Details

Time bar (total: 3.8s)

analyze455.0ms (12%)

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

sample42.0ms (1.1%)

Algorithm
intervals
Results
10.0ms33×body1280valid
9.0ms180×body80valid
6.0ms20×body2560valid
2.0ms13×body640valid
1.0ms25×body80nan
1.0msbody5120valid
1.0ms17×body80invalid
1.0msbody320valid
0.0msbody160valid

simplify173.0ms (4.6%)

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (172.0ms)

IterNodesCost
0178416
1178416

prune10.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.2b

Counts
2 → 2

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.8b
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
18.8b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
add-exp-log add-cbrt-cube
add-sqr-sqrt
add-cube-cbrt
associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
flip3-- sqrt-div sum-log flip-- distribute-lft-out
+-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 → 59
Calls

4 calls:

8.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms
(* (* 3.0 a) c)
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(- (* b b) (* (* 3.0 a) c))

series40.0ms (1.1%)

Counts
4 → 12
Calls

4 calls:

14.0ms
(+ (neg 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)

simplify62.0ms (1.6%)

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
04893791
14893791

prune160.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New63871
Fresh101
Picked011
Done000
Total64973

Merged error: 8.1b

Counts
73 → 9

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 3.0 (* a c)))
1.2b
(- (* b b) (* 3.0 (* a c)))
18.8b
(sqrt (- (* b b) (* 3.0 (* a c))))
18.8b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite17.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt add-log-exp
pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
add-exp-log flip3-- sqrt-div add-cbrt-cube flip--
sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log
Counts
4 → 52
Calls

4 calls:

4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms
(- (* b b) (* 3.0 (* a c)))
4.0ms
(- (* b b) (* 3.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series46.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

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

simplify36.0ms (0.9%)

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
05246824

prune183.0ms (4.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New63164
Fresh077
Picked011
Done011
Total631073

Merged error: 8.1b

Counts
73 → 10

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 3.0 (* a c)))
8.1b
(+ (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
19.6b
(cbrt (- (* b b) (* 3.0 (* a c))))
19.6b
(cbrt (- (* b b) (* 3.0 (* a c))))

rewrite17.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
pow1 add-exp-log cbrt-div add-cbrt-cube
flip3-- flip--
pow1/3 sum-log
+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 50
Calls

4 calls:

4.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
4.0ms
(- (* b b) (* 3.0 (* a c)))
4.0ms
(cbrt (- (* b b) (* 3.0 (* a c))))
4.0ms
(cbrt (- (* b b) (* 3.0 (* a c))))

series88.0ms (2.3%)

Counts
4 → 12
Calls

4 calls:

32.0ms
(+ (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
24.0ms
(cbrt (- (* b b) (* 3.0 (* a c))))
24.0ms
(cbrt (- (* b b) (* 3.0 (* a c))))
8.0ms
(- (* b b) (* 3.0 (* a c)))

simplify64.0ms (1.7%)

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
049051133
149051133

prune178.0ms (4.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New61162
Fresh167
Picked011
Done022
Total621072

Merged error: 8.1b

Counts
72 → 10

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

13.7b
(+ (neg b) (* (* (cbrt (sqrt (- (* b b) (* 3.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))))
18.8b
(sqrt (- (* b b) (* 3.0 (* a c))))
18.8b
(sqrt (- (* b b) (* 3.0 (* a c))))
18.8b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite20.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
sqrt-prod
add-log-exp
pow1 add-cube-cbrt *-un-lft-identity
sqrt-div
add-exp-log add-cbrt-cube
rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
sum-log
+-commutative neg-sub0 associate-+l- flip3-+ neg-log flip-+
Counts
4 → 58
Calls

4 calls:

7.0ms
(+ (neg b) (* (* (cbrt (sqrt (- (* b b) (* 3.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
4.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

series70.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

23.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
20.0ms
(+ (neg b) (* (* (cbrt (sqrt (- (* b b) (* 3.0 (* a c))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))) (cbrt (sqrt (- (* b b) (* 3.0 (* a c)))))))
14.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))
13.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify35.0ms (0.9%)

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
04917893
14917893

prune186.0ms (4.9%)

Pruning

10 alts after pruning (6 fresh and 4 done)

PrunedKeptTotal
New70070
Fresh066
Picked011
Done033
Total701080

Merged error: 8.1b

Counts
80 → 10

regimes490.0ms (13%)

Accuracy

Total 1.6b remaining (13.3%)

Threshold costs 0b (0%)

bsearch90.0ms (2.4%)

Steps
ItersRangePoint
7
7.497846501147866e+151
1.3137550991139276e+154
1.2940411791043692e+154
9
2.053163735367116e-113
1.5168780676120168e-108
2.0737225518150114e-113
8
-6.383117637049118e+125
-2.998422293648943e+121
-2.846912681280906e+123

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
013677
113677

end0.0ms (0%)

sample1.2s (32.5%)

Algorithm
intervals
Results
315.0ms1064×body2560valid
267.0ms5180×body80valid
204.0ms870×body1280valid
88.0ms452×body640valid
46.0ms126×body5120valid
33.0ms643×body80nan
33.0ms219×body320valid
19.0ms384×body80invalid
10.0ms89×body160valid

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