Details

Time bar (total: 11.5s)

sample17.0ms

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))

rewrite60.0ms

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:
12.0ms
(+ (+ (* 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))

series256.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
52.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
167.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.5s

Counts
76 → 76
Iterations

Useful iterations: 3 (404.0ms)

IterNodesCost
01231541
12601473
28251346
336741330
done50001330

prune231.0ms

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)))

rewrite119.0ms

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:
67.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
19.0ms
(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)))
16.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
171.0ms
(sqrt (* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
102.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify601.0ms

Counts
110 → 110
Iterations

Useful iterations: done (598.0ms)

IterNodesCost
01423195
13322567
211062267
done50002227

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (* x x) (* y y)) (* z z))
0.1b
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
0.4b
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
36.2b
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
51×add-exp-log times-frac
37×*-un-lft-identity
34×add-cube-cbrt
24×cbrt-prod
22×associate-*r*
20×prod-exp
19×add-cbrt-cube
16×div-exp
9×pow1 add-log-exp unswap-sqr
8×cbrt-undiv cbrt-unprod
7×associate-*l*
6×associate-/r*
4×rec-exp 1-exp
3×sqrt-div sum-log div-inv associate-/l*
2×frac-times sqrt-pow1 flip3-+ associate-*r/ pow-prod-down associate-*l/ flip-+ associate-/l/
1×+-commutative associate-+l+ frac-2neg pow1/2 clear-num sqrt-prod *-commutative
Counts
4 → 138
Calls
4 calls:
12.0ms
(+ (+ (* x x) (* y y)) (* z z))
64.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
34.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
30.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

series672.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ (+ (* x x) (* y y)) (* z z))
146.0ms
(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))
136.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
354.0ms
(sqrt (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))

simplify882.0ms

Counts
150 → 150
Iterations

Useful iterations: 2 (294.0ms)

IterNodesCost
02253861
16293614
223913061
done50003061

prune416.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.9b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
726×times-frac
429×cbrt-prod
385×add-sqr-sqrt
383×add-cube-cbrt *-un-lft-identity
322×sqrt-prod
58×associate-/l*
14×pow1
9×add-exp-log
8×sqrt-pow1 div-inv
7×sqrt-div
6×associate-/r* add-cbrt-cube
4×add-log-exp
3×cbrt-undiv rem-sqrt-square pow1/2 div-exp
2×flip3-+ flip-+
1×pow2 frac-times frac-2neg pow-plus associate-*r/ pow-prod-down associate-*l/ clear-num pow-sqr pow-prod-up associate-/l/
Counts
4 → 476
Calls
4 calls:
44.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0))
71.0ms
(sqrt (* (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0)) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0))))
13.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
14.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series1.9s

Counts
4 → 12
Calls
4 calls:
843.0ms
(/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0))
851.0ms
(sqrt (* (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0)) (/ (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt (sqrt 3.0))) (cbrt 3.0))))
109.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
117.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.3s

Counts
488 → 488
Iterations

Useful iterations: 2 (673.0ms)

IterNodesCost
054518450
1119116632
2304716456
done500116456

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.9b

regimes445.0ms

Accuracy

61.1% (7.7b remaining)

Error of 26.4b against oracle of 18.7b and baseline of 38.4b

bsearch71.0ms

Steps
ItersRangePoint
8
3.196397393917939e+72
1.0649312883679304e+77
1.0479353069555717e+77
8
-1.3887243973495253e+108
-7.060621971491881e+103
-1.356128363832856e+108

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02345
13145
23345
done3345

end0.0ms

sample617.0ms

Algorithm
intervals
Results
454.0ms8000×body80valid