Details

Time bar (total: 5.7s)

analyze776.0ms

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
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
0%74.9%25.1%8
0%74.9%25.1%9
9.4%65.5%25.1%10
9.4%53%37.6%11
14%48.4%37.6%12
16.4%46%37.6%13
16.4%39.8%43.8%14

sample95.0ms

Algorithm
intervals
Results
11.0ms35×body1280valid
11.0ms161×body80valid
8.0ms32×body640valid
4.0ms19×body320valid
1.0ms9×body160valid

simplify34.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0522527

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 42.5b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
19.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
26.2b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 79
Calls
4 calls:
17.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
15.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series340.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
58.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
187.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify44.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050442021

prune202.0ms

Filtered
67 candidates to 91 candidates (-35.8%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New87491
Fresh101
Picked101
Done000
Total89493

Merged error: 3.0b

Counts
93 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
0.4b
(+ (* t t) (/ l (/ x l)))
4.0b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.2b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r/ add-log-exp
7×pow1 sqrt-prod
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sqrt-div frac-add
3×associate-*r*
2×+-commutative associate-+r+ sum-log unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
11.0ms
(+ (* t t) (/ l (/ x l)))
10.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
11.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
9.0ms
(+ (* t t) (/ l (/ x l)))
15.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
25.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify28.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
052461361

prune160.0ms

Filtered
61 candidates to 77 candidates (-26.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New72577
Fresh123
Picked011
Done000
Total73881

Merged error: 2.9b

Counts
81 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
0.4b
(+ (* t t) (* l (/ l x)))
4.0b
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
26.2b
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r/
8×add-cube-cbrt *-un-lft-identity add-log-exp
7×pow1 sqrt-prod
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sqrt-div frac-add
3×associate-*r*
2×+-commutative associate-+r+ sum-log unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
4.0ms
(+ (* t t) (* l (/ l x)))
8.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
9.0ms
(+ (* t t) (* l (/ l x)))
16.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify39.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050021369

prune141.0ms

Filtered
57 candidates to 77 candidates (-35.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New76177
Fresh156
Picked101
Done011
Total78785

Merged error: 2.9b

Counts
85 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
0.4b
(+ (* t t) (* l (/ l x)))
4.0b
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
26.2b
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*r/ sqrt-prod
10×pow1
9×add-exp-log add-sqr-sqrt associate-*l* add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity add-log-exp
5×flip3-+ flip-+
4×sqrt-div frac-add
3×pow-prod-down prod-exp cbrt-unprod
2×+-commutative associate-+r+ sum-log
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 67
Calls
4 calls:
9.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
4.0ms
(+ (* t t) (* l (/ l x)))
8.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
9.0ms
(+ (* t t) (* l (/ l x)))
15.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify171.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
049811386
149811386

prune151.0ms

Filtered
58 candidates to 79 candidates (-36.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New77279
Fresh055
Picked011
Done011
Total77986

Merged error: 2.9b

Counts
86 → 9

regimes533.0ms

Accuracy

77.5% (5.1b remaining)

Error of 9.0b against oracle of 4.0b and baseline of 26.5b

bsearch150.0ms

Steps
ItersRangePoint
7
9.580741354953985e+78
7.742539171109439e+80
7.625086325191854e+80
10
-2.664639300346167e+52
-3.772339677570164e+38
-2.6108511127275833e+52

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010898
110898

end0.0ms

sample2.4s

Algorithm
intervals
Results
331.0ms5022×body80valid
289.0ms895×body1280valid
278.0ms1080×body640valid
127.0ms667×body320valid
44.0ms336×body160valid

Profiling

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