Details

Time bar (total: 16.8s)

sample37.0ms

Algorithm
intervals
Results
17.0ms413×body80valid

simplify80.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (13.0ms)

IterNodesCost
0815
11515
22513
3379
4459
5489
done489

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite250.0ms

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:
8.0ms
(+ (* x y) (* z z))
42.0ms
(+ (+ (* x y) (* z z)) (* z z))
198.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series189.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(+ (* x y) (* z z))
51.0ms
(+ (+ (* x y) (* z z)) (* z z))
70.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify2.3s

Counts
47 → 47
Iterations

Useful iterations: 3 (914.0ms)

IterNodesCost
070791
1208667
2737601
32926519
done5000519

prune177.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(+ (* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y)))) (* z z))
0.4b
(* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y))))
2.1b
(sqrt (+ (* 2 (pow z 2)) (* x y)))
2.1b
(sqrt (+ (* 2 (pow z 2)) (* x y)))

rewrite210.0ms

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-+
8×swap-sqr
6×add-exp-log associate-*r* associate-*l* add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
49.0ms
(+ (* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y)))) (* z z))
109.0ms
(* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y))))
23.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))
25.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(+ (* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y)))) (* z z))
48.0ms
(* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y))))
168.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))
142.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))

simplify3.6s

Counts
110 → 110
Iterations

Useful iterations: done (3.6s)

IterNodesCost
01122756
12701797
29521627
336391519
done50001491

prune392.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (pow z 2))
0.3b
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
2.0b
(sqrt (+ (* 3 (pow z 2)) (* x y)))
2.0b
(sqrt (+ (* 3 (pow z 2)) (* x y)))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
24×sqrt-prod
21×pow1
17×add-cube-cbrt *-un-lft-identity
16×sqrt-div
14×associate-*r*
11×add-exp-log
10×sqrt-pow1 pow1/2
9×associate-*l*
8×flip3-+ swap-sqr add-cbrt-cube flip-+ unswap-sqr
5×pow-prod-up
4×frac-times unpow-prod-down prod-exp add-log-exp
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/ *-commutative cbrt-unprod unpow2 sqr-pow
1×pow2 pow-to-exp pow-plus sqrt-unprod pow-exp rem-square-sqrt
Counts
4 → 114
Calls
4 calls:
17.0ms
(* 3 (pow z 2))
119.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
20.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
20.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* 3 (pow z 2))
46.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
138.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
140.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))

simplify2.6s

Counts
126 → 126
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01322492
12731709
27711576
326591505
done50001474

prune425.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* z (* z 3))
0.3b
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* z (* z 3)) (* x y))))
2.0b
(sqrt (+ (* 3 (pow z 2)) (* x y)))
2.0b
(sqrt (+ (* z (* z 3)) (* x y)))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
16×sqrt-div sqrt-prod
15×pow1
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*l*
8×flip3-+ flip-+
7×associate-*r*
6×pow-prod-down
4×frac-times sqrt-pow1 pow1/2 prod-exp cbrt-unprod add-log-exp unswap-sqr
2×rem-sqrt-square associate-*r/ associate-*l/ *-commutative
1×sqrt-unprod
Counts
4 → 86
Calls
4 calls:
21.0ms
(* z (* z 3))
104.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* z (* z 3)) (* x y))))
20.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
51.0ms
(sqrt (+ (* z (* z 3)) (* x y)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* z (* z 3))
51.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* z (* z 3)) (* x y))))
142.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
147.0ms
(sqrt (+ (* z (* z 3)) (* x y)))

simplify2.6s

Counts
98 → 98
Iterations

Useful iterations: 3 (974.0ms)

IterNodesCost
01302005
13101663
28681397
322781290
done50001290

prune387.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes176.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0815
11215
done1215

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.2s12223×body80valid