Details

Time bar (total: 10.4s)

sample30.0ms

Algorithm
intervals
Results
14.0ms441×body80valid

simplify58.0ms

Counts
1 → 1
Iterations
IterNodes
done51
551
447
336
223
113
07

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
0.0b
(+ (+ (* x x) (* y y)) (* y y))
0.2b
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
10×sum-log
3×add-sqr-sqrt pow1 +-commutative *-un-lft-identity flip3-+ add-cbrt-cube add-exp-log add-cube-cbrt flip-+
2×associate-+l+
Counts
3 → 38
Calls
3 calls:
6.0ms
(+ (* x x) (* y y))
27.0ms
(+ (+ (* x x) (* y y)) (* y y))
155.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series171.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ (* x x) (* y y))
57.0ms
(+ (+ (* x x) (* y y)) (* y y))
68.0ms
(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify733.0ms

Counts
47 → 47
Iterations
IterNodes
done5001
21438
1254
070

prune243.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
0.2b
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))
6.6b
(sqrt (+ (* x x) (* y (+ y y))))
6.6b
(sqrt (+ (* x x) (* y (+ y y))))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 +-commutative sum-log rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 98
Calls
4 calls:
22.0ms
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
68.0ms
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))
13.0ms
(sqrt (+ (* x x) (* y (+ y y))))
13.0ms
(sqrt (+ (* x x) (* y (+ y y))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y))))) (* y y))
51.0ms
(* (sqrt (+ (* x x) (* y (+ y y)))) (sqrt (+ (* x x) (* y (+ y y)))))
67.0ms
(sqrt (+ (* x x) (* y (+ y y))))
81.0ms
(sqrt (+ (* x x) (* y (+ y y))))

simplify979.0ms

Counts
110 → 110
Iterations
IterNodes
done5000
21778
1309
0112

prune619.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (* y y) (+ (* x x) (* y (+ y y))))
0.2b
(* (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))) (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))))
6.6b
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))
6.6b
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
16×sqrt-div
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ add-log-exp
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×frac-times unswap-sqr
3×sum-log pow-prod-down pow-sqr
2×rem-sqrt-square associate-*l/ associate-*r/
1×pow2 +-commutative associate-+r+ rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 100
Calls
4 calls:
23.0ms
(+ (* y y) (+ (* x x) (* y (+ y y))))
164.0ms
(* (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))) (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))))
40.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))
29.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

series245.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* y y) (+ (* x x) (* y (+ y y))))
49.0ms
(* (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))) (sqrt (+ (* y y) (+ (* x x) (* y (+ y y))))))
84.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))
72.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

simplify797.0ms

Counts
112 → 112
Iterations
IterNodes
done5000
21375
1270
0103

prune682.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))) (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))))
6.6b
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
6.6b
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
6.6b
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

rewrite542.0ms

Algorithm
rewrite-expression-head
Rules
93×sqrt-prod
52×add-sqr-sqrt
37×*-un-lft-identity
35×sqrt-pow1
30×pow1 sqrt-div
19×pow1/2 add-cube-cbrt
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ pow-prod-up flip-+ unswap-sqr
8×distribute-lft-out
6×add-cbrt-cube add-exp-log
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×rem-sqrt-square
2×associate-*l/ associate-*r/
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 135
Calls
4 calls:
359.0ms
(* (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))) (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))))
67.0ms
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
73.0ms
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
37.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

series347.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))) (sqrt (sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))))
90.0ms
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
97.0ms
(sqrt (+ (+ (pow y 2) (* (* y 2) y)) (pow x 2)))
69.0ms
(sqrt (+ (* y y) (+ (* x x) (* y (+ y y)))))

simplify1.2s

Counts
147 → 147
Iterations
IterNodes
done5000
21727
1350
0149

prune884.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes561.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done10
110
07

end0.0ms

sample1.3s

Algorithm
intervals
Results
814.0ms14081×body80valid