Details

Time bar (total: 12.8s)

sample27.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify11.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11312
22012
32212
done2212

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize10.0ms

Local error

Found 1 expressions with local error:

36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
1 → 15
Calls
1 calls:
39.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series107.0ms

Counts
1 → 3
Calls
1 calls:
107.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.1s

Counts
18 → 18
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
041305
192270
2270256
3907246
43276246
done5000246

prune72.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
0.5b
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (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)))

rewrite352.0ms

Algorithm
rewrite-expression-head
Rules
82×sqrt-prod
54×add-sqr-sqrt
38×sqrt-pow1
32×sqrt-div
31×pow1
20×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
45.0ms
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
208.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
43.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
49.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series552.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))
129.0ms
(* (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))) (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
141.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
138.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts
146 → 146
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01304100
12472674
26862489
323672368
done50002311

prune292.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
1.1b
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (+ 4 1))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
24×sqrt-prod
18×cbrt-prod
16×add-sqr-sqrt *-un-lft-identity
14×add-cube-cbrt
12×unpow-prod-down
8×sqrt-div
7×pow1
5×add-exp-log
4×pow-unpow add-cbrt-cube add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square cbrt-div pow-pow sqrt-pow1 pow1/2 pow1/3
1×unpow-prod-up pow-to-exp pow-exp distribute-lft-out sqr-pow
Counts
4 → 78
Calls
4 calls:
19.0ms
(cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
41.0ms
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (+ 4 1))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
181.0ms
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (+ 4 1))
145.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
120.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.6s

Counts
90 → 90
Iterations

Useful iterations: 3 (579.0ms)

IterNodesCost
01462058
13291794
27751691
321161638
done50001638

prune444.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

localize54.0ms

Local error

Found 4 expressions with local error:

5.3b
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5))
6.4b
(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5)) (sqrt (+ 4 1)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.2b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
40×unpow-prod-down
31×sqrt-prod
21×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
18×cbrt-prod
13×pow-unpow
7×pow1 add-exp-log
5×pow-exp
4×sqrt-div add-cbrt-cube add-log-exp
3×pow-to-exp pow-pow sqr-pow
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow1/3 distribute-lft-out
Counts
4 → 96
Calls
4 calls:
52.0ms
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5))
84.0ms
(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5)) (sqrt (+ 4 1)))
43.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
59.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series1.2s

Counts
4 → 12
Calls
4 calls:
305.0ms
(pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5))
536.0ms
(pow (pow (cbrt (sqrt (sqrt (+ (+ (* x x) (* y y)) (* z z))))) (sqrt 5)) (sqrt (+ 4 1)))
146.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
164.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.4s

Counts
108 → 108
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01672760
13672405
28522284
324852264
done50012261

prune495.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 20.4b

regimes490.0ms

Accuracy

64.4% (7.1b remaining)

Error of 25.6b against oracle of 18.5b and baseline of 38.4b

bsearch71.0ms

Steps
ItersRangePoint
7
1.3902720376798892e+132
1.3995183731881648e+134
2.2733836340085665e+132
10
-7.258963654046787e+141
-6.600088119136522e+124
-1.514147348156685e+135

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01623
11823
done1823

end0.0ms

sample768.0ms

Algorithm
intervals
Results
471.0ms8000×body80valid