Details

Time bar (total: 15.8s)

sample110.0ms

Algorithm
intervals
Results
26.0ms43×body2560valid
18.0ms176×body80valid
16.0ms31×body1280valid
11.0ms106×body80nan
7.0ms18×body640valid
3.0ms4×body5120valid
2.0ms7×body320valid
1.0ms4×body160valid

simplify165.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (15.0ms)

IterNodesCost
01417
12517
24616
38616
410816
511616
done11616

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize37.0ms

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)))

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-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 neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
120.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
19.0ms
(- (* b b) (* (* 4.0 a) c))
46.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series498.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
87.0ms
(- (* b b) (* (* 4.0 a) c))
120.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
100.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.8s

Counts
102 → 102
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01671697
14331584
214881361
done50001347

prune477.0ms

Pruning

8 alts after pruning (8 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)))

rewrite334.0ms

Algorithm
rewrite-expression-head
Rules
125×add-sqr-sqrt
124×*-un-lft-identity
90×times-frac
80×add-cube-cbrt
60×prod-diff
44×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
10×fma-neg
8×associate-/r* add-log-exp
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u 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 → 232
Calls
4 calls:
48.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
127.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
115.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series803.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
268.0ms
(/ (/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
307.0ms
(/ (+ 0 (* (* c 4.0) a)) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
106.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
244 → 244
Iterations

Useful iterations: done (2.0s)

IterNodesCost
033810067
18117605
230636508
done50006422

prune818.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.2b

localize31.0ms

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)))

rewrite373.0ms

Algorithm
rewrite-expression-head
Rules
162×add-sqr-sqrt
152×times-frac
150×*-un-lft-identity
109×add-cube-cbrt
94×add-exp-log
85×associate-*r*
61×prod-diff
58×add-cbrt-cube
43×sqrt-prod
39×div-exp
35×prod-exp
31×distribute-rgt-neg-in
21×cbrt-undiv distribute-lft-neg-in cbrt-unprod
20×distribute-lft-out-- difference-of-squares
11×fma-neg
10×add-log-exp
7×pow1 neg-mul-1 associate-*l*
6×flip3-- associate-/r/ flip--
5×div-inv
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u 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 → 265
Calls
4 calls:
19.0ms
(- (* b b) (* (* 4.0 a) c))
39.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
281.0ms
(* (/ (* (* 4.0 a) c) 2.0) (/ (/ 1 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) a))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series541.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (* b b) (* (* 4.0 a) c))
138.0ms
(- (- 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))
125.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.8s

Counts
277 → 277
Iterations

Useful iterations: done (2.8s)

IterNodesCost
044210420
112257945
241806391
done50006342

prune873.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.2b

localize30.0ms

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))))
14.8b
(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite249.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
7×neg-mul-1
5×pow1
4×expm1-log1p-u flip3-- associate-*r/ flip-- log1p-expm1-u
3×cbrt-undiv times-frac diff-log div-exp prod-exp cbrt-unprod associate-/l*
2×sub-neg sqrt-div associate-/r/ associate-/l/ distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 neg-log clear-num associate-/r* flip-+ div-inv
Counts
4 → 152
Calls
4 calls:
19.0ms
(- (* b b) (* (* 4.0 a) c))
42.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
148.0ms
(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
24.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series554.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (* b b) (* (* 4.0 a) c))
116.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
267.0ms
(/ (+ 0 (* (* c 4.0) a)) (* a (* 2.0 (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.1s

Counts
164 → 164
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02676876
16484772
229583777
done50003692

prune627.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.2b

regimes323.0ms

bsearch3.0ms