Details

Time bar (total: 17.7s)

sample36.0ms

Algorithm
intervals
Results
18.0ms413×body80valid

simplify72.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
0815
11515
22513
3379
4459
5489
done489

prune11.0ms

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))

rewrite224.0ms

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))
46.0ms
(+ (+ (* x y) (* z z)) (* z z))
169.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series171.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(+ (* x y) (* z z))
69.0ms
(+ (+ (* x y) (* z z)) (* z z))
61.0ms
(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify2.6s

Counts
47 → 47
Iterations

Useful iterations: 3 (1.0s)

IterNodesCost
070791
1208667
2737601
32926519
done5000519

prune149.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

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)))

rewrite182.0ms

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:
69.0ms
(+ (* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y)))) (* z z))
79.0ms
(* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y))))
16.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))
12.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y)))) (* z z))
68.0ms
(* (sqrt (+ (* 2 (pow z 2)) (* x y))) (sqrt (+ (* 2 (pow z 2)) (* x y))))
154.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))
182.0ms
(sqrt (+ (* 2 (pow z 2)) (* x y)))

simplify3.3s

Counts
110 → 110
Iterations

Useful iterations: done (3.3s)

IterNodesCost
01122756
12701797
29521627
336391519
done50001491

prune408.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite169.0ms

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:
25.0ms
(* 3 (pow z 2))
112.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
10.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
15.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))

series440.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 3 (pow z 2))
65.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* 3 (pow z 2)) (* x y))))
162.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
185.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))

simplify2.5s

Counts
126 → 126
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01322492
12731709
27711576
326591505
done50001474

prune399.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×add-exp-log
16×sqrt-div sqrt-prod
13×associate-*r*
12×add-cube-cbrt *-un-lft-identity
11×add-cbrt-cube
10×pow1 prod-exp
8×flip3-+ flip-+
7×associate-*l*
4×frac-times sqrt-pow1 pow1/2 cbrt-unprod add-log-exp unswap-sqr
3×unpow-prod-down pow-prod-down
2×pow-to-exp rem-sqrt-square associate-*r/ associate-*l/ pow-exp *-commutative
1×sqrt-unprod sqr-pow
Counts
4 → 92
Calls
4 calls:
35.0ms
(* (* z 3) (pow z (/ 2 2)))
120.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* (* z 3) (pow z (/ 2 2))) (* x y))))
20.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
56.0ms
(sqrt (+ (* (* z 3) (pow z (/ 2 2))) (* x y)))

series371.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* z 3) (pow z (/ 2 2)))
45.0ms
(* (sqrt (+ (* 3 (pow z 2)) (* x y))) (sqrt (+ (* (* z 3) (pow z (/ 2 2))) (* x y))))
155.0ms
(sqrt (+ (* 3 (pow z 2)) (* x y)))
122.0ms
(sqrt (+ (* (* z 3) (pow z (/ 2 2))) (* x y)))

simplify4.0s

Counts
104 → 104
Iterations

Useful iterations: done (4.0s)

IterNodesCost
01532495
13782025
210601578
335051362
done50011326

prune386.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes303.0ms

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
708.0ms12223×body80valid