Details

Time bar (total: 9.5s)

analyze2.0s

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
31.2%68.7%0.1%7
34.3%65.6%0.1%8
37.5%59.3%3.2%9
42.9%53.5%3.6%10
44.5%50%5.6%11
47.8%45.8%6.4%12
48.7%43.7%7.6%13
50.5%41.3%8.2%14

sample143.0ms

Algorithm
intervals
Results
48.0ms217×body80valid
45.0ms206×body80invalid
14.0ms16×body640valid
7.0ms4×body1280valid
7.0ms10×body320valid
4.0ms9×body160valid

simplify454.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05054109

prune16.0ms

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: 0.5b

Counts
2 → 2

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 6.0 (* x1 x1))
0.2b
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
3.2b
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
4.5b
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
18×associate-*l*
15×*-un-lft-identity
14×add-exp-log add-cbrt-cube
13×add-cube-cbrt
11×pow1 times-frac
8×add-log-exp
5×prod-exp cbrt-unprod
4×associate-*r* pow-prod-down
3×flip3-+ flip-+ unswap-sqr
2×distribute-rgt-in frac-times sub-neg flip3-- distribute-lft-in diff-log associate-*r/ associate--l+ associate-/r/ *-commutative flip-- difference-of-squares
1×cbrt-undiv associate--l- associate-+r- div-sub div-exp associate-*l/ div-inv distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
5.0ms
(* 6.0 (* x1 x1))
41.0ms
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
17.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
36.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))

series125.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 6.0 (* x1 x1))
30.0ms
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
14.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
77.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* 6.0 (* x1 x1)))

simplify42.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
053833593

prune504.0ms

Filtered
80 candidates to 99 candidates (-23.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New891099
Fresh101
Picked101
Done000
Total9110101

Merged error: 0.4b

Counts
101 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
0.2b
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
3.2b
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
4.5b
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 6.0) x1))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×associate-*l*
15×*-un-lft-identity
14×add-exp-log add-cbrt-cube
13×add-cube-cbrt
11×pow1 times-frac
8×add-log-exp
6×distribute-rgt-in distribute-lft-in associate-*r/
5×prod-exp cbrt-unprod
4×flip3-+ associate-*r* pow-prod-down flip-+
2×frac-times sub-neg flip3-- diff-log associate--l+ associate-/r/ *-commutative flip-- difference-of-squares unswap-sqr
1×cbrt-undiv associate--l- associate-+r- div-sub div-exp associate-*l/ div-inv distribute-lft-out--
Counts
4 → 92
Calls
4 calls:
19.0ms
(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
36.0ms
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
20.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
34.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 6.0) x1))

series131.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* x1 (* x1 (+ (* 3.0 (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0))) x1)))
31.0ms
(* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1))))
14.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
67.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 6.0) x1))

simplify45.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
050754129

prune515.0ms

Filtered
82 candidates to 104 candidates (-26.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1040104
Fresh099
Picked011
Done000
Total10410114

Merged error: 0.4b

Counts
114 → 10

localize44.0ms

Local error

Found 4 expressions with local error:

3.2b
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
6.7b
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (sqrt (* x1 (* x1 6.0))) (sqrt (* x1 (* x1 6.0)))))
22.1b
(sqrt (* x1 (* x1 6.0)))
22.1b
(sqrt (* x1 (* x1 6.0)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
9×add-sqr-sqrt
8×add-log-exp
6×*-un-lft-identity sqrt-pow1 pow-prod-down
4×add-exp-log add-cube-cbrt add-cbrt-cube
2×sub-neg flip3-- pow1/2 diff-log associate--l+ sqrt-prod flip-- difference-of-squares
1×associate--l- distribute-rgt-in associate-+r- distribute-lft-in times-frac div-sub distribute-lft-out--
Counts
4 → 52
Calls
4 calls:
21.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
35.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (sqrt (* x1 (* x1 6.0))) (sqrt (* x1 (* x1 6.0)))))
4.0ms
(sqrt (* x1 (* x1 6.0)))
4.0ms
(sqrt (* x1 (* x1 6.0)))

series93.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
68.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (sqrt (* x1 (* x1 6.0))) (sqrt (* x1 (* x1 6.0)))))
4.0ms
(sqrt (* x1 (* x1 6.0)))
4.0ms
(sqrt (* x1 (* x1 6.0)))

simplify39.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049651496
149651496

prune308.0ms

Filtered
51 candidates to 64 candidates (-25.5%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New61364
Fresh268
Picked011
Done011
Total631174

Merged error: 0.4b

Counts
74 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b
(* x1 (sqrt 6.0))
0.6b
(* x1 (sqrt 6.0))
3.2b
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
6.7b
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 (sqrt 6.0)) (* x1 (sqrt 6.0))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
12×*-un-lft-identity associate-*r*
10×add-cube-cbrt
8×pow1 add-exp-log sqrt-prod add-cbrt-cube add-log-exp
6×associate-*l*
4×unswap-sqr
2×sub-neg flip3-- diff-log pow-prod-down prod-exp associate--l+ *-commutative flip-- cbrt-unprod difference-of-squares
1×associate--l- distribute-rgt-in associate-+r- distribute-lft-in times-frac div-sub distribute-lft-out--
Counts
4 → 72
Calls
4 calls:
5.0ms
(* x1 (sqrt 6.0))
5.0ms
(* x1 (sqrt 6.0))
17.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
35.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 (sqrt 6.0)) (* x1 (sqrt 6.0))))

series91.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* x1 (sqrt 6.0))
4.0ms
(* x1 (sqrt 6.0))
14.0ms
(- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0)
70.0ms
(- (* (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) (+ (* x1 (* 2.0 (- (/ (+ (* x1 (* x1 3.0)) (- (* 2.0 x2) x1)) (+ (* x1 x1) 1.0)) 3.0))) (* 4.0 (* x1 x1)))) (* (* x1 (sqrt 6.0)) (* x1 (sqrt 6.0))))

simplify40.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049581611
149581611

prune285.0ms

Filtered
56 candidates to 84 candidates (-50.0%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New82284
Fresh178
Picked101
Done022
Total841195

Merged error: 0.4b

Counts
95 → 11

regimes310.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0140109
1140109

end0.0ms

sample3.8s

Algorithm
intervals
Results
1.5s6933×body80valid
1.2s5695×body80invalid
346.0ms393×body640valid
201.0ms313×body320valid
190.0ms169×body1280valid
82.0ms192×body160valid

Profiling

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