Details

Time bar (total: 12.2s)

sample31.0ms

Algorithm
intervals
Results
11.0ms244×body80valid
1.0ms4×body1280valid
1.0ms5×body320valid
0.0ms1×body2560valid
0.0ms1×body640valid
0.0ms1×body160valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2118
done118

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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:
11.0ms
(+ x (/ (fabs (- y x)) 2.0))

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify2.8s

Counts
15 → 15
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
031195
184187
2209171
3459171
41200171
52875171
done5001171

prune46.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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

rewrite214.0ms

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:
15.0ms
(+ x (/ (fabs (- y x)) 2.0))
19.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
35.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
137.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series197.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ x (/ (fabs (- y x)) 2.0))
65.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
77.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
36.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.1s

Counts
118 → 118
Iterations

Useful iterations: done (2.0s)

IterNodesCost
01292569
12681841
27461711
323141658
done50001574

prune300.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
112×sqrt-prod
97×sqrt-pow1
75×pow1
60×add-sqr-sqrt
53×pow1/2
43×pow-prod-up
42×*-un-lft-identity
35×flip3-+ flip-+
32×frac-times
22×add-cube-cbrt
20×swap-sqr
17×associate-*r*
16×associate-*l/
13×pow-sqr
12×pow-prod-down
11×add-exp-log associate-*l* add-cbrt-cube unswap-sqr
10×associate-*r/
9×distribute-lft-out
7×pow-plus
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 rem-square-sqrt
Counts
4 → 211
Calls
4 calls:
32.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
28.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
200.0ms
(* (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
149.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
107.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
34.0ms
(* (* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
99.0ms
(* (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))

simplify1.3s

Counts
223 → 223
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02726891
15964409
216383821
done50003751

prune660.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.3b
(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
0.6b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.6b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
17×associate-*r*
16×add-sqr-sqrt
14×sqrt-div
12×cbrt-prod add-cube-cbrt sqrt-prod
11×pow1 add-exp-log add-cbrt-cube
10×cbrt-div associate-*r/
9×flip3-+ flip-+
4×frac-times associate-*l* pow-prod-down prod-exp cbrt-unprod distribute-lft-out add-log-exp
2×pow1/3 associate-*l/ *-commutative unswap-sqr
Counts
4 → 86
Calls
4 calls:
55.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
129.0ms
(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
8.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
139.0ms
(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
78.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
74.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.8s

Counts
98 → 98
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02543374
16383140
219302896
done50012758

prune552.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes144.0ms

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

sample602.0ms

Algorithm
intervals
Results
331.0ms7722×body80valid
15.0ms101×body1280valid
10.0ms56×body2560valid
8.0ms66×body640valid
3.0ms35×body320valid
1.0ms21×body160valid