Details

Time bar (total: 12.4s)

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))

rewrite59.0ms

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:
2.0ms
(+ (* x x) (* y y))
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
28.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
14.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series290.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ (* x x) (* y y))
35.0ms
(+ (+ (* x x) (* y y)) (* z z))
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
172.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.7s

Counts
90 → 90
Iterations

Useful iterations: 3 (692.0ms)

IterNodesCost
01391707
13241620
210571477
339381461
done50011461

prune255.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.4b

localize11.0ms

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))))))

rewrite141.0ms

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:
42.0ms
(/ (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)))
47.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

series404.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z)))))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
96.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
161.0ms
(sqrt (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ 3.0 (sqrt (+ (+ (* x x) (* y y)) (* z z))))))

simplify986.0ms

Counts
399 → 399
Iterations

Useful iterations: 2 (455.0ms)

IterNodesCost
048820659
185618771
2278016790
done500016790

prune722.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* z z) (+ (* x x) (* y y)))
0.2b
(/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))
0.5b
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))))
35.2b
(sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0)))

rewrite116.0ms

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-+r+ frac-2neg sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod
Counts
4 → 157
Calls
4 calls:
7.0ms
(+ (* z z) (+ (* x x) (* y y)))
24.0ms
(/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))
64.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))))
15.0ms
(sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0)))

series880.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (* z z) (+ (* x x) (* y y)))
138.0ms
(/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))
342.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0))))
363.0ms
(sqrt (/ (+ (* z z) (+ (* x x) (* y y))) (cbrt 3.0)))

simplify2.1s

Counts
169 → 169
Iterations

Useful iterations: 3 (1.1s)

IterNodesCost
02234498
14394291
212934058
346024054
done50004054

prune578.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
49×sqrt-prod
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
14×pow1
9×sqrt-div
8×sqrt-pow1
6×add-exp-log associate-/r* add-cbrt-cube associate-/l*
4×add-log-exp
3×rem-sqrt-square flip3-+ pow1/2 flip-+
2×associate-/l/
1×cbrt-undiv pow2 frac-times sqrt-undiv frac-2neg pow-plus associate-*r/ div-exp pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up div-inv
Counts
4 → 112
Calls
4 calls:
21.0ms
(/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0))
12.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
12.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
25.0ms
(sqrt (* (/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0)) (/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0))))

series897.0ms

Counts
4 → 12
Calls
4 calls:
440.0ms
(/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0))
109.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
107.0ms
(sqrt (+ (* z z) (+ (* x x) (* y y))))
241.0ms
(sqrt (* (/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0)) (/ (sqrt (+ (* z z) (+ (* x x) (* y y)))) (sqrt 3.0))))

simplify1.8s

Counts
124 → 124
Iterations

Useful iterations: 3 (228.0ms)

IterNodesCost
01382888
12432387
25342293
313652283
438412283
done50002283

prune342.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.1b

regimes459.0ms

Accuracy

38.9% (19.3b remaining)

Error of 25.8b against oracle of 6.6b and baseline of 38.1b

bsearch77.0ms

Steps
ItersRangePoint
9
6.367322558950871e+56
2.9131270869485945e+65
2.8539710068846394e+65
8
-6.818135621868607e+134
-9.818251175618728e+131
-2.2291282360035104e+133

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02545
13045
done3045

end0.0ms

sample441.0ms

Algorithm
intervals
Results
268.0ms8000×body80valid