Details

Time bar (total: 10.8s)

sample23.0ms

Algorithm
intervals
Results
8.0ms241×body80valid
1.0ms8×body1280valid
0.0ms2×body2560valid
0.0ms3×body160valid
0.0ms2×body640valid

simplify8.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2118
done118

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:

0.0b
(+ x (/ (fabs (- y x)) 2.0))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
3×*-un-lft-identity add-log-exp
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt flip3-+ sum-log add-cbrt-cube flip-+ distribute-lft-out
Counts
1 → 12
Calls
1 calls:
16.0ms
(+ x (/ (fabs (- y x)) 2.0))

series30.0ms

Counts
1 → 3
Calls
1 calls:
30.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify1.2s

Counts
15 → 15
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
031195
184187
2215171
3586171
41712171
done5001171

prune39.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ (fabs (- y x)) 2.0))
0.0b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.0b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite185.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity sqrt-prod
28×add-sqr-sqrt
21×pow1
16×sqrt-div
14×add-cube-cbrt
11×swap-sqr
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log 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 → 106
Calls
4 calls:
19.0ms
(+ x (/ (fabs (- y x)) 2.0))
17.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
24.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
119.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ x (/ (fabs (- y x)) 2.0))
65.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
61.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
22.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.1s

Counts
118 → 118
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01292569
13021852
214201711
done50021678

prune291.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b
(sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x)))
0.2b
(* (pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
0.5b
(pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3)

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
121×sqrt-prod
74×add-sqr-sqrt
39×*-un-lft-identity
36×sqrt-div
29×unpow-prod-down cube-prod
26×associate-*l*
25×add-cube-cbrt
24×unswap-sqr
12×sqrt-pow1
11×pow1
10×add-exp-log associate-*r*
9×flip3-+ flip-+
8×cube-div
7×add-cbrt-cube distribute-lft-out
6×pow1/2
5×pow-pow sqr-pow
4×frac-times rem-sqrt-square add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 associate-*r/ associate-*l/ pow-exp
1×*-commutative sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 168
Calls
4 calls:
20.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
38.0ms
(sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x)))
189.0ms
(* (pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
45.0ms
(pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3)

series262.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
64.0ms
(sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x)))
28.0ms
(* (pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
110.0ms
(pow (sqrt (sqrt (+ (/ (fabs (- y x)) 2.0) x))) 3)

simplify2.6s

Counts
180 → 180
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02764898
17434471
233104268
done50013297

prune630.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.2b
(* (pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
0.5b
(pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3)

rewrite355.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
51×sqrt-prod
47×unpow-prod-down
34×*-un-lft-identity
25×cube-prod
24×unswap-sqr
22×associate-*l*
20×add-cube-cbrt
15×sqr-pow
14×add-exp-log
10×sqrt-div associate-*r*
8×pow-exp
7×pow1 add-cbrt-cube distribute-lft-out
5×sqrt-pow1 prod-exp
4×pow-to-exp add-log-exp
3×rem-sqrt-square pow-unpow flip3-+ pow1/2 flip-+
2×cube-mult unpow3 associate-*r/
1×pow-pow *-commutative cbrt-unprod rem-cube-cbrt
Counts
4 → 145
Calls
4 calls:
18.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
255.0ms
(* (pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
59.0ms
(pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3)

series230.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
57.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
32.0ms
(* (pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
77.0ms
(pow (pow (+ (/ (fabs (- y x)) 2.0) x) 1/4) 3)

simplify1.9s

Counts
157 → 157
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02734198
16823848
228063720
done50003703

prune630.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.0b 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
078
188
done88

end0.0ms

sample731.0ms

Algorithm
intervals
Results
405.0ms7665×body80valid
22.0ms128×body1280valid
13.0ms90×body640valid
9.0ms42×body2560valid
5.0ms46×body320valid
2.0ms30×body160valid