Details

Time bar (total: 2.4s)

analyze15.0ms

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

sample26.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 35.4b

Counts
2 → 1

localize10.0ms

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)
32.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite24.0ms

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:
3.0ms
(+ (* x x) (* y y))
5.0ms
(+ (+ (* x x) (* y y)) (* z z))
8.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
6.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series56.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* x x) (* y y))
10.0ms
(+ (+ (* x x) (* y y)) (* z z))
15.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
26.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
052981461

prune149.0ms

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

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New85590
Fresh000
Picked101
Done000
Total86591

Merged error: 15.8b

Counts
91 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* y y) (* z z))
0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.3b
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
32.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
29×sqrt-prod
17×*-un-lft-identity
16×associate-*r*
15×add-cube-cbrt
13×times-frac
11×add-log-exp
9×pow1 sqrt-div
8×unswap-sqr
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sum-log
3×sqrt-pow1 pow1/2 pow-prod-down
2×+-commutative frac-times associate-*l/
1×rem-sqrt-square associate-+r+ sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 88
Calls
4 calls:
3.0ms
(+ (* y y) (* z z))
5.0ms
(+ (* x x) (+ (* y y) (* z z)))
13.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
5.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (* y y) (* z z))
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
26.0ms
(* (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt (/ 1 3.0)))
18.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify35.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
049801672
149801672

prune135.0ms

Filtered
68 candidates to 100 candidates (-47.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh044
Picked011
Done000
Total1005105

Merged error: 15.8b

Counts
105 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.0b
(+ (* y y) (* z z))
0.4b
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
32.9b
(sqrt (+ (* x x) (+ (* y y) (* z z))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
34×add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
11×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×+-commutative associate-/l/
1×cbrt-undiv rem-sqrt-square associate-+r+ sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 102
Calls
4 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
3.0ms
(+ (* y y) (* z z))
9.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
5.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
5.0ms
(+ (* y y) (* z z))
32.0ms
(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3.0))
19.0ms
(sqrt (+ (* x x) (+ (* y y) (* z z))))

simplify38.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
057482173

prune138.0ms

Filtered
71 candidates to 114 candidates (-60.6%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1113114
Fresh033
Picked011
Done011
Total1118119

Merged error: 15.6b

Counts
119 → 8

localize3.0ms

Local error

Found 1 expressions with local error:

0.2b
(* x (sqrt 0.3333333333333333))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×associate-*r*
4×add-cube-cbrt *-un-lft-identity sqrt-prod
3×pow1 add-exp-log associate-*l* add-cbrt-cube
2×unswap-sqr
1×pow-prod-down prod-exp *-commutative cbrt-unprod add-log-exp
Counts
1 → 22
Calls
1 calls:
5.0ms
(* x (sqrt 0.3333333333333333))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(* x (sqrt 0.3333333333333333))

simplify44.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04982133
14982133

prune29.0ms

Filtered
14 candidates to 25 candidates (-78.6%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New21425
Fresh055
Picked011
Done022
Total211233

Merged error: 15.6b

Counts
33 → 12

regimes648.0ms

Accuracy

60.3% (7.8b remaining)

Error of 25.9b against oracle of 18.1b and baseline of 37.7b

bsearch74.0ms

Steps
ItersRangePoint
7
4.971198022482152e+51
2.4182398885745636e+53
2.376324303767219e+53
10
-9.228755819352994e+114
-4.900386327726624e+104
-9.146593474358907e+114

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03334
13334

end0.0ms

analyze15.0ms

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

sample735.0ms

Algorithm
intervals
Results
572.0ms8000×body80valid

Profiling

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