Details

Time bar (total: 13.1s)

sample25.0ms

Algorithm
intervals
Results
11.0ms256×body80valid

simplify13.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01114
11514
22214
32514
done2514

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.2b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite174.0ms

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:
122.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
49.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series365.0ms

Counts
2 → 6
Calls
2 calls:
97.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
268.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify780.0ms

Counts
60 → 60
Iterations

Useful iterations: done (777.0ms)

IterNodesCost
01071270
12241209
29791112
done50011102

prune281.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite173.0ms

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:
138.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
30.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series693.0ms

Counts
2 → 6
Calls
2 calls:
547.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
146.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify4.6s

Counts
70 → 70
Iterations

Useful iterations: 3 (990.0ms)

IterNodesCost
01181522
12411403
27431320
343591298
done50001298

prune295.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 17.0b

localize15.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
35.1b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite112.0ms

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:
59.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
47.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series368.0ms

Counts
2 → 6
Calls
2 calls:
245.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
121.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify1.9s

Counts
84 → 84
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01192087
12171888
27031834
332481816
done50011814

prune302.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.2b

localize10.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ (- x) (sqrt 3.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
60×times-frac
44×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
33×sqrt-prod
21×distribute-lft-neg-in distribute-rgt-neg-in
10×associate-/l*
7×neg-mul-1
6×associate-/r*
3×add-exp-log add-cbrt-cube
1×pow1 cbrt-undiv neg-sub0 frac-2neg div-sub distribute-frac-neg div-exp clear-num div-inv add-log-exp
Counts
1 → 90
Calls
1 calls:
15.0ms
(/ (- x) (sqrt 3.0))

series89.0ms

Counts
1 → 3
Calls
1 calls:
89.0ms
(/ (- x) (sqrt 3.0))

simplify458.0ms

Counts
93 → 93
Iterations

Useful iterations: 2 (128.0ms)

IterNodesCost
01311039
1258932
2802918
done5000918

prune220.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 12.2b

regimes825.0ms

Accuracy

43% (14.8b remaining)

Error of 26.7b against oracle of 11.9b and baseline of 37.9b

bsearch354.0ms

Steps
ItersRangePoint
4
1.1364981935794327e+76
1.80666735968266e+76
1.7760088569329647e+76
8
3.7740427348779304e+65
4.0812815848014643e+68
3.815593598445296e+65
8
6.902561535359867e-39
5.766067317398849e-36
1.0996263613919995e-36
7
7.117929345426062e-290
5.1703930432881434e-288
6.773085673229095e-289
8
-1.927354152525488e-232
-1.23458780308109e-235
-5.0002323658555836e-234
3
-4.6429132007061446e-119
-3.960314028393182e-119
-4.6002507524365845e-119
11
-4.6038908143152406e-51
-6.51097445607371e-73
-3.312387562883202e-69
5
-8.945616726736062e+128
-4.093952998244274e+128
-4.394319598461054e+128

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
046125
153125
done53125

end0.0ms

sample980.0ms

Algorithm
intervals
Results
615.0ms8000×body80valid