Details

Time bar (total: 15.6s)

sample80.0ms

Algorithm
intervals
Results
44.0ms88×body1280valid
12.0ms138×body80valid
8.0ms16×body640valid
3.0ms10×body320valid
1.0ms4×body160valid

simplify58.0ms

Counts
1 → 1
Iterations
IterNodes
done90
590
471
355
239
121
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
2.2b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
13×add-cube-cbrt
9×times-frac
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* distribute-lft-out associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 78
Calls
4 calls:
8.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms
(/ 1/2 (hypot 1 x))
25.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series191.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
47.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
11.0ms
(/ 1/2 (hypot 1 x))
85.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.1s

Counts
90 → 90
Iterations
IterNodes
done2001
32001
2747
1247
0118

prune722.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.6b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
4×pow1 insert-posit16 distribute-lft-out
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod div-inv difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
4.0ms
(/ 1/2 (hypot 1 x))
4.0ms
(/ 1/2 (hypot 1 x))
14.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
6.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series112.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1/2 (hypot 1 x))
11.0ms
(/ 1/2 (hypot 1 x))
46.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
44.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify992.0ms

Counts
99 → 99
Iterations
IterNodes
done2006
32006
2715
1232
0106

prune954.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ 1/2 (/ 1/2 (hypot 1 x))))))
0.1b
(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
0.7b
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
1.6b
(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
72×times-frac
44×*-un-lft-identity
34×add-cube-cbrt
20×add-cbrt-cube add-exp-log
17×associate-/l*
15×difference-of-squares
8×cbrt-undiv div-exp
7×associate-/r* div-inv
6×add-log-exp
5×distribute-lft-out--
4×pow1 insert-posit16
3×clear-num frac-2neg associate-/l/
2×flip3-- prod-exp associate-/r/ cbrt-unprod flip--
1×sub-neg flip3-+ diff-log div-sub flip-+
Counts
4 → 137
Calls
4 calls:
34.0ms
(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ 1/2 (/ 1/2 (hypot 1 x))))))
11.0ms
(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
7.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
15.0ms
(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
197.0ms
(/ (- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))) (+ 1/4 (* (/ 1/2 (hypot 1 x)) (+ 1/2 (/ 1/2 (hypot 1 x))))))
35.0ms
(/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x))
24.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
78.0ms
(- 1/8 (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)))

simplify1.6s

Counts
149 → 149
Iterations
IterNodes
done2001
32001
21800
1576
0231

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.0b

localize106.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
0.7b
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
0.7b
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
1.5b
(- (pow 1/8 3) (pow (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)) 3))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
33×times-frac
32×difference-of-squares
24×unpow-prod-down cube-prod
20×*-un-lft-identity
19×add-cbrt-cube add-exp-log
12×sqr-pow
10×add-cube-cbrt
9×associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out--
4×pow1 insert-posit16
3×clear-num associate-/r* frac-2neg prod-exp cbrt-unprod div-inv
1×difference-cubes sub-neg flip3-- diff-log flip--
Counts
4 → 117
Calls
4 calls:
13.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
12.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
14.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
33.0ms
(- (pow 1/8 3) (pow (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)) 3))

series200.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
23.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
26.0ms
(/ 1/8 (* (hypot 1 x) (hypot 1 x)))
120.0ms
(- (pow 1/8 3) (pow (/ (/ 1/8 (* (hypot 1 x) (hypot 1 x))) (hypot 1 x)) 3))

simplify1.2s

Counts
129 → 129
Iterations
IterNodes
done2008
32008
21034
1309
0126

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.0b

regimes138.0ms

Accuracy

0% (0.3b remaining)

Error of 14.3b against oracle of 14.1b and baseline of 14.3b

bsearch0.0ms

simplify11.0ms

Iterations
IterNodes
done37
137
026

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s2845×body1280valid
448.0ms4095×body80valid
355.0ms603×body640valid
89.0ms306×body320valid
28.0ms151×body160valid