Details

Time bar (total: 3.2s)

analyze18.0ms

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
49.9%49.9%0.1%5
74.9%25%0.1%6
87.4%12.5%0.1%7
93.6%6.2%0.1%8
96.7%3.1%0.1%9
98.3%1.6%0.1%10
99.1%0.8%0.1%11
99.5%0.4%0.1%12
99.7%0.2%0.1%13
99.8%0.1%0.1%14

sample24.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02114
12114

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: 34.5b

Counts
2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
32.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×sqrt-prod
11×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1
4×sum-log
3×flip3-+ associate-/r* flip-+ associate-/l*
2×+-commutative rem-sqrt-square div-inv associate-/l/
1×cbrt-undiv associate-+l+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
4 → 78
Calls
4 calls:
4.0ms
(+ (* x x) (* y y))
6.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
7.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series55.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* x x) (* y y))
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
12.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049461461
149461461

prune151.0ms

Filtered
72 candidates to 90 candidates (-25.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New83790
Fresh000
Picked011
Done000
Total83891

Merged error: 18.7b

Counts
91 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.0b
(+ (* y y) (* z z))
0.1b
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
32.0b
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
9×pow1
8×add-sqr-sqrt
6×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×flip3-+ associate-*l/ sum-log flip-+
3×associate-*r* associate-*l*
2×+-commutative sqrt-pow1 sqrt-div pow-prod-down
1×associate-+r+ pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
4 → 57
Calls
4 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
4.0ms
(+ (* y y) (* z z))
8.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
7.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

series53.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
5.0ms
(+ (* y y) (* z z))
12.0ms
(* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333)
26.0ms
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 0.3333333333333333))

simplify63.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
04945928
14945928

prune89.0ms

Filtered
47 candidates to 69 candidates (-46.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New69069
Fresh066
Picked011
Done011
Total69877

Merged error: 18.7b

Counts
77 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
0.4b
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
31.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))
31.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
102×sqrt-prod
73×add-sqr-sqrt
44×times-frac
36×add-cube-cbrt *-un-lft-identity
25×associate-*r*
16×sqrt-div
12×unswap-sqr
11×pow1
9×associate-*l*
6×add-exp-log add-cbrt-cube
5×rem-sqrt-square sqrt-pow1 pow1/2
4×flip3-+ flip-+ add-log-exp
3×pow-prod-down
2×frac-times associate-*l/ div-inv
1×sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
8.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
23.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
5.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series105.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0))
26.0ms
(* (sqrt (sqrt (+ (* x x) (+ (* y y) (* z z))))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) 3.0)))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify51.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
054773569

prune203.0ms

Filtered
96 candidates to 142 candidates (-47.9%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New1420142
Fresh055
Picked011
Done022
Total1428150

Merged error: 18.7b

Counts
150 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
0.4b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
31.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))
31.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
150×sqrt-prod
130×add-sqr-sqrt
106×times-frac
64×add-cube-cbrt *-un-lft-identity
47×cbrt-prod
43×associate-*r*
24×unswap-sqr
13×associate-*l*
10×pow1 sqrt-div
8×add-exp-log
7×add-cbrt-cube
6×associate-/r* associate-/l*
4×sqrt-pow1 pow1/2 add-log-exp
3×flip3-+ pow-prod-down flip-+ div-inv
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 189
Calls
4 calls:
43.0ms
(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
9.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
6.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series116.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))))
36.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (cbrt 3.0))
19.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify74.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
049756176
149756176

prune391.0ms

Filtered
134 candidates to 201 candidates (-50.0%)
Pruning

8 alts after pruning (4 fresh and 4 done)

PrunedKeptTotal
New2010201
Fresh044
Picked011
Done033
Total2018209

Merged error: 18.7b

Counts
209 → 8

regimes995.0ms

Accuracy

60.7% (7.6b remaining)

Error of 25.8b against oracle of 18.2b and baseline of 37.6b

bsearch31.0ms

Steps
ItersRangePoint
8
7.549412984073061e+69
1.9330809061291948e+73
1.9019574387521618e+73
9
-4.010902430270259e+81
-3.84232038861762e+72
-2.2756566799824152e+79

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04731
14731

end0.0ms

sample503.0ms

Algorithm
intervals
Results
354.0ms8000×body80valid

Profiling

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