Details

Time bar (total: 19.9s)

sample26.0ms

Algorithm
intervals
Results
13.0ms256×body80valid

simplify20.0ms

Counts
1 → 1
Iterations
IterNodes
done22
322
221
115
011

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
36.0b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×*-un-lft-identity add-cube-cbrt
13×sqrt-prod
4×add-cbrt-cube add-exp-log
3×pow1 associate-/r* associate-/l*
2×rem-sqrt-square div-inv add-log-exp associate-/l/
1×cbrt-undiv clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp flip-+
Counts
2 → 54
Calls
2 calls:
126.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
43.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series283.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
218.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify2.2s

Counts
60 → 60
Iterations
IterNodes
done5010
32998
2647
1217
0107

prune546.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 19.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.0b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

rewrite274.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×times-frac
38×*-un-lft-identity
36×sqrt-prod
32×add-cube-cbrt
22×associate-*r* associate-*l*
21×add-exp-log
16×add-cbrt-cube
15×unswap-sqr
11×pow1
7×sqrt-div div-exp
6×prod-exp
4×cbrt-undiv sqrt-pow1 cbrt-unprod add-log-exp
3×pow1/2
2×frac-times rem-sqrt-square flip3-+ 1-exp pow-prod-down associate-*l/ associate-*r/ flip-+ div-inv
1×*-commutative
Counts
4 → 125
Calls
4 calls:
155.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
26.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
24.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
62.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

series681.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0))
184.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
153.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
271.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 3.0)))

simplify3.3s

Counts
137 → 137
Iterations
IterNodes
done5007
34722
21235
1538
0179

prune892.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 19.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
36.0b
(sqrt (* (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite431.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×*-un-lft-identity add-cube-cbrt
28×sqrt-prod
21×cbrt-prod
15×sqrt-div
12×pow1
6×frac-times associate-/r* associate-*l/ add-exp-log associate-/l*
5×sqrt-pow1 add-cbrt-cube
4×add-log-exp
3×flip3-+ pow1/2 pow-prod-down associate-*r/ flip-+
2×rem-sqrt-square un-div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 113
Calls
4 calls:
76.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
27.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
28.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
292.0ms
(sqrt (* (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.1s

Counts
4 → 12
Calls
4 calls:
318.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
162.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
156.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
438.0ms
(sqrt (* (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) 1) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify1.7s

Counts
125 → 125
Iterations
IterNodes
done5000
32039
2674
1314
0168

prune744.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 19.0b

localize33.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (+ (+ (* 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))))
35.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite246.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
75×times-frac sqrt-prod
52×*-un-lft-identity
48×add-cube-cbrt
35×cbrt-prod
25×associate-*r*
16×unswap-sqr
10×associate-*l*
8×pow1
7×add-exp-log
6×associate-/r* add-cbrt-cube
5×sqrt-div
4×div-inv
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-/l* add-log-exp
2×associate-/l/
1×frac-times cbrt-undiv clear-num frac-2neg flip3-+ sqrt-unprod div-exp associate-*l/ prod-exp associate-*r/ *-commutative cbrt-unprod flip-+
Counts
3 → 144
Calls
3 calls:
67.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
124.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
46.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.0s

Counts
3 → 9
Calls
3 calls:
184.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
467.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
393.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify2.7s

Counts
153 → 153
Iterations
IterNodes
done5016
34376
21118
1389
0205

prune991.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 18.9b

regimes1.3s

Accuracy

61.5% (7.7b remaining)

Error of 26.0b against oracle of 18.3b and baseline of 38.2b

bsearch81.0ms

Steps
ItersRangePoint
8
3.398993182490229e+96
5.75514727762621e+100
5.659091314574308e+100
7
-9.896805901397743e+60
-5.191765127262994e+58
-9.708346480390896e+60

simplify23.0ms

Iterations
IterNodes
done55
355
251
143
033

end0.0ms

sample1.1s

Algorithm
intervals
Results
848.0ms8000×body80valid