Details

Time bar (total: 11.0s)

sample95.0ms

Algorithm
intervals
Results
22.0ms43×body2560valid
16.0ms176×body80valid
12.0ms31×body1280valid
8.0ms106×body80nan
6.0ms18×body640valid
2.0msbody5120valid
2.0msbody320valid
1.0msbody160valid

simplify139.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
01417
12417
24416
37816
49116
59916
done9916

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite228.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
13×*-un-lft-identity
add-exp-log add-cbrt-cube
add-log-exp
add-cube-cbrt
times-frac sqrt-prod associate-/l* difference-of-squares
pow1
flip3-- flip--
distribute-lft-out--
cbrt-undiv sub-neg sqrt-div diff-log div-exp associate-/l/
rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 72
Calls
4 calls:
132.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
8.0ms
(- (* b b) (* (* 4.0 a) c))
67.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
16.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series422.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
71.0ms
(- (* b b) (* (* 4.0 a) c))
111.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
102.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts
84 → 84
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01541592
13861488
212331332
346481324
done50021324

prune342.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize4.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify0.0ms

Counts
0 → 0
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
done00

prune17.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.8b
(- (* b b) (* (* 4.0 a) c))
1.4b
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
24.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
47×add-sqr-sqrt
36×*-un-lft-identity
26×add-cube-cbrt
25×add-exp-log
13×add-cbrt-cube
12×div-exp associate-/r*
10×difference-of-squares
associate-/r/
sqrt-prod add-log-exp
flip3-- flip--
pow1
cbrt-undiv div-inv distribute-lft-out--
rec-exp 1-exp prod-exp associate-/l*
sub-neg sqrt-div diff-log
rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 clear-num cbrt-unprod inv-pow
Counts
4 → 118
Calls
4 calls:
97.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
9.0ms
(- (* b b) (* (* 4.0 a) c))
58.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
19.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series542.0ms

Counts
4 → 12
Calls
4 calls:
217.0ms
(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
70.0ms
(- (* b b) (* (* 4.0 a) c))
131.0ms
(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
124.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts
130 → 130
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02203137
14972801
214612561
done50002481

prune410.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (/ c b) (/ b a))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
*-un-lft-identity
times-frac
difference-of-squares
add-log-exp
distribute-lft-out--
pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log frac-sub add-cbrt-cube flip--
Counts
1 → 19
Calls
1 calls:
42.0ms
(- (/ c b) (/ b a))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(- (/ c b) (/ b a))

simplify3.4s

Counts
22 → 22
Iterations

Useful iterations: 5 (1.9s)

IterNodesCost
047278
1105273
2230259
3528259
41400259
54344257
done5000257

prune81.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.2b

regimes333.0ms

bsearch2.0ms