Details

Time bar (total: 3.9s)

analyze592.0ms

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
12.5%87.4%0.1%5
18.7%81.1%0.1%6
18.7%76.5%4.8%7
28.1%66.3%5.6%8
35.1%55%9.9%9
36.3%50.9%12.8%10
42.1%42.4%15.5%11
47.5%33.8%18.7%12
48.8%30.7%20.6%13
51.8%25.6%22.5%14

sample40.0ms

Algorithm
intervals
Results
8.0ms33×body2560valid
8.0ms166×body80valid
6.0ms27×body1280valid
2.0ms14×body640valid
1.0ms28×body80nan
1.0ms9×body320valid
1.0ms2×body5120valid
0.0ms5×body160valid
0.0ms8×body80invalid

simplify505.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
071313
171313

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.2b
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
37×*-un-lft-identity
21×times-frac
17×add-cube-cbrt
10×distribute-lft-out-- add-log-exp difference-of-squares
8×sqrt-prod
7×associate-/l*
6×add-exp-log add-cbrt-cube
5×pow1 distribute-rgt-neg-in
4×flip3-- flip--
3×diff-log associate-/r*
2×sub-neg sqrt-div associate-/l/
1×cbrt-undiv associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log clear-num div-inv
Counts
4 → 89
Calls
4 calls:
11.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
4.0ms
(- (* b_2 b_2) (* a c))
8.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series70.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms
(- (* b_2 b_2) (* a c))
24.0ms
(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (52.0ms)

IterNodesCost
049361587
149361587

prune144.0ms

Filtered
72 candidates to 101 candidates (-40.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New9110101
Fresh000
Picked011
Done000
Total9111102

Merged error: 6.7b

Counts
102 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
3.0b
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.1b
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
53×add-sqr-sqrt
40×*-un-lft-identity
28×add-cube-cbrt
18×add-exp-log add-cbrt-cube
13×associate-/l*
12×difference-of-squares
10×associate-/r/
9×associate-/r* sqrt-prod
7×cbrt-undiv flip3-- div-exp flip--
6×div-inv distribute-lft-out-- add-log-exp
5×pow1
2×frac-2neg sqrt-div prod-exp clear-num cbrt-unprod
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 123
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series116.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
40.0ms
(/ (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
56.0ms
(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049612488
149612488

prune146.0ms

Filtered
102 candidates to 135 candidates (-32.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh549
Picked101
Done101
Total1388146

Merged error: 6.6b

Counts
146 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
0.2b
(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.6b
(- (* b_2 b_2) (* a c))
22.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
144×add-sqr-sqrt
111×*-un-lft-identity
79×add-cube-cbrt
32×difference-of-squares
25×associate-/r*
19×sqrt-prod
17×add-exp-log
16×distribute-lft-out--
11×add-cbrt-cube
9×associate-/l*
8×div-exp
6×pow1 div-inv add-log-exp
4×cbrt-undiv
3×flip3-- flip--
2×rec-exp frac-2neg sqrt-div 1-exp clear-num associate-/l/
1×sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log div-sub associate-/r/ inv-pow
Counts
4 → 180
Calls
4 calls:
10.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
11.0ms
(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.0ms
(- (* b_2 b_2) (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)
22.0ms
(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
7.0ms
(- (* b_2 b_2) (* a c))
13.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify84.0ms

Algorithm
egg-herbie
Counts
192 → 192
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
055733700

prune156.0ms

Filtered
114 candidates to 192 candidates (-68.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1902192
Fresh077
Picked011
Done000
Total19010200

Merged error: 6.6b

Counts
200 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(- (* b_2 b_2) (* a c))
1.3b
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0b
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
22.8b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
24×*-un-lft-identity associate-*r*
22×times-frac
18×add-exp-log add-cube-cbrt add-cbrt-cube
7×pow1
6×sqrt-prod add-log-exp difference-of-squares
5×cbrt-undiv div-exp
4×prod-exp cbrt-unprod
3×flip3-- associate-*l* associate-/r* flip-- distribute-lft-out--
2×sqrt-div associate-*r/ associate-/r/ div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative associate-/l/ associate-/l*
Counts
4 → 93
Calls
4 calls:
4.0ms
(- (* b_2 b_2) (* a c))
14.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
14.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series112.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(- (* b_2 b_2) (* a c))
54.0ms
(* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
39.0ms
(/ (* a (/ c (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
12.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify53.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049431387
149431387

prune84.0ms

Filtered
75 candidates to 105 candidates (-40.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1050105
Fresh088
Picked011
Done011
Total10510115

Merged error: 6.6b

Counts
115 → 10

regimes272.0ms

Accuracy

91.6% (2.0b remaining)

Error of 7.6b against oracle of 5.6b and baseline of 29.1b

bsearch57.0ms

Steps
ItersRangePoint
4
877860292913033.9
1745942468524521.0
1711063662601362.2
8
-2.9175484817946755e-230
-1.9267304998895037e-234
-3.588930332240471e-234
5
-1.2131696375005362e+112
-6.032663126350738e+111
-1.0769602548878653e+112

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
013950
113950

end0.0ms

sample1.1s

Algorithm
intervals
Results
267.0ms1023×body2560valid
222.0ms5186×body80valid
184.0ms922×body1280valid
71.0ms418×body640valid
36.0ms119×body5120valid
33.0ms811×body80nan
27.0ms229×body320valid
11.0ms267×body80invalid
8.0ms103×body160valid

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