Details

Time bar (total: 4.6s)

analyze445.0ms

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
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14

sample41.0ms

Algorithm
intervals
Results
9.0ms31×body2560valid
8.0ms168×body80valid
8.0ms34×body1280valid
2.0ms13×body640valid
1.0ms23×body80nan
1.0ms7×body320valid
1.0ms12×body80invalid
0.0ms1×body5120valid
0.0ms2×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03017
13017

prune7.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 33.8b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 4.0 (* a c))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.9b
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
14×add-exp-log add-cbrt-cube
10×pow1
9×add-sqr-sqrt
8×add-cube-cbrt add-log-exp
6×distribute-lft-out
5×times-frac associate-/l*
4×prod-exp cbrt-unprod
3×distribute-rgt-neg-in associate-*l* pow-prod-down sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-+ sqrt-div div-exp sum-log flip-+ associate-/l/
1×+-commutative rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 div-sub associate-*r* neg-log clear-num associate-/r* *-commutative flip-- div-inv
Counts
4 → 76
Calls
4 calls:
5.0ms
(* 4.0 (* a c))
13.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 4.0 (* a c))
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
054071206

prune147.0ms

Filtered
63 candidates to 88 candidates (-39.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New80888
Fresh000
Picked101
Done000
Total81889

Merged error: 5.0b

Counts
89 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* b b) (* (* 4.0 a) c))
0.1b
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.9b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-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 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 69
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series61.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
050921264

prune125.0ms

Filtered
57 candidates to 81 candidates (-42.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New79281
Fresh077
Picked011
Done000
Total791089

Merged error: 4.9b

Counts
89 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
0.2b
(/ 1 (* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))))
0.9b
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
30×add-exp-log
23×add-sqr-sqrt
21×associate-*r*
19×times-frac
18×add-cbrt-cube
17×add-cube-cbrt
10×pow1 div-exp
8×prod-exp distribute-lft-out add-log-exp
5×cbrt-undiv
4×distribute-rgt-neg-in cbrt-unprod
3×rec-exp 1-exp associate-*l* sqrt-prod associate-/r/ associate-/l*
2×pow-flip flip3-+ sqrt-div associate-*r/ pow-prod-down sum-log flip-+ div-inv unswap-sqr
1×+-commutative neg-sub0 associate-+r- rem-sqrt-square flip3-- frac-2neg sqrt-pow1 pow1/2 unsub-neg neg-log clear-num associate-/r* *-commutative flip-- inv-pow
Counts
4 → 104
Calls
4 calls:
15.0ms
(* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
13.0ms
(/ 1 (* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))))
8.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series117.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))))
35.0ms
(/ 1 (* a (/ 2.0 (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))))
14.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
16.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify56.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049631674
149631674

prune173.0ms

Filtered
80 candidates to 116 candidates (-45.0%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1124116
Fresh268
Picked011
Done011
Total11412126

Merged error: 4.9b

Counts
126 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.9b
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
0.9b
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.2b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
14×*-un-lft-identity
12×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div sum-log add-cbrt-cube distribute-lft-out
2×+-commutative neg-sub0 rem-sqrt-square flip3-- distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 neg-log flip-- flip-+
1×associate-+l- associate-+r- unsub-neg
Counts
4 → 61
Calls
4 calls:
8.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
7.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series57.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
14.0ms
(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify80.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
04827976
14827976

prune141.0ms

Filtered
61 candidates to 73 candidates (-19.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New72173
Fresh099
Picked101
Done022
Total731285

Merged error: 4.9b

Counts
85 → 12

regimes371.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 34.1b

bsearch564.0ms

Steps
ItersRangePoint
10
3.871189569794153e-134
8.390398378442516e-122
5.194362910626694e-122
10
-1.8268856981153665e+137
-5.174635489623954e+120
-1.3847614318092212e+134

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03746
13746

end0.0ms

analyze449.0ms

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
21.8%71.8%6.4%7
31.2%62.4%6.4%8
35.9%55.4%8.7%9
37.8%48.8%13.4%10
42.7%42.3%15%11
47.7%34.2%18.1%12
49.1%30.4%20.5%13
51.9%25.8%22.3%14

sample1.4s

Algorithm
intervals
Results
519.0ms1067×body2560valid
269.0ms5126×body80valid
216.0ms887×body1280valid
92.0ms474×body640valid
40.0ms114×body5120valid
34.0ms694×body80nan
31.0ms221×body320valid
22.0ms385×body80invalid
11.0ms111×body160valid

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