Details

Time bar (total: 3.9s)

analyze476.0ms (12.1%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%74.9%0.1%6
25%68.6%6.4%7
31.2%62.4%6.4%8
36.7%54.6%8.7%9
38.2%48.4%13.4%10
42.7%42.3%15%11
47.8%34.1%18.1%12
49.1%30.3%20.5%13
51.9%25.8%22.3%14

sample48.0ms (1.2%)

Algorithm
intervals
Results
10.0ms32×body1280valid
10.0ms32×body2560valid
9.0ms160×body80valid
3.0ms17×body640valid
2.0msbody320valid
1.0msbody5120valid
1.0ms15×body80nan
0.0msbody80invalid
0.0msbody160valid

simplify212.0ms (5.4%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (211.0ms)

IterNodesCost
0178416
1178416

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 34.5b

Counts
2 → 1

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.0b
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
1.2b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite27.0ms (0.7%)

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 → 70
Calls

4 calls:

11.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
7.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(- (* b b) (* (* 3.0 a) c))

series63.0ms (1.6%)

Counts
4 → 12
Calls

4 calls:

24.0ms
(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
16.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
14.0ms
(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms
(- (* b b) (* (* 3.0 a) c))

simplify34.0ms (0.9%)

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
049311311
149311311

prune198.0ms (5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New721082
Fresh000
Picked101
Done000
Total731083

Merged error: 4.6b

Counts
83 → 10

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
3.3b
(/ (/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.5b
(/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms (1%)

Algorithm
rewrite-expression-head
Rules
102×times-frac
77×*-un-lft-identity
40×add-sqr-sqrt
39×add-cube-cbrt
36×associate-/l*
19×distribute-lft-out
18×add-exp-log add-cbrt-cube
13×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
cbrt-undiv div-exp
associate-/r/ add-log-exp
pow1 associate-/r*
div-inv
flip3-+ div-sub distribute-frac-neg sqrt-prod flip-+
neg-sub0 flip3-- frac-2neg sqrt-div prod-exp clear-num flip-- cbrt-unprod
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 158
Calls

4 calls:

13.0ms
(/ (/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.0ms
(/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
6.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series118.0ms (3%)

Counts
4 → 12
Calls

4 calls:

52.0ms
(/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))
44.0ms
(/ (/ (neg (* (* 3.0 a) c)) (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
8.0ms
(- (* b b) (* (* 3.0 a) c))

simplify58.0ms (1.5%)

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
049613865
149613865

prune402.0ms (10.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1682170
Fresh279
Picked011
Done000
Total17010180

Merged error: 4.6b

Counts
180 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.3b
(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
10×pow1
add-exp-log add-cbrt-cube
*-un-lft-identity add-log-exp
add-sqr-sqrt
add-cube-cbrt
associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
flip3-- sqrt-div flip--
+-commutative sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* sum-log *-commutative flip-+ distribute-lft-out
Counts
4 → 56
Calls

4 calls:

6.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
6.0ms
(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms
(* (* 3.0 a) c)
4.0ms
(- (* b b) (* (* 3.0 a) c))

series40.0ms (1%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(+ b (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
9.0ms
(- (* b b) (* (* 3.0 a) c))
3.0ms
(* (* 3.0 a) c)

simplify26.0ms (0.7%)

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
05122753

prune131.0ms (3.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New67168
Fresh178
Picked011
Done011
Total681078

Merged error: 4.6b

Counts
78 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(* 3.0 (* a c))
0.3b
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
1.2b
(- (* b b) (* 3.0 (* a c)))
23.0b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite20.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
10×pow1
add-exp-log add-cbrt-cube
*-un-lft-identity add-log-exp
add-sqr-sqrt
add-cube-cbrt
associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
flip3-- sqrt-div flip--
+-commutative sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r* sum-log *-commutative flip-+ distribute-lft-out
Counts
4 → 56
Calls

4 calls:

6.0ms
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
5.0ms
(* 3.0 (* a c))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms
(- (* b b) (* 3.0 (* a c)))

series39.0ms (1%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(+ b (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
8.0ms
(- (* b b) (* 3.0 (* a c)))
3.0ms
(* 3.0 (* a c))

simplify46.0ms (1.2%)

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04953752
14953752

prune104.0ms (2.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New68068
Fresh077
Picked011
Done022
Total681078

Merged error: 4.6b

Counts
78 → 10

regimes344.0ms (8.7%)

Accuracy

Total 1.0b remaining (16.1%)

Threshold costs 0b (0%)

bsearch110.0ms (2.8%)

Steps
ItersRangePoint
8
1.20489196718021e+121
2.0599351254817446e+124
2.3119185569929864e+122
10
-3.3146832752641835e-294
-2.1880019819224353e-304
-3.0932591459060287e-302
11
-1.3592398439034167e+155
-2.591577042876611e+131
-5.05350087668616e+142

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
014859
114859

end0.0ms (0%)

sample1.3s (33.6%)

Algorithm
intervals
Results
355.0ms1127×body2560valid
277.0ms5052×body80valid
228.0ms878×body1280valid
99.0ms478×body640valid
39.0ms106×body5120valid
37.0ms247×body320valid
32.0ms635×body80nan
21.0ms383×body80invalid
11.0ms112×body160valid

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