Details

sample214.0ms

Algorithm

intervals

Results

70.0ms	310×	body	80	nan
48.0ms	152×	body	160	valid
36.0ms	566×	pre	80	true
21.0ms	44×	body	320	valid
9.0ms	60×	body	80	valid

simplify141.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

141.0ms

(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.6b

localize47.0ms

Local error

Found 4 expressions with local error:

39.3b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.2b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b	(- (* b b) (* (* c a) 4))
0.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

Slowest

111.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
36.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
7.0ms	(- (* b b) (* (* c a) 4))
7.0ms	(sqrt (- (* b b) (* (* c a) 4)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

129.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
109.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
91.0ms	(sqrt (- (* b b) (* (* c a) 4)))
47.0ms	(- (* b b) (* (* c a) 4))

simplify5.4s

Counts

49 → 88

Calls

49 calls:

Slowest

615.0ms	(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
415.0ms	(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
304.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
291.0ms	(/ (exp (* b b)) (exp (* (* c a) 4)))
253.0ms	(- b (* 2 (/ (* a c) b)))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize6.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

Calls

0 calls:

Slowest

series0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

simplify0.0ms

Counts

0 → 0

Calls

0 calls:

Slowest

prune41.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.5b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* -2 (/ (* a c) b)) (* 2 a))
0.2b	(/ (* a c) b)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

Slowest

26.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms	(/ (* a c) b)

series55.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

34.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
21.0ms	(/ (* a c) b)

simplify11.7s

Counts

37 → 59

Calls

37 calls:

Slowest

1.8s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.3s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.2s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
961.0ms	(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune522.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 4.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* -2 (/ (* a c) b)) (* 2 a))
0.2b	(/ (* a c) b)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-cbrt-cube` `add-exp-log`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
2×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
1×	`associate-*r/` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

Slowest

24.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
8.0ms	(/ (* a c) b)

series43.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

21.0ms	(/ (* a c) b)
21.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))

simplify10.8s

Counts

37 → 59

Calls

37 calls:

Slowest

1.4s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.2s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.1s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
893.0ms	(/ (* (* (* -2 (/ (* a c) b)) (* -2 (/ (* a c) b))) (* -2 (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune459.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 4.4b

regimes351.0ms

Accuracy

0% (6.9b remaining)

Error of 12.0b against oracle of 5.1b and baseline of 12.0b

bsearch1.0ms

end0.0ms

sample6.0s

Algorithm

intervals

Results

1.5s	4838×	body	160	valid
1.4s	1373×	body	320	valid
1.2s	8244×	body	80	nan
1.1s	16244×	pre	80	true
267.0ms	1789×	body	80	valid