Details

Time bar (total: 12.9s)

sample33.0ms

Algorithm
intervals
Results
13.0ms249×body80valid
1.0ms3×body1280valid
1.0ms2×body2560valid
0.0ms2×body320valid

simplify9.0ms

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: 0.0b

localize14.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:
22.0ms
(+ x (/ (fabs (- y x)) 2.0))

series36.0ms

Counts
1 → 3
Calls
1 calls:
36.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify3.0s

Counts
15 → 15
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
031195
184187
2209171
3459171
41200171
52875171
done5001171

prune77.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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))))

rewrite204.0ms

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:
22.0ms
(+ x (/ (fabs (- y x)) 2.0))
18.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
20.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
135.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ x (/ (fabs (- y x)) 2.0))
74.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
64.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
29.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.1s

Counts
118 → 118
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01292569
12681841
27461711
323141658
done50001574

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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

rewrite204.0ms

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:
112.0ms
(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
68.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
135.0ms
(* (* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))))
136.0ms
(* (fabs (cbrt (+ x (/ (fabs (- y x)) 2.0)))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))
77.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
99.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.4s

Counts
98 → 98
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02543374
16383140
219332896
done50012758

prune530.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (* (pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4) (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.7b
(pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
17×add-sqr-sqrt
13×add-cube-cbrt sqrt-prod
12×cbrt-prod sqrt-div
10×pow1 unpow-prod-down cbrt-div
8×flip3-+ associate-*r/ flip-+
7×add-exp-log associate-*l*
6×add-cbrt-cube
4×frac-times pow-pow sqrt-pow1 associate-*r* distribute-lft-out add-log-exp
3×pow-unpow pow1/2 pow1/3 pow-prod-down
2×associate-*l/ unswap-sqr
1×pow-to-exp sqrt-unprod pow-exp prod-exp *-commutative sqrt-pow2 cbrt-unprod sqr-pow
Counts
4 → 91
Calls
4 calls:
159.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (* (pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4) (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
14.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
32.0ms
(pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

series308.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (* (pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4) (cbrt (+ x (/ (fabs (- y x)) 2.0))))))
64.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
68.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
145.0ms
(pow (sqrt (cbrt (+ x (/ (fabs (- y x)) 2.0)))) 4)

simplify2.5s

Counts
103 → 103
Iterations

Useful iterations: done (2.5s)

IterNodesCost
02333012
15282816
213412290
340111929
done50001863

prune490.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
188
done88

end0.0ms

sample687.0ms

Algorithm
intervals
Results
355.0ms7698×body80valid
18.0ms105×body1280valid
10.0ms73×body640valid
6.0ms33×body2560valid
6.0ms61×body320valid
2.0ms32×body160valid