Details

Time bar (total: 15.5s)

sample71.0ms

Algorithm
intervals
Results
34.0ms87×body1280valid
10.0ms130×body80valid
6.0ms20×body640valid
3.0ms13×body320valid
1.0ms6×body160valid

simplify62.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22412
32812
43012
53512
63612
done3612

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 61
Calls
4 calls:
0.0ms
(hypot 1.0 x)
10.0ms
(/ 1.0 (hypot 1.0 x))
19.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(hypot 1.0 x)
14.0ms
(/ 1.0 (hypot 1.0 x))
96.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
156.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.3s

Counts
73 → 73
Iterations

Useful iterations: 4 (1.9s)

IterNodesCost
0106904
1203828
2472778
31198776
44102774
done5001774

prune268.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
2.1b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-/r* associate-/l* add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 sqrt-div associate-*r/ div-exp clear-num div-inv associate--r+
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+
Counts
4 → 81
Calls
4 calls:
23.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
21.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series151.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
54.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.4s

Counts
93 → 93
Iterations

Useful iterations: 3 (878.0ms)

IterNodesCost
01121111
12441028
2720960
32865953
done5002953

prune304.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.5 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.1b
(- 0.5 (/ 0.5 (hypot 1.0 x)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-/r* associate-/l* add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 sqrt-div associate-*r/ div-exp clear-num div-inv difference-of-squares
1×sub-neg flip3-- flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+ distribute-lft-out--
Counts
4 → 82
Calls
4 calls:
5.0ms
(/ 0.5 (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
21.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
23.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

series138.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 0.5 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
89.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
34.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify1.9s

Counts
94 → 94
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01431026
1275955
2603905
31570905
done5001901

prune344.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
0.1b
(pow (/ 0.5 (hypot 1.0 x)) 3)
2.1b
(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

rewrite266.0ms

Algorithm
rewrite-expression-head
Rules
295×add-sqr-sqrt
166×times-frac
120×difference-of-squares
115×*-un-lft-identity
103×unpow-prod-down cube-prod
65×add-cube-cbrt
51×sqr-pow
36×associate-/l*
25×distribute-lft-out--
11×add-exp-log add-cbrt-cube
6×associate-/r* add-log-exp
5×pow1 difference-cubes
4×div-inv
3×cbrt-undiv pow-unpow div-exp
2×flip3-- frac-2neg pow-exp clear-num associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×cube-div cube-mult pow-to-exp sub-neg pow-pow flip3-+ diff-log unpow3 div-sub flip-+
Counts
4 → 267
Calls
4 calls:
10.0ms
(/ 1.0 (hypot 1.0 x))
172.0ms
(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
7.0ms
(pow (/ 0.5 (hypot 1.0 x)) 3)
54.0ms
(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series360.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
224.0ms
(/ (- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3)) (+ (* 0.5 0.5) (* (/ 0.5 (hypot 1.0 x)) (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
39.0ms
(pow (/ 0.5 (hypot 1.0 x)) 3)
90.0ms
(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify2.2s

Counts
279 → 279
Iterations

Useful iterations: 2 (615.0ms)

IterNodesCost
033810152
18269727
227729459
done50009459

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 15.4b against oracle of 15.1b and baseline of 15.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03068
13968
done3968

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.1s2825×body1280valid
227.0ms309×body320valid
213.0ms4040×body80valid
187.0ms665×body640valid
16.0ms161×body160valid