Details

Time bar (total: 14.5s)

sample34.0ms

Algorithm
intervals
Results
12.0ms247×body80valid
1.0ms3×body1280valid
1.0ms2×body2560valid
1.0ms3×body640valid
0.0ms1×body160valid

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2118
done118

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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:
20.0ms
(+ x (/ (fabs (- y x)) 2.0))

series34.0ms

Counts
1 → 3
Calls
1 calls:
34.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify1.6s

Counts
15 → 15
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
031195
184187
2215171
3586171
41712171
done5001171

prune87.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (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)))
0.6b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

rewrite192.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
137.0ms
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
17.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
15.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
18.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))
108.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
89.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
96.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))

simplify1.2s

Counts
107 → 107
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01602656
13942458
215322330
done50012117

prune789.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b
(- x (/ (fabs (- y x)) 2.0))
12.2b
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
31.0b
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
30×times-frac
27×*-un-lft-identity
20×difference-of-squares
15×add-cube-cbrt
7×add-log-exp
6×associate-/r* distribute-lft-out--
5×add-exp-log add-cbrt-cube
4×flip3-- flip-- associate-/l*
3×pow1
2×sub-neg diff-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-sub div-exp clear-num div-inv
Counts
3 → 79
Calls
3 calls:
25.0ms
(- x (/ (fabs (- y x)) 2.0))
19.0ms
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
76.0ms
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

series193.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(- x (/ (fabs (- y x)) 2.0))
59.0ms
(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
93.0ms
(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: done (1.4s)

IterNodesCost
01372788
13582636
215492248
done50022037

prune663.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite795.0ms

Algorithm
rewrite-expression-head
Rules
385×add-sqr-sqrt
227×times-frac
222×*-un-lft-identity
144×sqrt-prod
130×difference-of-squares
72×associate-*r*
62×add-cube-cbrt
51×distribute-lft-out--
29×distribute-lft-out
26×associate-*l*
20×add-exp-log add-cbrt-cube
16×associate-/r*
10×associate-/l*
8×associate-/r/
6×pow1 cbrt-undiv div-exp add-log-exp
4×flip3-- prod-exp flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
3×flip3-+ flip-+
2×frac-2neg clear-num
1×frac-times sub-neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 287
Calls
4 calls:
120.0ms
(/ (- x (/ (fabs (- y x)) 2.0)) (- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0))))
36.0ms
(- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))
132.0ms
(/ (+ x (/ (fabs (- y x)) 2.0)) (+ (sqrt x) (sqrt (/ (fabs (- y x)) 2.0))))
468.0ms
(* (/ (+ x (/ (fabs (- y x)) 2.0)) (+ (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))) (/ (- x (/ (fabs (- y x)) 2.0)) (- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))))

series2.5s

Counts
4 → 12
Calls
4 calls:
473.0ms
(/ (- x (/ (fabs (- y x)) 2.0)) (- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0))))
105.0ms
(- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))
347.0ms
(/ (+ x (/ (fabs (- y x)) 2.0)) (+ (sqrt x) (sqrt (/ (fabs (- y x)) 2.0))))
1.6s
(* (/ (+ x (/ (fabs (- y x)) 2.0)) (+ (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))) (/ (- x (/ (fabs (- y x)) 2.0)) (- (sqrt x) (sqrt (/ (fabs (- y x)) 2.0)))))

simplify1.1s

Counts
299 → 299
Iterations

Useful iterations: done (1.1s)

IterNodesCost
041911992
1131111602
done500010895

prune1.8s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes304.0ms

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

sample966.0ms

Algorithm
intervals
Results
499.0ms7685×body80valid
29.0ms113×body1280valid
14.0ms49×body2560valid
13.0ms72×body640valid
7.0ms51×body320valid
6.0ms32×body160valid