Details

Time bar (total: 17.2s)

sample72.0ms

Algorithm
intervals
Results
35.0ms87×body1280valid
10.0ms130×body80valid
6.0ms20×body640valid
3.0ms13×body320valid
1.0ms6×body160valid

simplify80.0ms

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

localize10.0ms

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))))))

rewrite31.0ms

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)
5.0ms
(/ 1.0 (hypot 1.0 x))
18.0ms
(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))))))

series621.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(hypot 1.0 x)
8.0ms
(/ 1.0 (hypot 1.0 x))
125.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
487.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify3.7s

Counts
73 → 73
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
0106904
1203828
2472778
31198776
44102774
done5001774

prune224.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.3b

localize15.0ms

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)))))

rewrite41.0ms

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:
12.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
13.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series178.0ms

Counts
4 → 12
Calls
4 calls:
118.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
8.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ 1.0 (hypot 1.0 x))
45.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify2.6s

Counts
93 → 93
Iterations

Useful iterations: 3 (863.0ms)

IterNodesCost
01121111
12441028
2720960
32865953
done5002953

prune367.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 16.3b

localize15.0ms

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)))

rewrite67.0ms

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:
10.0ms
(/ 0.5 (hypot 1.0 x))
10.0ms
(/ 1.0 (hypot 1.0 x))
24.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
18.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ 0.5 (hypot 1.0 x))
15.0ms
(/ 1.0 (hypot 1.0 x))
137.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
37.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))

simplify2.4s

Counts
94 → 94
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01431026
1275955
2603905
31570905
done5001901

prune359.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 16.0b

localize46.0ms

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))

rewrite270.0ms

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:
5.0ms
(/ 1.0 (hypot 1.0 x))
164.0ms
(/ (- (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))))))
13.0ms
(pow (/ 0.5 (hypot 1.0 x)) 3)
71.0ms
(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

series401.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (hypot 1.0 x))
230.0ms
(/ (- (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))))))
64.0ms
(pow (/ 0.5 (hypot 1.0 x)) 3)
99.0ms
(- (pow 0.5 3) (pow (/ 0.5 (hypot 1.0 x)) 3))

simplify1.9s

Counts
279 → 279
Iterations

Useful iterations: 2 (730.0ms)

IterNodesCost
033810152
18269727
227729459
done50009459

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 16.0b

regimes161.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
03068
13968
done3968

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s2825×body1280valid
772.0ms4040×body80valid
171.0ms665×body640valid
75.0ms161×body160valid
53.0ms309×body320valid