Details

Time bar (total: 12.4s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify7.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22114
done2114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.3b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
19×times-frac
18×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
8×add-log-exp
5×add-exp-log add-cbrt-cube
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+ frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num
Counts
3 → 67
Calls
3 calls:
11.0ms
(+ (+ (* x x) (* y y)) (* z z))
29.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
17.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series262.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ (+ (* x x) (* y y)) (* z z))
55.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
170.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: 3 (612.0ms)

IterNodesCost
01231541
12601473
27901346
330181330
done50011330

prune213.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
36.2b
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
24×sqrt-prod
22×times-frac associate-*r*
21×add-cube-cbrt *-un-lft-identity
17×sqrt-div
11×pow1
9×add-exp-log add-cbrt-cube
6×flip3-+ associate-*l* flip-+ unswap-sqr
4×frac-times sqrt-pow1 associate-*l/ add-log-exp
3×pow1/2
2×rem-sqrt-square associate-*r/ pow-prod-down prod-exp cbrt-unprod
1×cbrt-undiv div-exp *-commutative div-inv
Counts
4 → 98
Calls
4 calls:
65.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
18.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
15.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
175.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
99.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.6s

Counts
110 → 110
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01423195
13322567
210732267
346952139
done50002139

prune337.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
36.2b
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
36.4b
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt *-un-lft-identity times-frac
34×add-cube-cbrt
29×sqrt-prod
21×cbrt-prod
9×pow1 sqrt-div
6×add-exp-log associate-/r* associate-/l*
5×add-cbrt-cube
4×sqrt-pow1 add-log-exp
3×flip3-+ pow1/2 flip-+
2×rem-sqrt-square associate-/l/
1×cbrt-undiv frac-times frac-2neg associate-*r/ div-exp pow-prod-down associate-*l/ clear-num div-inv distribute-lft-out
Counts
4 → 107
Calls
4 calls:
23.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
30.0ms
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
20.0ms
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series808.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
347.0ms
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))
112.0ms
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
105.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify951.0ms

Counts
119 → 119
Iterations

Useful iterations: 3 (333.0ms)

IterNodesCost
01732906
13202453
27402332
321752302
done50002302

prune427.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
36.2b
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
36.4b
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
36.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite198.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
992×sqrt-prod
555×add-sqr-sqrt *-un-lft-identity
553×add-cube-cbrt
357×cbrt-prod
58×associate-/l*
11×div-inv
9×pow1 add-exp-log associate-/r* add-cbrt-cube
7×sqrt-div
4×sqrt-pow1 add-log-exp
3×cbrt-undiv pow1/2 div-exp
2×rem-sqrt-square sqrt-undiv flip3-+ flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/l/ distribute-lft-out
Counts
4 → 650
Calls
4 calls:
46.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
64.0ms
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
17.0ms
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series810.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))
353.0ms
(sqrt (* (/ (sqrt (+ (pow z 2) (+ (* x x) (* y y)))) (* (cbrt 3.0) (cbrt 3.0))) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (cbrt 3.0))) (sqrt (cbrt 3.0)))))
104.0ms
(sqrt (+ (pow z 2) (+ (* x x) (* y y))))
109.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.3s

Counts
662 → 662
Iterations

Useful iterations: done (1.3s)

IterNodesCost
067927389
1150124059
2288323209
done500123207

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 7.5b

regimes447.0ms

Accuracy

39.8% (18.9b remaining)

Error of 25.9b against oracle of 7.1b and baseline of 38.4b

bsearch85.0ms

Steps
ItersRangePoint
8
2.5276388439093147e+123
1.40601076113088e+127
1.2750016565346138e+127
8
-1.8239455871173137e+105
-1.6711626844852712e+102
-1.8013280713396678e+105

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03052
13952
24152
done4152

end0.0ms

sample441.0ms

Algorithm
intervals
Results
273.0ms8000×body80valid