Details

Time bar (total: 12.2s)

sample45.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01114
11514
22214
32514
done2514

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
33.9b
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite172.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×times-frac
17×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
add-exp-log add-cbrt-cube
pow1 associate-/r* associate-/l*
rem-sqrt-square div-inv associate-/l/ add-log-exp
cbrt-undiv frac-2neg sqrt-pow1 flip3-+ pow1/2 sqrt-div div-exp clear-num flip-+
Counts
2 → 54
Calls
2 calls:
113.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
56.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series315.0ms

Counts
2 → 6
Calls
2 calls:
70.0ms
(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
245.0ms
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify658.0ms

Counts
60 → 60
Iterations

Useful iterations: done (654.0ms)

IterNodesCost
01071270
12241209
29791112
done50011102

prune304.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.6b

localize27.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
33.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
45×sqrt-prod
36×times-frac
32×add-sqr-sqrt
31×add-cube-cbrt *-un-lft-identity
associate-/r* associate-/l*
add-exp-log sqrt-div add-cbrt-cube
pow1
flip3-+ flip-+ associate-/l/ add-log-exp
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:
99.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
42.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series446.0ms

Counts
2 → 6
Calls
2 calls:
313.0ms
(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
133.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify2.0s

Counts
84 → 84
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01192087
12171888
27031834
332481816
done50011814

prune263.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
33.9b
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite159.0ms

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
sqrt-div
unswap-sqr
pow1
associate-*l*
add-exp-log add-cbrt-cube
sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
frac-times associate-*l/ add-log-exp
rem-sqrt-square sqrt-unprod associate-*r/ prod-exp *-commutative cbrt-unprod div-inv
Counts
2 → 64
Calls
2 calls:
108.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
48.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series369.0ms

Counts
2 → 6
Calls
2 calls:
222.0ms
(* (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (/ 1 3.0)))
147.0ms
(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify3.7s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
01181522
12411403
27431320
343591298
done50001298

prune233.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.6b

localize8.0ms

Local error

Found 1 expressions with local error:

0.4b
(/ z (sqrt 3.0))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
18×times-frac
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×sqrt-prod
associate-/r*
add-exp-log add-cbrt-cube associate-/l*
pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 39
Calls
1 calls:
10.0ms
(/ z (sqrt 3.0))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(/ z (sqrt 3.0))

simplify943.0ms

Counts
42 → 42
Iterations

Useful iterations: done (941.0ms)

IterNodesCost
066371
1108334
2277324
31023324
done5001322

prune110.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 12.6b

regimes1.0s

Accuracy

53.3% (12.0b remaining)

Error of 23.7b against oracle of 11.7b and baseline of 37.3b

bsearch2.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02958
13658
done3658

end0.0ms

sample1.1s

Algorithm
intervals
Results
693.0ms8000×body80valid