Details

Time bar (total: 18.9s)

sample23.0ms

Algorithm
intervals
Results
12.0ms256×body80valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite165.0ms

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:
117.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
46.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series320.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
255.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.7s

Counts
60 → 60
Iterations

Useful iterations: 3 (612.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune268.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.4b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

rewrite252.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt times-frac
34×add-cube-cbrt *-un-lft-identity
28×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
Counts
4 → 106
Calls
4 calls:
61.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
46.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
43.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
95.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

series1.2s

Counts
4 → 12
Calls
4 calls:
354.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
161.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
150.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
513.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify4.1s

Counts
118 → 118
Iterations

Useful iterations: 3 (529.0ms)

IterNodesCost
01452892
12502456
25622347
314582289
444722289
done50012289

prune489.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
35.5b
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

rewrite214.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×associate-*r*
11×add-exp-log *-un-lft-identity times-frac
10×add-cube-cbrt
7×pow1 add-cbrt-cube
6×sqrt-div
4×frac-times flip3-+ associate-*l/ prod-exp flip-+
3×associate-*l* unswap-sqr
2×sqrt-pow1 associate-*r/ div-exp pow-prod-down un-div-inv cbrt-unprod add-log-exp
1×cbrt-undiv rec-exp pow1/2 1-exp sqrt-prod *-commutative div-inv
Counts
2 → 57
Calls
2 calls:
154.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
56.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

series324.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0))
257.0ms
(sqrt (* (+ (+ (* x x) (* y y)) (* z z)) (/ 1 3.0)))

simplify3.7s

Counts
63 → 63
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01281346
13081182
210611042
347801018
done50001018

prune235.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.1b

localize38.0ms

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))))
35.5b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

rewrite365.0ms

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×cbrt-undiv frac-times frac-2neg flip3-+ sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num *-commutative cbrt-unprod flip-+
Counts
3 → 144
Calls
3 calls:
89.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
212.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
57.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series954.0ms

Counts
3 → 9
Calls
3 calls:
175.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
387.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
392.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify2.3s

Counts
153 → 153
Iterations

Useful iterations: done (2.3s)

IterNodesCost
02074227
13844035
210373834
332593826
done50003804

prune685.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.0b

regimes553.0ms

Accuracy

62.9% (7.1b remaining)

Error of 25.7b against oracle of 18.6b and baseline of 37.8b

bsearch109.0ms

Steps
ItersRangePoint
10
6.354887178636514e+84
5.5948430977787605e+100
1.7580652535677755e+99
8
-2.9035053730289993e+141
-3.6215165741309817e+137
-7.934591556850649e+139

simplify12.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03176
14476
24976
done4976

end0.0ms

sample840.0ms

Algorithm
intervals
Results
608.0ms8000×body80valid