Details

Time bar (total: 18.2s)

sample56.0ms

Algorithm
intervals
Results
29.0ms83×body1280valid
8.0ms130×body80valid
8.0ms28×body640valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify62.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
1.4b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
20×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
4×pow1 sqrt-prod insert-posit16 difference-of-squares
3×associate-/r* associate-/l* distribute-lft-out--
2×distribute-lft-out
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip--
Counts
4 → 69
Calls
4 calls:
9.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
3.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)
36.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series110.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
10.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)
53.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.7s

Counts
81 → 81
Iterations
IterNodes
done5002
32165
2705
1234
0107

prune252.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1/2 (hypot 1 x))
0.0b
(hypot 1 x)
0.0b
(hypot 1 x)
0.8b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
10×times-frac
6×add-cbrt-cube add-exp-log add-log-exp
4×pow1 insert-posit16
3×associate-/r* associate-/l*
2×difference-of-squares
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- distribute-lft-out--
Counts
4 → 60
Calls
4 calls:
3.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)
0.0ms
(hypot 1 x)
6.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(/ 1/2 (hypot 1 x))
2.0ms
(hypot 1 x)
2.0ms
(hypot 1 x)
39.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.5s

Counts
72 → 72
Iterations
IterNodes
done5003
31357
2475
1163
080

prune241.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
0.1b
(/ (/ 1/8 (hypot 1 x)) (hypot 1 x))
0.1b
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
0.8b
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
522×times-frac
313×add-sqr-sqrt
253×*-un-lft-identity
243×add-cube-cbrt
64×associate-/l*
23×div-inv
20×add-cbrt-cube add-exp-log difference-of-squares
10×cbrt-undiv div-exp
9×associate-/r*
6×add-log-exp
5×distribute-lft-out--
4×pow1 insert-posit16 associate-/l/
3×clear-num frac-2neg
2×flip3-- associate-/r/ flip--
1×sub-neg flip3-+ diff-log div-sub flip-+
Counts
4 → 335
Calls
4 calls:
63.0ms
(/ (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
7.0ms
(/ (/ 1/8 (hypot 1 x)) (hypot 1 x))
11.0ms
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
14.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

series302.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))) (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4))
25.0ms
(/ (/ 1/8 (hypot 1 x)) (hypot 1 x))
33.0ms
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
64.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

simplify3.0s

Counts
347 → 347
Iterations
IterNodes
done5001
23357
11218
0547

prune2.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
0.5b
(/ (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4) (sqrt (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))))
0.8b
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
0.8b
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
462×times-frac
292×add-sqr-sqrt
220×*-un-lft-identity
208×add-cube-cbrt
46×associate-/l*
32×sqrt-prod
24×difference-of-squares
18×div-inv
15×add-cbrt-cube add-exp-log
14×associate-/r*
8×add-log-exp
7×cbrt-undiv div-exp
6×distribute-lft-out--
4×pow1 insert-posit16
3×flip3-- flip-- associate-/l/
2×clear-num sub-neg frac-2neg sqrt-div diff-log associate-/r/
1×flip3-+ flip-+
Counts
4 → 293
Calls
4 calls:
17.0ms
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
59.0ms
(/ (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4) (sqrt (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))))
11.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
15.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

series484.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x))
277.0ms
(/ (+ (* (/ 1/2 (hypot 1 x)) (+ (/ 1/2 (hypot 1 x)) 1/2)) 1/4) (sqrt (- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))))
80.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))
77.0ms
(- 1/8 (/ (/ (/ 1/8 (hypot 1 x)) (hypot 1 x)) (hypot 1 x)))

simplify2.4s

Counts
305 → 305
Iterations
IterNodes
done5000
23044
11190
0562

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

regimes93.0ms

Accuracy

0% (0.8b remaining)

Error of 16.0b against oracle of 15.3b and baseline of 16.0b

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done36
136
030

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s2865×body1280valid
480.0ms3961×body80valid
265.0ms654×body640valid
134.0ms344×body320valid
74.0ms176×body160valid