrt-cube` `add-exp-log`
18×	`prod-diff`
16×	`sqrt-prod`
14×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `associate-/l*`
2×	`clear-num` `frac-2neg` `flip3--` `associate-*r/` `flip--` `difference-of-squares` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `distribute-lft-out--`

Counts

4 → 157

Calls

4 calls:

Slowest

73.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
11.0ms	(/ a (/ b c))
9.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

141.0ms	(sqrt (fma (* -4 a) c (* b b)))
97.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
55.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
39.0ms	(/ a (/ b c))

simplify1.1s

Counts: 169 → 169

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.6b

localize161.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (fma (* -4 a) c (* b b)))
17.1b	(cbrt (/ a (/ b c)))
17.1b	(cbrt (/ a (/ b c)))
17.1b	(cbrt (/ a (/ b c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
132×	`cbrt-prod`
111×	`add-sqr-sqrt`
110×	`*-un-lft-identity` `add-cube-cbrt`
12×	`div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/r/` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 184

Calls

4 calls:

Slowest

4.0ms	(cbrt (/ a (/ b c)))
4.0ms	(cbrt (/ a (/ b c)))
4.0ms	(cbrt (/ a (/ b c)))
3.0ms	(sqrt (fma (* -4 a) c (* b b)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

143.0ms	(sqrt (fma (* -4 a) c (* b b)))
115.0ms	(cbrt (/ a (/ b c)))
114.0ms	(cbrt (/ a (/ b c)))
91.0ms	(cbrt (/ a (/ b c)))

simplify1.3s

Counts: 196 → 196

prune4.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.6b

localize182.0ms

Local error

Found 4 expressions with local error:

24.8b	(sqrt (fma (* -4 a) c (* b b)))
24.8b	(sqrt (fma (* -4 a) c (* b b)))
17.1b	(cbrt (/ a (/ b c)))
17.1b	(cbrt (/ a (/ b c)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
88×	`cbrt-prod`
78×	`add-sqr-sqrt`
76×	`*-un-lft-identity` `add-cube-cbrt`
8×	`div-inv`
6×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `pow1/3` `associate-/r/`

Counts

4 → 144

Calls

4 calls:

Slowest

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

series466.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(cbrt (/ a (/ b c)))
116.0ms	(sqrt (fma (* -4 a) c (* b b)))
114.0ms	(cbrt (/ a (/ b c)))
110.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.2s

Counts: 156 → 156

prune3.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.6b

regimes431.0ms

Accuracy

93.4% (0.6b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 21.0b

bsearch130.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.6s	8770×	body	80	valid
487.0ms	2917×	body	80	nan