Details

Time bar (total: 16.0s)

sample54.0ms

Algorithm
intervals
Results
12.0ms43×body2560valid
9.0ms175×body80valid
7.0ms31×body1280valid
5.0ms106×body80nan
3.0ms18×body640valid
1.0ms4×body5120valid
1.0ms6×body320valid
0.0ms5×body160valid

simplify97.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (7.0ms)

IterNodesCost
01217
12117
24116
37516
48816
59616
done9616

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(- (* b b) (* (* 3.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
8.0ms
(- (* b b) (* (* 3.0 a) c))
23.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series383.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (* 3.0 a) c)
83.0ms
(- (* b b) (* (* 3.0 a) c))
134.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
127.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify4.7s

Counts
72 → 72
Iterations

Useful iterations: done (4.7s)

IterNodesCost
01221001
1303907
21069805
34068795
done5000793

prune260.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 13.3b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.2b
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite293.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
34×times-frac
32×add-sqr-sqrt
31×*-un-lft-identity
17×cbrt-undiv div-exp
14×associate-/l*
13×prod-exp cbrt-unprod
11×add-cube-cbrt
10×distribute-lft-out-- difference-of-squares
8×associate-/r* sqrt-prod add-log-exp
6×associate-/r/
5×pow1 flip3-- distribute-rgt-neg-in flip--
4×div-inv
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log associate-/l/
Counts
4 → 120
Calls
4 calls:
36.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
109.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
124.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
19.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series740.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
211.0ms
(/ (/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
313.0ms
(/ (* (* 3.0 a) c) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
98.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
132 → 132
Iterations

Useful iterations: 2 (704.0ms)

IterNodesCost
02243580
15913368
225382782
done50012782

prune388.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 9.7b

localize29.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.9b
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
5.2b
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite227.0ms

Algorithm
rewrite-expression-head
Rules
57×add-exp-log add-cbrt-cube
33×add-sqr-sqrt
32×*-un-lft-identity
27×associate-*r*
23×prod-exp cbrt-unprod
22×times-frac
16×cbrt-undiv add-cube-cbrt div-exp
10×pow1
8×distribute-lft-out-- add-log-exp difference-of-squares
7×sqrt-prod
4×distribute-rgt-neg-in
3×flip3-- pow-prod-down flip--
2×sqrt-div diff-log associate-*r/ associate-/r/ div-inv
1×associate--l- neg-sub0 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*l* neg-log clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
4 → 114
Calls
4 calls:
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
102.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
77.0ms
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
11.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series708.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
286.0ms
(* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
232.0ms
(/ (* (* 3.0 a) (/ c (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
93.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.8s

Counts
126 → 126
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02233204
16423041
231362125
done50002124

prune419.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 3.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0b
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.7b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
40×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
10×add-sqr-sqrt add-log-exp
9×cbrt-undiv *-un-lft-identity div-exp
5×pow1 add-cube-cbrt
4×flip3-- sqrt-prod flip--
3×diff-log
2×sub-neg sqrt-div associate-*r/ associate-/r/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 times-frac pow1/2 neg-log clear-num associate-/r* div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
18.0ms
(- (* b b) (* (* 3.0 a) c))
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
85.0ms
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
17.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series514.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- (* b b) (* (* 3.0 a) c))
139.0ms
(- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
207.0ms
(/ (* (* 3.0 a) c) (* (* 3.0 a) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
114.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.9s

Counts
90 → 90
Iterations

Useful iterations: 2 (695.0ms)

IterNodesCost
01762254
14931964
226961356
done50001356

prune320.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.6b

regimes6.0ms