Details

sample118.0ms

Algorithm

intervals

Results

60.0ms	275×	body	80	valid
34.0ms	87×	body	80	nan

simplify293.0ms

Counts: 1 → 1

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize153.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
22.1b	(sqrt (fma (* -4 a) c (* b b)))
2.0b	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
0.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite24.0ms

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

11.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))
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)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

139.0ms	(sqrt (fma (* -4 a) c (* b b)))
129.0ms	(sqrt (fma (* -4 a) c (* b b)))
113.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
108.0ms	(- (- b) (sqrt (fma (* -4 a) c (* b b))))

simplify1.0s

Counts: 177 → 177

prune2.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize182.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
5.6b	(/ a (/ b c))
3.4b	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
0.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)

rewrite84.0ms

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

66.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
8.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
6.0ms	(/ a (/ b c))
1.0ms	(sqrt (fma (* -4 a) c (* b b)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

125.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
110.0ms	(sqrt (fma (* -4 a) c (* b b)))
64.0ms	(/ (* 2 (- (/ a (/ b c)) b)) (* 2 a))
25.0ms	(/ a (/ b c))

simplify1.0s

Counts: 169 → 169

prune2.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.0b

localize141.0ms

Local error

Found 3 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
0.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)
0.1b	(/ (* 2 c) (- (sqrt (fma (* -4 a) c (* b b))) b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 90

Calls

3 calls:

Slowest

27.0ms	(/ (* 2 c) (- (sqrt (fma (* -4 a) c (* b b))) b))
15.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series523.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

246.0ms	(/ (* 2 c) (- (sqrt (fma (* -4 a) c (* b b))) b))
145.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
132.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify1.8s

Counts: 99 → 99

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.0b

localize144.0ms

Local error

Found 4 expressions with local error:

22.1b	(sqrt (fma (* -4 a) c (* b b)))
0.3b	(- (sqrt (fma (* -4 a) c (* b b))) b)
0.2b	(/ 2 (/ (- (sqrt (fma (* -4 a) c (* b b))) b) c))
0.1b	(/ (- (sqrt (fma (* -4 a) c (* b b))) b) c)

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-sqr-sqrt`
156×	`times-frac`
127×	`*-un-lft-identity`
93×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
25×	`associate-/r*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
6×	`fma-neg` `div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg` `flip3--` `flip--` `associate-/l/`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-/r/`

Counts

4 → 212

Calls

4 calls:

Slowest

30.0ms	(/ (- (sqrt (fma (* -4 a) c (* b b))) b) c)
12.0ms	(/ 2 (/ (- (sqrt (fma (* -4 a) c (* b b))) b) c))
8.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
2.0ms	(sqrt (fma (* -4 a) c (* b b)))

series561.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

239.0ms	(/ 2 (/ (- (sqrt (fma (* -4 a) c (* b b))) b) c))
109.0ms	(- (sqrt (fma (* -4 a) c (* b b))) b)
109.0ms	(/ (- (sqrt (fma (* -4 a) c (* b b))) b) c)
104.0ms	(sqrt (fma (* -4 a) c (* b b)))

simplify963.0ms

Counts: 224 → 224

prune3.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.0b

regimes493.0ms

Accuracy

93.2% (0.6b remaining)

Error of 13.1b against oracle of 12.5b and baseline of 21.1b

bsearch235.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.9s	8719×	body	80	valid
564.0ms	2867×	body	80	nan