Details

Time bar (total: 3.7s)

analyze446.0ms

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

sample46.0ms

Algorithm
intervals
Results
10.0ms32×body1280valid
10.0ms33×body2560valid
8.0ms156×body80valid
3.0ms17×body640valid
1.0ms4×body5120valid
1.0ms9×body320valid
1.0ms22×body80nan
0.0ms5×body160valid
0.0ms7×body80invalid

simplify213.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (211.0ms)

IterNodesCost
0193117
1193117

prune6.0ms

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: 33.2b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.2b
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b
(- (* b b) (* 4.0 (* a c)))
21.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 75
Calls
4 calls:
12.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms
(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms
(- (* b b) (* 4.0 (* a c)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify42.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
059461448

prune152.0ms

Filtered
64 candidates to 87 candidates (-35.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New79887
Fresh000
Picked101
Done000
Total80888

Merged error: 4.3b

Counts
88 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
3.5b
(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
9.6b
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
21.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
45×add-exp-log add-cbrt-cube
30×times-frac
28×add-sqr-sqrt
19×*-un-lft-identity
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod associate-/l*
11×add-cube-cbrt
8×difference-of-squares
7×associate-/r* sqrt-prod
6×associate-/r/ add-log-exp
5×pow1 flip3-- flip--
4×div-inv distribute-lft-out--
2×frac-2neg sqrt-div clear-num
1×sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 109
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
15.0ms
(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
12.0ms
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series127.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
46.0ms
(/ (/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
57.0ms
(/ (* 4.0 (* a c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
052872393

prune173.0ms

Filtered
81 candidates to 121 candidates (-49.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1183121
Fresh257
Picked101
Done000
Total1218129

Merged error: 4.2b

Counts
129 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* 4.0 (* a c)))
1.9b
(* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
3.5b
(/ (* 4.0 (* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)) (* 2.0 a))
21.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
41×add-exp-log add-cbrt-cube
34×add-sqr-sqrt
24×associate-*l*
22×*-un-lft-identity
20×times-frac
16×add-cube-cbrt prod-exp cbrt-unprod
11×cbrt-undiv div-exp
7×pow1
6×sqrt-prod add-log-exp difference-of-squares
3×flip3-- associate-*r* flip-- distribute-lft-out--
2×sqrt-div associate-*l/ associate-/r/ div-inv unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down clear-num associate-/r* *-commutative associate-/l/ associate-/l*
Counts
4 → 99
Calls
4 calls:
4.0ms
(- (* b b) (* 4.0 (* a c)))
13.0ms
(* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
16.0ms
(/ (* 4.0 (* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)) (* 2.0 a))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series126.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (* b b) (* 4.0 (* a c)))
51.0ms
(* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)
53.0ms
(/ (* 4.0 (* (/ c (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a)) (* 2.0 a))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify33.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
054811820

prune155.0ms

Filtered
76 candidates to 111 candidates (-46.1%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1101111
Fresh167
Picked011
Done000
Total1118119

Merged error: 4.2b

Counts
119 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
1.2b
(- (* b b) (* 4.0 (* a c)))
4.7b
(- (/ (neg b) (* a 2.0)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)))
21.0b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-exp-log add-cube-cbrt sqrt-prod add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 74
Calls
4 calls:
8.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
4.0ms
(- (* b b) (* 4.0 (* a c)))
16.0ms
(- (/ (neg b) (* a 2.0)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series78.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0))
8.0ms
(- (* b b) (* 4.0 (* a c)))
23.0ms
(- (/ (neg b) (* a 2.0)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* a 2.0)))
14.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify39.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
050811490

prune116.0ms

Filtered
68 candidates to 86 candidates (-26.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New86086
Fresh066
Picked011
Done011
Total86894

Merged error: 4.2b

Counts
94 → 8

regimes293.0ms

Accuracy

87.6% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 31.1b

bsearch80.0ms

Steps
ItersRangePoint
7
9.974136383297584e+76
2.1784240515364043e+79
1.2263949802898786e+78
10
1.730558515977129e-188
1.681496733816519e-176
1.758515410924943e-188
8
-8.157994636639643e-22
-7.232878152281043e-25
-7.400321642610797e-22

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012975
112975

end0.0ms

sample1.2s

Algorithm
intervals
Results
323.0ms1102×body2560valid
275.0ms5090×body80valid
218.0ms888×body1280valid
90.0ms472×body640valid
37.0ms99×body5120valid
33.0ms688×body80nan
33.0ms233×body320valid
21.0ms395×body80invalid
11.0ms116×body160valid

Profiling

Loading profile data...