Details

sample345.0ms

Algorithm

intervals

Results

101.0ms	124×	body	320	valid
45.0ms	541×	pre	80	true
44.0ms	285×	body	80	nan
33.0ms	91×	body	160	valid
10.0ms	16×	body	640	valid
4.0ms	25×	body	80	valid

simplify560.0ms

Calls

1 calls:

Slowest

559.0ms

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize23.0ms

Local error

Found 4 expressions with local error:

24.6b	(- (sqrt (- (* b b) (* (* c a) 4))) b)
0.1b	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
0.1b	(- (* b b) (* (* c a) 4))
0.1b	(sqrt (- (* b b) (* (* c a) 4)))

rewrite999.0ms

Algorithm

rewrite-expression-head

Rules

200×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
72×	`times-frac`
58×	`difference-of-squares`
43×	`unswap-sqr`
39×	`associate-l` `add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-lft-out--`
21×	`associate-r`
13×	`*-commutative`
12×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
6×	`swap-sqr` `associate-/l*`
5×	`pow1`
4×	`flip3--` `insert-posit16` `flip--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Calls

4 calls:

Slowest

549.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
323.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
76.0ms	(sqrt (- (* b b) (* (* c a) 4)))
41.0ms	(- (* b b) (* (* c a) 4))

series444.0ms

Calls

4 calls:

Slowest

130.0ms	(/ (- (sqrt (- (* b b) (* (* c a) 4))) b) (* 2 a))
123.0ms	(sqrt (- (* b b) (* (* c a) 4)))
111.0ms	(- (sqrt (- (* b b) (* (* c a) 4))) b)
79.0ms	(- (* b b) (* (* c a) 4))

simplify19.3s

Calls

247 calls:

Slowest

497.0ms	(- (* (sqrt (- (* b b) (* (* c a) 4))) (sqrt (- (* b b) (* (* c a) 4)))) (* b b))
328.0ms	(/ (* (* (- (sqrt (- (* b b) (* (* c a) 4))) b) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (- (sqrt (- (* b b) (* (* c a) 4))) b)) (* (* (* 2 a) (* 2 a)) (* 2 a)))
320.0ms	(- (pow (sqrt (- (* b b) (* (* c a) 4))) 3) (pow b 3))
319.0ms	(sqrt (- (* (* b b) (* b b)) (* (* (* c a) 4) (* (* c a) 4))))
221.0ms	(/ (* (cbrt (- (sqrt (- (* b b) (* (* c a) 4))) b)) (cbrt (- (sqrt (- (* b b) (* (* c a) 4))) b))) (* 2 (* (cbrt a) (cbrt a))))

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.5b

localize4.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Calls

0 calls:

Slowest

series0.0ms

Calls

0 calls:

Slowest

simplify0.0ms

Calls

0 calls:

Slowest

prune92.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 2.5b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

1142×	`times-frac`
808×	`add-sqr-sqrt` `associate-r`
501×	`*-un-lft-identity`
499×	`add-cube-cbrt`
328×	`associate-l`
148×	`unswap-sqr`
109×	`*-commutative`
77×	`associate-/l*`
39×	`add-cbrt-cube` `add-exp-log`
21×	`associate-/l/`
18×	`associate-/r` `associate-r/`
15×	`div-inv`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`clear-num`
3×	`frac-2neg` `un-div-inv`
2×	`pow1` `insert-posit16` `add-log-exp`

Calls

2 calls:

Slowest

65.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
17.0ms	(/ (* a c) b)

series54.0ms

Calls

2 calls:

Slowest

32.0ms	(/ (* -2 (/ (* a c) b)) (* 2 a))
22.0ms	(/ (* a c) b)

simplify3.6m

Calls

1407 calls:

Slowest

1.5s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.4s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.3s	(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 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 c) b) (/ (* a c) b)) (/ (* a c) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))

prune7.4s

Pruning

29 alts after pruning (28 fresh and 1 done)

Merged error: 2.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
0.6b	(cbrt a)
0.4b	(* (* (/ -2 (/ (sqrt b) (cbrt a))) (cbrt a)) (/ (/ (* (cbrt a) c) (sqrt b)) (* 2 a)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

12794×	`times-frac`
11196×	`add-sqr-sqrt`
7886×	`*-un-lft-identity`
7883×	`add-cube-cbrt`
6532×	`associate-*l/`
6492×	`associate-/r*`
6440×	`frac-times`
5884×	`associate-/l*`
5710×	`sqrt-prod`
4423×	`cbrt-prod`
3149×	`associate-l`
2854×	`associate-r`
1531×	`unswap-sqr`
1178×	`associate-/l/`
550×	`*-commutative`
454×	`add-cbrt-cube`
238×	`clear-num`
236×	`frac-2neg`
225×	`cbrt-unprod`
216×	`cbrt-undiv`
205×	`div-inv`
162×	`add-exp-log`
140×	`associate-*r/`
69×	`prod-exp`
61×	`div-exp`
15×	`associate-/r/`
9×	`pow1`
5×	`un-div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`pow1/3` `pow-prod-down`

Calls

4 calls:

Slowest

521.0ms	(* (* (/ -2 (/ (sqrt b) (cbrt a))) (cbrt a)) (/ (/ (* (cbrt a) c) (sqrt b)) (* 2 a)))
1.0ms	(cbrt a)
1.0ms	(cbrt a)
1.0ms	(cbrt a)

series976.0ms

Calls

4 calls:

Slowest

341.0ms	(cbrt a)
319.0ms	(cbrt a)
238.0ms	(cbrt a)
78.0ms	(* (* (/ -2 (/ (sqrt b) (cbrt a))) (cbrt a)) (/ (/ (* (cbrt a) c) (sqrt b)) (* 2 a)))