Details

Time bar (total: 17.5s)

sample29.0ms

Algorithm
intervals
Results
16.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done25
325
222
115
011

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
8×add-log-exp
5×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* sum-log associate-/l*
2×rem-sqrt-square flip3-+ flip-+ div-inv associate-/l/
1×cbrt-undiv +-commutative associate-+l+ clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp
Counts
3 → 67
Calls
3 calls:
24.0ms
(+ (+ (* x x) (* y y)) (* z z))
87.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
31.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series395.0ms

Counts
3 → 9
Calls
3 calls:
51.0ms
(+ (+ (* x x) (* y y)) (* z z))
68.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
276.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
done5002
21232
1285
0123

prune563.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
1.0b
(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
33.7b
(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
168×times-frac
102×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
50×sqrt-prod
18×associate-/r* associate-/r/
17×add-exp-log
11×add-cbrt-cube
10×div-inv
9×flip3-+ flip-+ add-log-exp
8×div-exp
7×pow1
6×associate-/l*
5×rem-sqrt-square
4×cbrt-undiv
3×sum-log sqrt-pow1
2×rec-exp clear-num frac-2neg 1-exp pow-flip inv-pow
1×+-commutative associate-+l+ pow1/2 sqrt-div
Counts
4 → 193
Calls
4 calls:
46.0ms
(+ (+ (* x x) (* y y)) (* z z))
42.0ms
(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
52.0ms
(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
49.0ms
(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

series478.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ (+ (* x x) (* y y)) (* z z))
98.0ms
(/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z))))
88.0ms
(/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))
241.0ms
(sqrt (/ 1 (/ 3.0 (+ (+ (* x x) (* y y)) (* z z)))))

simplify2.5s

Counts
205 → 205
Iterations
IterNodes
done5000
23591
1642
0298

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 17.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
33.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.7b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
33.7b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
28×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×associate-/r* add-exp-log associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×frac-times cbrt-undiv clear-num frac-2neg div-exp pow-prod-down associate-*l/ associate-*r/ div-inv
Counts
4 → 106
Calls
4 calls:
72.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
25.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
61.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
316.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
168.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
135.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
483.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify2.4s

Counts
118 → 118
Iterations
IterNodes
done5000
34256
2828
1262
0145

prune718.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 17.3b

localize36.0ms

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 3.0))
0.4b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
33.7b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite305.0ms

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 sum-log sqrt-pow1 pow1/2 pow-prod-down associate-/l*
2×flip3-+ flip-+ associate-/l/
1×frac-times cbrt-undiv +-commutative associate-+l+ clear-num frac-2neg sqrt-unprod div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
77.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
154.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
32.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
42.0ms
(+ (+ (* x x) (* y y)) (* z z))
176.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
477.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
451.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify1.2s

Counts
169 → 169
Iterations
IterNodes
done5000
22087
1458
0221

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 17.2b

regimes1.0s

Accuracy

60.1% (7.9b remaining)

Error of 25.9b against oracle of 18.0b and baseline of 37.9b

bsearch114.0ms

Steps
ItersRangePoint
8
7.95134694153949e+90
1.3754392491595687e+95
7.495231207769667e+94
11
-1.718776312539675e+54
-2.0346378402041832e+34
-8.211230074550795e+53

simplify23.0ms

Iterations
IterNodes
done59
359
255
142
030

end0.0ms

sample1.2s

Algorithm
intervals
Results
935.0ms8000×body80valid