Details

Time bar (total: 6.0s)

sample13.0ms

Algorithm
intervals
Results
5.0ms249×body80valid
0.0ms3×body1280valid
0.0ms3×body640valid
0.0ms1×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
078
1108
2118
done118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

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:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))

series19.0ms

Counts
1 → 3
Calls
1 calls:
19.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify1.2s

Counts
15 → 15
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
031195
184187
2180171
3399171
4960171
52501171
done5001171

prune33.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

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))))

rewrite81.0ms

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:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))
10.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
13.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
48.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ x (/ (fabs (- y x)) 2.0))
45.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
49.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
17.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.0s

Counts
118 → 118
Iterations

Useful iterations: 3 (427.0ms)

IterNodesCost
01292569
12711841
27361711
325331676
done50011676

prune219.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
0.4b
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

rewrite177.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
112×sqrt-prod
91×sqrt-pow1
69×pow1
60×add-sqr-sqrt
47×pow1/2
42×*-un-lft-identity
39×pow-prod-up
35×flip3-+ flip-+
32×frac-times
22×add-cube-cbrt
20×swap-sqr
17×associate-*l*
16×associate-*r/
12×pow-prod-down
11×add-exp-log associate-*r* pow-sqr add-cbrt-cube unswap-sqr
10×associate-*l/
9×distribute-lft-out
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 205
Calls
4 calls:
11.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
11.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
87.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
57.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
57.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
19.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))))
54.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify617.0ms

Counts
217 → 217
Iterations

Useful iterations: done (610.0ms)

IterNodesCost
02716852
16314317
216243944
done50003936

prune430.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(cbrt (+ (/ (fabs (- y x)) 2.0) x))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-sqr-sqrt
14×sqrt-div
13×cbrt-prod sqrt-prod
12×add-cube-cbrt cbrt-div
11×pow1 add-exp-log associate-*r* add-cbrt-cube
10×associate-*r/ associate-*l*
9×flip3-+ flip-+
4×frac-times pow-prod-down prod-exp cbrt-unprod distribute-lft-out add-log-exp
3×unswap-sqr
2×pow1/3 associate-*l/ *-commutative
Counts
4 → 87
Calls
4 calls:
27.0ms
(* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
53.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
6.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
7.0ms
(cbrt (+ (/ (fabs (- y x)) 2.0) x))

series267.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
76.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (* (fabs (cbrt (+ (/ (fabs (- y x)) 2.0) x))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
52.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
62.0ms
(cbrt (+ (/ (fabs (- y x)) 2.0) x))

simplify647.0ms

Counts
99 → 99
Iterations

Useful iterations: 2 (216.0ms)

IterNodesCost
02963441
17153238
222052981
done50012981

prune380.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes88.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
188
done88

end0.0ms

sample299.0ms

Algorithm
intervals
Results
154.0ms7713×body80valid
8.0ms94×body1280valid
5.0ms74×body640valid
5.0ms46×body2560valid
3.0ms49×body320valid
1.0ms27×body160valid