Details

Time bar (total: 10.1s)

sample73.0ms

Algorithm
intervals
Results
45.0ms91×body1280valid
8.0ms26×body640valid
8.0ms125×body80valid
2.0ms9×body320valid
1.0ms5×body160valid

simplify61.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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:
4.0ms
(/ 1/2 (hypot 1 x))
8.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
39.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series135.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1/2 (hypot 1 x))
35.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
40.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
54.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify518.0ms

Counts
90 → 90
Iterations
IterNodes
done2001
2712
1247
0118

prune326.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.5b

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
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
1.1b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
25×*-un-lft-identity
21×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×sqrt-prod insert-posit16
2×cbrt-undiv clear-num frac-2neg sqrt-div div-exp div-inv difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip-- distribute-lft-out distribute-lft-out--
Counts
4 → 89
Calls
4 calls:
7.0ms
(/ 1/2 (hypot 1 x))
12.0ms
(/ 1/2 (hypot 1 x))
10.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
6.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series124.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1/2 (hypot 1 x))
11.0ms
(/ 1/2 (hypot 1 x))
67.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
36.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify817.0ms

Counts
101 → 101
Iterations
IterNodes
done2002
31480
2547
1194
0102

prune830.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
1.0b
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
40×times-frac
37×*-un-lft-identity
33×add-cube-cbrt
16×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
12×pow1
8×add-log-exp
4×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod insert-posit16 div-inv unswap-sqr
2×flip3-+ sqrt-div flip-+ distribute-lft-out
1×pow2 frac-times +-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 pow-plus flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up flip-- difference-of-squares
Counts
4 → 112
Calls
4 calls:
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
16.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
7.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series194.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
63.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
29.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
68.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

simplify915.0ms

Counts
124 → 124
Iterations
IterNodes
done2013
21632
1525
0172

prune622.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)))
1.0b
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite257.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
34×distribute-lft-out
21×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt
8×sqrt-prod
7×associate-/r* flip3-+ flip-+
6×pow1 add-cbrt-cube add-exp-log associate-/r/ add-log-exp
4×sqrt-div frac-add insert-posit16
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 flip-- associate--r+ associate-/l/
1×distribute-rgt-in cbrt-undiv clear-num sub-neg frac-2neg distribute-lft-in diff-log div-sub div-exp div-inv
Counts
4 → 102
Calls
4 calls:
14.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
15.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
221.0ms
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)))
4.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
48.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
239.0ms
(/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (+ (+ 1/2 (/ 1/2 (hypot 1 x))) (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)))
120.0ms
(- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify696.0ms

Counts
114 → 114
Iterations
IterNodes
done2000
1441
0153

prune444.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.3b

regimes73.0ms

Accuracy

0% (0.3b remaining)

Error of 14.9b against oracle of 14.6b and baseline of 14.9b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done29
129
020

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.2s2848×body1280valid
407.0ms4058×body80valid
369.0ms626×body640valid
99.0ms316×body320valid
30.0ms152×body160valid