Details

Time bar (total: 11.0s)

sample39.0ms

Algorithm
intervals
Results
16.0ms407×body80valid

simplify66.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (20.0ms)

IterNodesCost
0815
11515
22513
3389
4489
5529
done529

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (* x y) (* z z)) (* z z))
0.0b
(+ (* x y) (* z z))
0.1b
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt *-un-lft-identity flip3-+ add-cbrt-cube flip-+
2×associate-+l+
Counts
3 → 38
Calls
3 calls:
65.0ms
(+ (+ (* x y) (* z z)) (* z z))
18.0ms
(+ (* x y) (* z z))
173.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series229.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ (+ (* x y) (* z z)) (* z z))
72.0ms
(+ (* x y) (* z z))
97.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify845.0ms

Counts
47 → 47
Iterations

Useful iterations: done (843.0ms)

IterNodesCost
070791
1247733
21250601
done5002579

prune175.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
3.8b
(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.8b
(cbrt (+ (* 2 (pow z 2)) (* x y)))
3.8b
(cbrt (+ (* 2 (pow z 2)) (* x y)))

rewrite127.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×flip3-+ pow1/3 flip-+
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 87
Calls
4 calls:
88.0ms
(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
13.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))
12.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))
8.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))

series733.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(* (cbrt (+ (* 2 (pow z 2)) (* x y))) (cbrt (+ (* 2 (pow z 2)) (* x y))))
191.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))
174.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))
174.0ms
(cbrt (+ (* 2 (pow z 2)) (* x y)))

simplify890.0ms

Counts
99 → 99
Iterations

Useful iterations: done (887.0ms)

IterNodesCost
01242420
13092231
211002017
done50001848

prune545.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* z z) (+ (* 2 (pow z 2)) (* x y)))
0.4b
(* (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))) (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))))
3.4b
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
3.4b
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))

rewrite418.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×add-cube-cbrt *-un-lft-identity
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ add-log-exp
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down sum-log pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 associate-+r+ pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 100
Calls
4 calls:
39.0ms
(+ (* z z) (+ (* 2 (pow z 2)) (* x y)))
267.0ms
(* (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))) (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))))
50.0ms
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
57.0ms
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))

series391.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(+ (* z z) (+ (* 2 (pow z 2)) (* x y)))
61.0ms
(* (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))) (sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y)))))
125.0ms
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
136.0ms
(sqrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))

simplify1.5s

Counts
112 → 112
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01053333
12712428
213911756
done50011717

prune496.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (+ (* x y) (* (* z z) 3))) (fabs (cbrt (+ (* x y) (* (* z z) 3)))))
3.4b
(sqrt (+ (* x y) (* (* z z) 3)))
3.9b
(cbrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
3.9b
(cbrt (+ (* x y) (* (* z z) 3)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
7×pow1 sqrt-prod
6×add-exp-log cbrt-prod associate-*l* add-cbrt-cube
4×cbrt-div flip3-+ sqrt-div flip-+ add-log-exp
3×associate-*r*
2×pow1/3 associate-*l/ unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
50.0ms
(* (sqrt (+ (* x y) (* (* z z) 3))) (fabs (cbrt (+ (* x y) (* (* z z) 3)))))
9.0ms
(sqrt (+ (* x y) (* (* z z) 3)))
31.0ms
(cbrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
10.0ms
(cbrt (+ (* x y) (* (* z z) 3)))

series863.0ms

Counts
4 → 12
Calls
4 calls:
242.0ms
(* (sqrt (+ (* x y) (* (* z z) 3))) (fabs (cbrt (+ (* x y) (* (* z z) 3)))))
188.0ms
(sqrt (+ (* x y) (* (* z z) 3)))
191.0ms
(cbrt (+ (* z z) (+ (* 2 (pow z 2)) (* x y))))
242.0ms
(cbrt (+ (* x y) (* (* z z) 3)))

simplify828.0ms

Counts
77 → 77
Iterations

Useful iterations: done (825.0ms)

IterNodesCost
01731712
14281633
214961394
done50001362

prune579.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes396.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11215
done1215

end0.0ms

sample1.3s

Algorithm
intervals
Results
760.0ms12341×body80valid