Details

Time bar (total: 14.8s)

sample34.0ms

Algorithm
intervals
Results
15.0ms256×body80valid

simplify38.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
101.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series285.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
206.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.6s

Counts
60 → 60
Iterations

Useful iterations: 3 (630.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune302.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.5b

localize18.0ms

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)))))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.3b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

rewrite398.0ms

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:
138.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
60.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
50.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
124.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series631.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
175.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
141.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
238.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify2.6s

Counts
399 → 399
Iterations

Useful iterations: done (2.5s)

IterNodesCost
048820659
183418715
2235416762
done500015594

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
0.3b
(* (sqrt (sqrt (+ (* z z) (+ (* x x) (* y y))))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b
(sqrt (+ (* z z) (+ (* x x) (* y y))))

rewrite278.0ms

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:
50.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
155.0ms
(* (sqrt (sqrt (+ (* z z) (+ (* x x) (* y y))))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
37.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
26.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))

series751.0ms

Counts
4 → 12
Calls
4 calls:
208.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
237.0ms
(* (sqrt (sqrt (+ (* z z) (+ (* x x) (* y y))))) (sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
144.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
163.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))

simplify2.3s

Counts
142 → 142
Iterations

Useful iterations: 3 (959.0ms)

IterNodesCost
02114152
13923742
210633580
329663561
done50013561

prune523.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.3b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
4×add-exp-log add-cbrt-cube
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
100.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
61.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series289.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
214.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.3s

Counts
60 → 60
Iterations

Useful iterations: 3 (595.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune163.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.6b

regimes687.0ms

Accuracy

40.1% (19.1b remaining)

Error of 25.7b against oracle of 6.6b and baseline of 38.5b

bsearch124.0ms

Steps
ItersRangePoint
7
1.3902720376798892e+132
1.3995183731881648e+134
2.2733836340085665e+132
10
-7.258963654046787e+141
-6.600088119136522e+124
-2.8004366194075308e+135

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02445
12945
23245
done3245

end0.0ms

sample892.0ms

Algorithm
intervals
Results
565.0ms8000×body80valid