Details

Time bar (total: 31.0s)

sample121.0ms

Algorithm
intervals
Results
73.0ms89×body1280valid
17.0ms126×body80valid
10.0ms19×body640valid
8.0ms19×body320valid
1.0ms3×body160valid

simplify17.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
119
09

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite351.0ms

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:
4.0ms
(/ 1/2 (hypot 1 x))
0.0ms
(hypot 1 x)
304.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
42.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ 1/2 (hypot 1 x))
1.0ms
(hypot 1 x)
31.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
53.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify8.7s

Counts
81 → 81
Iterations
IterNodes
45438
31603
2554
1217
0107

prune817.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(hypot 1 x)
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.7b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
8×add-log-exp
4×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 distribute-lft-out
2×sqrt-prod difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ times-frac flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 47
Calls
4 calls:
0.0ms
(hypot 1 x)
0.0ms
(hypot 1 x)
27.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series114.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1 x)
1.0ms
(hypot 1 x)
54.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
57.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify4.7s

Counts
59 → 59
Iterations
IterNodes
43442
31138
2420
1161
075

prune609.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
1.7b
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
56×add-sqr-sqrt times-frac
42×add-cube-cbrt
18×add-cbrt-cube add-exp-log
13×swap-sqr associate-*r* associate-*l*
11×pow1
9×distribute-lft-out
8×add-log-exp
6×difference-of-squares
5×cbrt-undiv div-exp div-inv
4×associate-/r* prod-exp cbrt-unprod insert-posit16 associate-/l* unswap-sqr
2×flip3-+ flip3-- associate-/r/ sqrt-prod flip-+ flip-- associate-/l/
1×pow2 frac-times +-commutative clear-num sum-log sub-neg frac-2neg pow-plus diff-log div-sub pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
Counts
4 → 139
Calls
4 calls:
31.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
28.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
26.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
15.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series312.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
62.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
42.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
84.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

simplify1.7s

Counts
151 → 151
Iterations
IterNodes
22301
1684
0222

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
1.6b
(- (* (* 1/2 1/2) (* 1/2 1/2)) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
124×add-sqr-sqrt
120×times-frac
88×*-un-lft-identity add-cube-cbrt
40×add-cbrt-cube add-exp-log
39×swap-sqr associate-*r* associate-*l*
25×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
6×add-log-exp
4×insert-posit16
3×pow2 frac-times pow-plus pow-prod-down associate-*l/ associate-*r/ pow-sqr *-commutative pow-prod-up
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 218
Calls
4 calls:
27.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
17.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
14.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
45.0ms
(- (* (* 1/2 1/2) (* 1/2 1/2)) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
29.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
40.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
109.0ms
(- (* (* 1/2 1/2) (* 1/2 1/2)) (* (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))))

simplify4.1s

Counts
230 → 230
Iterations
IterNodes
34849
21477
1464
0144

prune3.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.8b

regimes124.0ms

Accuracy

0% (0.3b remaining)

Error of 15.6b against oracle of 15.4b and baseline of 15.6b

bsearch0.0ms

simplify9.0ms

Iterations
IterNodes
330
230
129
024

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.8s2877×body1280valid
548.0ms3970×body80valid
346.0ms667×body640valid
133.0ms341×body320valid
28.0ms145×body160valid