Details

Time bar (total: 12.5s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22114
done2114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite60.0ms

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))
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series295.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x x) (* y y))
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
169.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.7s

Counts
90 → 90
Iterations

Useful iterations: 3 (688.0ms)

IterNodesCost
01391707
13241620
210571477
339381461
done50011461

prune257.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.2b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
532×times-frac
424×sqrt-prod
293×add-sqr-sqrt
274×add-cube-cbrt *-un-lft-identity
33×sqrt-div
28×associate-/r/
24×associate-/r*
16×flip3-+ flip-+
15×div-inv
9×add-exp-log rem-sqrt-square add-cbrt-cube
7×pow1
6×associate-/l*
4×add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 div-exp
2×associate-/l/
1×frac-2neg clear-num
Counts
4 → 387
Calls
4 calls:
45.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
51.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
101.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
175.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify1.0s

Counts
399 → 399
Iterations

Useful iterations: 2 (471.0ms)

IterNodesCost
048820659
185618771
2278016790
done500016790

prune750.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 20.4b

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))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite136.0ms

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-+l+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
30.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
71.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
17.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series881.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
133.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
347.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
364.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify2.0s

Counts
169 → 169
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
02234498
14334299
212074074
342274054
done50004054

prune560.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 20.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
35.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×add-sqr-sqrt
9×add-exp-log add-cube-cbrt *-un-lft-identity sqrt-prod add-cbrt-cube
6×times-frac associate-/l*
5×pow1
4×flip3-+ sqrt-div sum-log flip-+
2×cbrt-undiv +-commutative div-exp associate-/l/
1×rem-sqrt-square associate-+l+ frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 68
Calls
4 calls:
3.0ms
(+ (* x x) (* y y))
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
25.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series1.2s

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* x x) (* y y))
36.0ms
(+ (+ (* x x) (* y y)) (* z z))
994.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (sqrt (cbrt 3.0)) (fabs (cbrt 3.0))))
103.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.8s

Counts
80 → 80
Iterations

Useful iterations: 3 (745.0ms)

IterNodesCost
01281616
13331495
211561353
343361329
done50011329

prune247.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 20.3b

regimes482.0ms

Accuracy

62% (7.5b remaining)

Error of 25.9b against oracle of 18.4b and baseline of 38.1b

bsearch78.0ms

Steps
ItersRangePoint
9
1.8684288122828866e+141
2.986210120284181e+149
5.567264714208594e+147
8
-2.153355663052235e+147
-1.4019887183603621e+144
-2.88352274157357e+144

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03257
14557
25057
35157
done5157

end0.0ms

sample426.0ms

Algorithm
intervals
Results
266.0ms8000×body80valid