Details

Time bar (total: 14.7s)

sample32.0ms

Algorithm
intervals
Results
13.0ms288×body80valid

simplify23.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1149
2219
3249
4259
done259

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (* x y) 2.0)
0.0b
(- (/ (* x y) 2.0) (/ z 8.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
7×add-exp-log add-cbrt-cube
6×*-un-lft-identity
4×add-cube-cbrt times-frac add-log-exp
3×associate-/r*
2×pow1 cbrt-undiv div-exp difference-of-squares
1×sub-neg flip3-- frac-2neg diff-log prod-exp clear-num frac-sub flip-- cbrt-unprod div-inv associate-/l* distribute-lft-out--
Counts
2 → 37
Calls
2 calls:
17.0ms
(/ (* x y) 2.0)
35.0ms
(- (/ (* x y) 2.0) (/ z 8.0))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(/ (* x y) 2.0)
69.0ms
(- (/ (* x y) 2.0) (/ z 8.0))

simplify2.7s

Counts
43 → 43
Iterations

Useful iterations: 3 (806.0ms)

IterNodesCost
089469
1209447
2629409
32536407
done5000407

prune84.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0)))
0.1b
(* (+ (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
8.7b
(sqrt (/ (* x y) 2.0))
8.7b
(sqrt (/ (* x y) 2.0))

rewrite307.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
34×sqrt-prod
22×*-un-lft-identity
20×sqrt-div
12×difference-of-squares
11×associate-*r*
10×add-cube-cbrt times-frac
9×frac-times
8×pow1
6×add-exp-log add-cbrt-cube add-log-exp
5×flip3-- associate-*l* frac-sub flip--
4×flip3-+ frac-add flip-+ distribute-lft-out--
3×sub-neg associate-*r/ associate-*l/
2×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 div-inv distribute-lft-out
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 104
Calls
4 calls:
30.0ms
(- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0)))
264.0ms
(* (+ (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
5.0ms
(sqrt (/ (* x y) 2.0))
5.0ms
(sqrt (/ (* x y) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
306.0ms
(- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0)))
716.0ms
(* (+ (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
140.0ms
(sqrt (/ (* x y) 2.0))
117.0ms
(sqrt (/ (* x y) 2.0))

simplify1.1s

Counts
116 → 116
Iterations

Useful iterations: 2 (296.0ms)

IterNodesCost
01952693
15062167
219102034
done50022034

prune432.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (exp (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
2.5b
(exp (log (sqrt (/ (* x y) 2.0))))
8.7b
(sqrt (/ (* x y) 2.0))
8.7b
(sqrt (/ (* x y) 2.0))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
30×sqrt-prod
20×*-un-lft-identity
19×sqrt-div
14×add-cube-cbrt
11×times-frac associate-*r*
10×pow1 log-prod exp-sum
9×frac-times
6×add-exp-log exp-prod add-cbrt-cube difference-of-squares
5×log-div exp-diff
4×flip3-- flip3-+ associate-*l* frac-add frac-sub flip-- flip-+ add-log-exp
3×sqrt-pow1 pow1/2 associate-*r/ associate-*l/ log-pow div-inv
2×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in distribute-lft-out--
1×pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log distribute-lft-out unswap-sqr
Counts
4 → 107
Calls
4 calls:
384.0ms
(* (+ (exp (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
22.0ms
(exp (log (sqrt (/ (* x y) 2.0))))
5.0ms
(sqrt (/ (* x y) 2.0))
5.0ms
(sqrt (/ (* x y) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
737.0ms
(* (+ (exp (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
123.0ms
(exp (log (sqrt (/ (* x y) 2.0))))
120.0ms
(sqrt (/ (* x y) 2.0))
149.0ms
(sqrt (/ (* x y) 2.0))

simplify952.0ms

Counts
119 → 119
Iterations

Useful iterations: done (947.0ms)

IterNodesCost
02302700
15081973
218411856
done50011848

prune416.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (pow E (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
2.6b
(pow E (log (sqrt (/ (* x y) 2.0))))
8.7b
(sqrt (/ (* x y) 2.0))
8.7b
(sqrt (/ (* x y) 2.0))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×sqrt-prod
21×*-un-lft-identity
19×sqrt-div
15×add-cube-cbrt
11×pow1 times-frac associate-*r*
10×unpow-prod-up log-prod
9×frac-times
7×add-exp-log
6×pow-unpow add-cbrt-cube difference-of-squares
5×log-div pow-sub
4×flip3-- flip3-+ associate-*l* frac-add frac-sub flip-- flip-+ add-log-exp
3×unpow-prod-down sqrt-pow1 pow1/2 associate-*r/ associate-*l/ log-pow div-inv
2×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in pow-exp distribute-lft-out--
1×pow-to-exp e-exp-1 pow-pow pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr sqr-pow
Counts
4 → 114
Calls
4 calls:
362.0ms
(* (+ (pow E (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
8.0ms
(pow E (log (sqrt (/ (* x y) 2.0))))
5.0ms
(sqrt (/ (* x y) 2.0))
5.0ms
(sqrt (/ (* x y) 2.0))

series2.2s

Counts
4 → 12
Calls
4 calls:
1.5s
(* (+ (pow E (log (sqrt (/ (* x y) 2.0)))) (sqrt (/ z 8.0))) (- (sqrt (/ (* x y) 2.0)) (sqrt (/ z 8.0))))
370.0ms
(pow E (log (sqrt (/ (* x y) 2.0))))
157.0ms
(sqrt (/ (* x y) 2.0))
155.0ms
(sqrt (/ (* x y) 2.0))

simplify1.4s

Counts
126 → 126
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02763005
17092680
224072546
done50002519

prune537.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099
1109
done109

end0.0ms

sample949.0ms

Algorithm
intervals
Results
477.0ms9148×body80valid
0.0ms1×body160valid