Details

Time bar (total: 34.3s)

sample61.0ms

Algorithm
intervals
Results
36.0ms100×body1280valid
8.0ms123×body80valid
5.0ms19×body640valid
2.0ms10×body320valid
1.0ms4×body160valid

simplify25.0ms

Counts
1 → 1
Iterations
IterNodes
323
223
119
09

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1 x)
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
1.3b
(- 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:
0.0ms
(hypot 1 x)
7.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
8.0ms
(/ 1/2 (hypot 1 x))
33.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series100.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1 x)
28.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))
62.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify11.8s

Counts
81 → 81
Iterations
IterNodes
45662
31680
2554
1217
0107

prune674.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.0b

localize40.0ms

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

rewrite51.0ms

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))
5.0ms
(/ 1/2 (hypot 1 x))
29.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
11.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series103.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1/2 (hypot 1 x))
9.0ms
(/ 1/2 (hypot 1 x))
48.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
36.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify8.1s

Counts
99 → 99
Iterations
IterNodes
44766
31450
2536
1213
0106

prune963.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.8b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.1b
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
0.7b
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

rewrite88.0ms

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:
15.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
28.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
28.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
15.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

series227.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
99.0ms
(/ (- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
23.0ms
(* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x)))
56.0ms
(- (* 1/2 1/2) (* (/ 1/2 (hypot 1 x)) (/ 1/2 (hypot 1 x))))

simplify1.7s

Counts
151 → 151
Iterations
IterNodes
22297
1684
0222

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x))
0.1b
(/ 1/2 (sqrt (hypot 1 x)))
0.1b
(/ 1/2 (sqrt (hypot 1 x)))
0.7b
(- (* 1/2 1/2) (* (/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (sqrt (hypot 1 x)))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
109×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
60×sqrt-prod
28×associate-/l*
15×associate-/r*
13×add-cbrt-cube add-exp-log
7×div-inv
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1 insert-posit16
3×clear-num frac-2neg
1×sub-neg flip3-- diff-log flip-- associate-/l/
Counts
4 → 200
Calls
4 calls:
15.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x))
9.0ms
(/ 1/2 (sqrt (hypot 1 x)))
8.0ms
(/ 1/2 (sqrt (hypot 1 x)))
13.0ms
(- (* 1/2 1/2) (* (/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (sqrt (hypot 1 x)))))

series243.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x))
39.0ms
(/ 1/2 (sqrt (hypot 1 x)))
47.0ms
(/ 1/2 (sqrt (hypot 1 x)))
61.0ms
(- (* 1/2 1/2) (* (/ (/ 1/2 (sqrt (hypot 1 x))) (hypot 1 x)) (/ 1/2 (sqrt (hypot 1 x)))))

simplify2.2s

Counts
212 → 212
Iterations
IterNodes
35311
21366
1556
0237

prune3.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.8b

regimes98.0ms

Accuracy

0% (0.3b remaining)

Error of 15.2b against oracle of 15.0b and baseline of 15.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
224
124
019

end0.0ms

sample3.1s

Algorithm
intervals
Results
2.2s2870×body1280valid
401.0ms4019×body80valid
255.0ms641×body640valid
90.0ms322×body320valid
27.0ms148×body160valid