Details

Time bar (total: 3.2s)

sample18.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0157
1227
2247
3247
done247

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite108.0ms

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:
76.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
30.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series218.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
157.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify90.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0214630
1835578
23408576
35001574
done5001574

prune209.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.5b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
6×associate-/r* associate-/l*
4×add-exp-log sqrt-div add-cbrt-cube
3×pow1
2×flip3-+ flip-+ associate-/l/ add-log-exp
1×cbrt-undiv rem-sqrt-square sqrt-undiv frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 78
Calls
2 calls:
52.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series312.0ms

Counts
2 → 6
Calls
2 calls:
213.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
100.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify53.0ms

Counts
84 → 84
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
02111118
16251058
222891035
350011035
done50011035

prune169.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
29×sqrt-prod
16×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt times-frac
9×sqrt-div
8×unswap-sqr
7×pow1
6×associate-*l*
4×add-exp-log add-cbrt-cube
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×frac-times associate-*l/ add-log-exp
1×rem-sqrt-square sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 64
Calls
2 calls:
83.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
32.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series274.0ms

Counts
2 → 6
Calls
2 calls:
176.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
97.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify66.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0235788
1772762
22635738
35001725
done5001725

prune165.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 19.4b

localize3.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ z (sqrt 3.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
6×associate-/r*
3×add-exp-log add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
6.0ms
(/ z (sqrt 3.0))

series58.0ms

Counts
1 → 3
Calls
1 calls:
57.0ms
(/ z (sqrt 3.0))

simplify52.0ms

Counts
42 → 42
Iterations

Useful iterations: 4 (49.0ms)

IterNodesCost
0103217
1273207
2729197
32027197
45001196
done5001196

prune62.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 19.4b

regimes501.0ms

Accuracy

60.4% (7.8b remaining)

Error of 26.0b against oracle of 18.2b and baseline of 37.9b

bsearch142.0ms

Steps
ItersRangePoint
8
3.829360511156205e+94
1.4205151901339496e+99
1.3881517315915455e+99
6
4.421061065096694e-156
2.2896112546321894e-155
4.463507529461489e-156
10
2.7679564059433344e-191
1.7023918448577627e-181
6.058132317483692e-184
9
-5.9618745358935405e+94
-1.3018241190180148e+88
-3.5794877859546974e+94

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04633
15033
25333
35333
done5333

end0.0ms

sample476.0ms

Algorithm
intervals
Results
251.0ms8000×body80valid