Details

Time bar (total: 18.2s)

sample43.0ms

Algorithm
intervals
Results
21.0ms256×body80valid

simplify27.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32414
done2414

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.3b

localize16.0ms

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))

rewrite198.0ms

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:
132.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
62.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series360.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
265.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify1.9s

Counts
60 → 60
Iterations

Useful iterations: 3 (983.0ms)

IterNodesCost
01071270
12131209
26241110
322441102
done50001102

prune305.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.1b

localize35.0ms

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))))

rewrite270.0ms

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:
84.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
55.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
47.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
78.0ms
(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:
344.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))
178.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
145.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))
502.0ms
(sqrt (* (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (* (cbrt 3.0) (cbrt 3.0))) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (cbrt 3.0))))

simplify3.5s

Counts
118 → 118
Iterations

Useful iterations: 3 (447.0ms)

IterNodesCost
01452892
12502456
25622347
314582289
444722289
done50012289

prune560.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
35.5b
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1
6×add-sqr-sqrt
4×add-exp-log add-cube-cbrt *-un-lft-identity associate-*r/ add-cbrt-cube
3×associate-*r* associate-*l*
2×sqrt-pow1 flip3-+ sqrt-div pow-prod-down flip-+ add-log-exp
1×distribute-rgt-in distribute-lft-in pow1/2 prod-exp sqrt-prod *-commutative cbrt-unprod unswap-sqr
Counts
2 → 35
Calls
2 calls:
131.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
23.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

series310.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z)))
247.0ms
(sqrt (* 0.3333333333333333 (+ (+ (* x x) (* y y)) (* z z))))

simplify3.1s

Counts
41 → 41
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
079721
1212681
2798605
34396597
done5000597

prune119.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.1b

localize19.0ms

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)))

rewrite321.0ms

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))
173.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
52.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

series1.2s

Counts
3 → 9
Calls
3 calls:
177.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))
532.0ms
(* (sqrt (/ 1 (* (cbrt 3.0) (cbrt 3.0)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0))))
470.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) (cbrt 3.0)))

simplify2.2s

Counts
153 → 153
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02074227
13844035
210373834
332593826
done50003804

prune608.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 18.0b

regimes685.0ms

Accuracy

62.9% (7.1b remaining)

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

bsearch118.0ms

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

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03176
14476
24976
done4976

end0.0ms

sample931.0ms

Algorithm
intervals
Results
594.0ms8000×body80valid