Details

Time bar (total: 4.8s)

analyze17.0ms

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

sample20.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02114
12114

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: 40.1b

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)
37.2b
(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)
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))
12.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
28.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
049461461
149461461

prune322.0ms

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: 19.0b

Counts
91 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.2b
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
37.2b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
75×times-frac sqrt-prod
53×*-un-lft-identity
49×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
9×pow1 add-log-exp
8×add-exp-log
7×add-cbrt-cube
6×associate-/r*
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down sum-log associate-/l*
2×flip3-+ flip-+ associate-/l/
1×cbrt-undiv +-commutative frac-times associate-+r+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
7.0ms
(+ (* x x) (+ (* y y) (* z z)))
10.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
24.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
8.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

series113.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
19.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))
44.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0))))
41.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt 3.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049644093
149644093

prune399.0ms

Filtered
132 candidates to 169 candidates (-28.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1654169
Fresh246
Picked011
Done011
Total16710177

Merged error: 19.0b

Counts
177 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (+ (* y y) (* z z)))
0.1b
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))
0.3b
(* (* (sqrt (/ 1 (cbrt (sqrt 3.0)))) (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0))))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))))
37.2b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
84×times-frac
72×add-sqr-sqrt
65×add-cube-cbrt *-un-lft-identity
62×cbrt-prod
34×associate-*r*
13×pow1 sqrt-div
11×add-exp-log
10×add-cbrt-cube
9×associate-/r* add-log-exp
7×pow-prod-down
5×frac-times associate-*l/
4×rem-sqrt-square sqrt-pow1 pow1/2
3×associate-*r/ prod-exp sum-log cbrt-unprod div-inv associate-/l*
2×flip3-+ sqrt-unprod flip-+ associate-/l/
1×cbrt-undiv +-commutative associate-+r+ frac-2neg div-exp associate-*l* clear-num *-commutative
Counts
4 → 170
Calls
4 calls:
6.0ms
(+ (* x x) (+ (* y y) (* z z)))
10.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))
35.0ms
(* (* (sqrt (/ 1 (cbrt (sqrt 3.0)))) (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0))))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))))
10.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0))))

series186.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* x x) (+ (* y y) (* z z)))
34.0ms
(/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))
79.0ms
(* (* (sqrt (/ 1 (cbrt (sqrt 3.0)))) (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0))))) (sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0)))))
63.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt 3.0))))

simplify73.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049564718
149564718

prune582.0ms

Filtered
137 candidates to 182 candidates (-32.8%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1757182
Fresh437
Picked011
Done112
Total18012192

Merged error: 18.9b

Counts
192 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(/ 1 (cbrt (fabs (cbrt 3.0))))
1.0b
(cbrt (sqrt (cbrt 3.0)))
1.0b
(sqrt (/ 1 (cbrt (fabs (cbrt 3.0)))))
37.2b
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt (cbrt 3.0)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
80×times-frac
76×add-sqr-sqrt
75×cbrt-prod
62×*-un-lft-identity
60×add-cube-cbrt
10×rem-sqrt-square
8×pow1 add-exp-log
6×associate-/r*
5×sqrt-pow1 add-cbrt-cube
4×pow-flip add-log-exp
3×pow1/3 div-inv associate-/l*
2×pow1/2 sqrt-div div-exp inv-pow
1×cbrt-undiv rec-exp frac-2neg 1-exp clear-num
Counts
4 → 156
Calls
4 calls:
4.0ms
(/ 1 (cbrt (fabs (cbrt 3.0))))
2.0ms
(cbrt (sqrt (cbrt 3.0)))
4.0ms
(sqrt (/ 1 (cbrt (fabs (cbrt 3.0)))))
13.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt (cbrt 3.0)))))

series60.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(/ 1 (cbrt (fabs (cbrt 3.0))))
0.0ms
(cbrt (sqrt (cbrt 3.0)))
0.0ms
(sqrt (/ 1 (cbrt (fabs (cbrt 3.0)))))
59.0ms
(sqrt (/ (+ (* x x) (+ (* y y) (* z z))) (cbrt (sqrt (cbrt 3.0)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 0 (95.0ms)

IterNodesCost
046692696
146692696

prune653.0ms

Filtered
118 candidates to 162 candidates (-37.3%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New1611162
Fresh099
Picked011
Done022
Total16113174

Merged error: 18.9b

Counts
174 → 13

regimes1.3s

Accuracy

64.4% (7.0b remaining)

Error of 25.5b against oracle of 18.4b and baseline of 38.2b

bsearch37.0ms

Steps
ItersRangePoint
10
6.947425896840144e+130
1.510175706478412e+143
2.142628107794844e+138
8
-4.223726535327663e+100
-1.608332396162618e+98
-3.729724887074998e+100

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09371
19371

end0.0ms

sample522.0ms

Algorithm
intervals
Results
360.0ms8000×body80valid

Profiling

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