Details

Time bar (total: 26.1s)

sample77.0ms

Algorithm
intervals
Results
40.0ms98×body1280valid
8.0ms115×body80valid
8.0ms24×body640valid
3.0ms13×body320valid
1.0ms6×body160valid

simplify47.0ms

Counts
1 → 1
Iterations
IterNodes
done37
637
535
430
328
224
119
09

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
2.2b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
5×add-cbrt-cube add-exp-log add-log-exp
3×pow1 associate-/r* associate-/l*
1×cbrt-undiv clear-num sub-neg frac-2neg flip3-- diff-log div-exp div-inv flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 48
Calls
3 calls:
0.0ms
(hypot 1.0 x)
4.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series129.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(hypot 1.0 x)
14.0ms
(/ 1.0 (hypot 1.0 x))
112.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.2s

Counts
57 → 57
Iterations
IterNodes
done5000
32794
2537
1169
086

prune305.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 17.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0))) (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
1.8b
(- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
21×add-sqr-sqrt times-frac add-cube-cbrt
8×add-cbrt-cube add-exp-log
7×associate-/r*
6×associate-/l* add-log-exp
4×pow1 flip3-- associate--l+ associate-*r/ frac-sub flip-- distribute-lft-out associate-/l/
3×sub-neg
2×distribute-rgt-in cbrt-undiv clear-num frac-2neg distribute-lft-in div-exp associate-/r/ div-inv
1×flip3-+ diff-log div-sub flip-+
Counts
4 → 90
Calls
4 calls:
0.0ms
(hypot 1.0 x)
4.0ms
(/ 1.0 (hypot 1.0 x))
67.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0))) (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
30.0ms
(- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))

series277.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(hypot 1.0 x)
15.0ms
(/ 1.0 (hypot 1.0 x))
205.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0))) (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
54.0ms
(- (* 1.0 (- 1.0 0.5)) (/ 0.5 (/ (hypot 1.0 x) 1.0)))

simplify1.1s

Counts
102 → 102
Iterations
IterNodes
done5001
21889
1434
0166

prune534.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)
0.0b
(/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
0.1b
(/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
1.8b
(- (/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)) (/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))

rewrite638.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
336×*-un-lft-identity
242×add-sqr-sqrt
228×add-cube-cbrt
52×distribute-lft-out
45×associate-/l*
24×div-inv
19×associate-/r/
18×add-cbrt-cube add-exp-log
9×distribute-rgt-out--
8×cbrt-undiv associate-/r* div-exp add-log-exp
5×flip3-+ flip-+
4×pow1 difference-of-squares
3×associate-/l/
2×clear-num frac-2neg flip3-- associate-*l/ flip--
1×+-commutative sum-log sub-neg diff-log prod-exp frac-sub cbrt-unprod distribute-lft-out-- sub-div
Counts
4 → 310
Calls
4 calls:
31.0ms
(+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)
66.0ms
(/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
57.0ms
(/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
447.0ms
(- (/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)) (/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))

series931.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)
198.0ms
(/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
189.0ms
(/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0))
452.0ms
(- (/ (* (- 1.0 0.5) 1.0) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)) (/ (/ 0.5 (/ (hypot 1.0 x) 1.0)) (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))

simplify824.0ms

Counts
322 → 322
Iterations
IterNodes
done5001
11530
0553

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1.0 (cbrt (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))
0.5b
(/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.7b
(/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.8b
(- (/ (/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

rewrite8.1s

Algorithm
rewrite-expression-head
Rules
1239×times-frac
1203×*-un-lft-identity
718×add-sqr-sqrt
712×cbrt-prod
296×add-cube-cbrt
261×distribute-lft-out--
190×distribute-lft-out
85×difference-of-squares
70×cbrt-div associate-/r/
48×distribute-rgt-out--
43×div-inv
35×flip3-+ flip-+
21×associate-/r* associate-/l*
13×add-exp-log
9×add-cbrt-cube
6×add-log-exp
5×cbrt-undiv div-exp
4×pow1
3×clear-num frac-2neg div-sub associate-/l/
2×flip3-- flip--
1×associate--l- sub-neg diff-log frac-sub sub-div
Counts
4 → 549
Calls
4 calls:
37.0ms
(/ 1.0 (cbrt (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))
27.0ms
(/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
17.0ms
(/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
8.0s
(- (/ (/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

series2.8s

Counts
4 → 12
Calls
4 calls:
435.0ms
(/ 1.0 (cbrt (+ (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))) 1.0)))
397.0ms
(/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
775.0ms
(/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.2s
(- (/ (/ (- 1.0 0.5) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (/ (/ (/ 0.5 (hypot 1.0 x)) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (cbrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

simplify859.0ms

Counts
561 → 561
Iterations
IterNodes
done5000
11550
0688

prune3.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 17.4b

regimes108.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations
IterNodes
done28
228
127
023

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.3s2820×body1280valid
293.0ms4078×body80valid
171.0ms635×body640valid
62.0ms317×body320valid
18.0ms150×body160valid