Details

Time bar (total: 18.8s)

sample42.0ms

Algorithm
intervals
Results
20.0ms256×body80valid

simplify25.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
34.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite184.0ms

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:
113.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
70.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series321.0ms

Counts
2 → 6
Calls
2 calls:
75.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
245.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts
60 → 60
Iterations

Useful iterations: 3 (569.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune301.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
34.9b
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity associate-*r/ add-cbrt-cube
3×associate-*r* associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
127.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
51.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series324.0ms

Counts
2 → 6
Calls
2 calls:
79.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
244.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify2.9s

Counts
41 → 41
Iterations

Useful iterations: 3 (1.2s)

IterNodesCost
079721
1212681
2798605
34396597
done5000597

prune122.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.4b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
0.2b
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
34.9b
(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

rewrite337.0ms

Algorithm
rewrite-expression-head
Rules
526×times-frac
405×sqrt-prod
295×add-sqr-sqrt
278×add-cube-cbrt *-un-lft-identity
25×associate-/l*
16×div-inv
12×associate-/r*
10×add-exp-log add-cbrt-cube
7×rem-sqrt-square
4×pow1 cbrt-undiv div-exp
3×associate-/l/ add-log-exp
2×frac-2neg clear-num
1×sqrt-pow1 flip3-+ pow1/2 sqrt-div flip-+
Counts
3 → 369
Calls
3 calls:
129.0ms
(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
106.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
63.0ms
(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

series808.0ms

Counts
3 → 9
Calls
3 calls:
311.0ms
(/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0))
207.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0))
290.0ms
(sqrt (/ (/ (+ (+ (* x x) (* y y)) (* z z)) (sqrt 3.0)) (sqrt 3.0)))

simplify2.9s

Counts
378 → 378
Iterations

Useful iterations: done (2.9s)

IterNodesCost
043713182
178912162
2158911520
3467411334
done500011281

prune819.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y))))))
34.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
34.9b
(sqrt (+ (* z z) (+ (* x x) (* y y))))
34.9b
(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y)))))))

rewrite629.0ms

Algorithm
rewrite-expression-head
Rules
5195×times-frac
3492×sqrt-prod
2356×add-sqr-sqrt
2291×*-un-lft-identity
2285×add-cube-cbrt
167×sqrt-div
164×associate-/r/
132×div-inv
83×flip3-+ flip-+
40×associate-/l*
24×rem-sqrt-square associate-/r*
16×add-exp-log add-cbrt-cube
8×cbrt-undiv div-exp
7×pow1
4×add-log-exp
3×sqrt-pow1 pow1/2
1×frac-2neg clear-num associate-/l/
Counts
4 → 2071
Calls
4 calls:
114.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y))))))
34.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
27.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
200.0ms
(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y)))))))

series576.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y))))))
125.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
147.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
237.0ms
(sqrt (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 1)) (/ 3.0 (sqrt (+ (* z z) (+ (* x x) (* y y)))))))

simplify2.6s

Counts
2083 → 2083
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02091138202
14155112279
done5000108281

prune1.7s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.3b

regimes690.0ms

Accuracy

59.3% (8.2b remaining)

Error of 26.4b against oracle of 18.2b and baseline of 38.2b

bsearch99.0ms

Steps
ItersRangePoint
9
1.6558114091021875e+84
4.612323731361669e+91
4.376373199179286e+91
7
-1.8875295458160305e+40
-3.852270064556066e+38
-1.8637040731758233e+40

simplify9.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02533
13333
done3333

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.1s8000×body80valid