Details

Time bar (total: 12.5s)

sample28.0ms

Algorithm
intervals
Results
13.0ms482×body80valid

simplify41.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (11.0ms)

IterNodesCost
0715
11315
22313
3359
4439
5469
done469

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
6×sum-log
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt associate-+l+ *-un-lft-identity flip3-+ add-cbrt-cube flip-+
Counts
1 → 14
Calls
1 calls:
154.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series51.0ms

Counts
1 → 3
Calls
1 calls:
51.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify1.5s

Counts
17 → 17
Iterations

Useful iterations: 3 (505.0ms)

IterNodesCost
041360
1118308
2411268
31951204
done5001204

prune59.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* 3 (pow y 2))
0.2b
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
7.8b
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
7.8b
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

rewrite155.0ms

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:
21.0ms
(* 3 (pow y 2))
97.0ms
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
17.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
13.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* 3 (pow y 2))
55.0ms
(* (sqrt (+ (pow x 2) (* 3 (pow y 2)))) (sqrt (+ (pow x 2) (* 3 (pow y 2)))))
73.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
83.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))

simplify1.9s

Counts
126 → 126
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01282444
12501633
26631498
321931415
done50001384

prune419.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 3) (fabs y))
0.4b
(* (sqrt 3) (fabs y))
7.8b
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
7.8b
(sqrt (+ (pow x 2) (* (* (sqrt 3) (fabs y)) (* (sqrt 3) (fabs y)))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
14×sqrt-prod
12×add-cube-cbrt *-un-lft-identity associate-*l*
10×pow1
8×add-exp-log add-cbrt-cube
6×associate-*r*
4×sqrt-div add-log-exp unswap-sqr
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
Counts
4 → 74
Calls
4 calls:
16.0ms
(* (sqrt 3) (fabs y))
10.0ms
(* (sqrt 3) (fabs y))
13.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
15.0ms
(sqrt (+ (pow x 2) (* (* (sqrt 3) (fabs y)) (* (sqrt 3) (fabs y)))))

series247.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(* (sqrt 3) (fabs y))
44.0ms
(* (sqrt 3) (fabs y))
54.0ms
(sqrt (+ (pow x 2) (* 3 (pow y 2))))
111.0ms
(sqrt (+ (pow x 2) (* (* (sqrt 3) (fabs y)) (* (sqrt 3) (fabs y)))))

simplify3.0s

Counts
86 → 86
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01081074
1238841
2761793
33147781
done5001780

prune489.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

7.8b
(sqrt (+ (pow x 2) (* (* 3 (* (cbrt (pow y 2)) (cbrt (pow y 2)))) (cbrt (pow y 2)))))
20.7b
(cbrt (pow y 2))
20.7b
(cbrt (pow y 2))
20.7b
(cbrt (pow y 2))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod unpow2 sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 63
Calls
4 calls:
22.0ms
(sqrt (+ (pow x 2) (* (* 3 (* (cbrt (pow y 2)) (cbrt (pow y 2)))) (cbrt (pow y 2)))))
3.0ms
(cbrt (pow y 2))
3.0ms
(cbrt (pow y 2))
4.0ms
(cbrt (pow y 2))

series936.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(sqrt (+ (pow x 2) (* (* 3 (* (cbrt (pow y 2)) (cbrt (pow y 2)))) (cbrt (pow y 2)))))
273.0ms
(cbrt (pow y 2))
292.0ms
(cbrt (pow y 2))
291.0ms
(cbrt (pow y 2))

simplify1.5s

Counts
75 → 75
Iterations

Useful iterations: done (1.5s)

IterNodesCost
075938
1156837
2406523
31479514
done5000512

prune344.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes219.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
11015
done1015

end0.0ms

sample1.1s

Algorithm
intervals
Results
709.0ms14191×body80valid