Details

Time bar (total: 10.9s)

sample102.0ms

Algorithm
intervals
Results
22.0ms43×body2560valid
16.0ms176×body80valid
14.0ms18×body640valid
13.0ms31×body1280valid
9.0ms106×body80nan
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify165.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite559.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
89.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms
(- (* b b) (* (* 4.0 a) c))
439.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
58.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
135.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01541565
14011461
213531245
done50011233

prune411.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.3b

localize40.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.1b
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
9.7b
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
84×add-sqr-sqrt
83×*-un-lft-identity
39×add-cube-cbrt
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
18×add-exp-log add-cbrt-cube
14×sqrt-prod
11×distribute-rgt-neg-in
8×associate-/r* add-log-exp
7×cbrt-undiv div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×div-inv
3×associate-/l/
2×frac-2neg sqrt-div diff-log prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 154
Calls
4 calls:
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
171.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
128.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
20.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series725.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
285.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
227.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
95.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.7s

Counts
166 → 166
Iterations

Useful iterations: 2 (649.0ms)

IterNodesCost
02575113
16344541
226394211
done50014211

prune707.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* (* 4.0 a) c))
1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.7b
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
152×times-frac
121×add-sqr-sqrt
109×*-un-lft-identity
94×add-exp-log
85×associate-*r*
68×add-cube-cbrt
58×add-cbrt-cube
39×div-exp
35×prod-exp
21×cbrt-undiv cbrt-unprod
20×distribute-lft-out-- difference-of-squares
13×sqrt-prod
10×distribute-rgt-neg-in add-log-exp
7×pow1 associate-*l*
6×flip3-- associate-/r/ flip--
5×div-inv
4×rec-exp 1-exp unswap-sqr
3×diff-log
2×sub-neg sqrt-div
1×associate--l- neg-sub0 frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative
Counts
4 → 185
Calls
4 calls:
10.0ms
(- (* b b) (* (* 4.0 a) c))
27.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
204.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
12.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(- (* b b) (* (* 4.0 a) c))
92.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
214.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
120.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.4s

Counts
197 → 197
Iterations

Useful iterations: 2 (871.0ms)

IterNodesCost
03565464
110434878
236824092
done50004092

prune803.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.2b

localize9.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify1.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune1.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

regimes332.0ms

bsearch3.0ms