Details

Time bar (total: 13.2s)

sample39.0ms

Algorithm
intervals
Results
19.0ms90×body1280valid
5.0ms129×body80valid
4.0ms22×body640valid
1.0ms8×body320valid
1.0ms7×body160valid

simplify37.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
2.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-cbrt-cube add-exp-log
4×pow1
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-+ flip3-- diff-log div-exp flip-+ div-inv flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
8.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0ms
(hypot 1.0 x)
4.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series156.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.0ms
(hypot 1.0 x)
7.0ms
(/ 1.0 (hypot 1.0 x))
110.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.8s

Counts
72 → 72
Iterations
IterNodes
done5001
34651
2762
1220
0101

prune307.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.7b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt add-cube-cbrt
12×times-frac
11×add-cbrt-cube add-exp-log
8×add-log-exp
6×associate-/r*
4×pow1 associate--l+ associate-/l*
3×cbrt-undiv sub-neg div-exp
2×distribute-rgt-in clear-num frac-2neg distribute-lft-in flip3-- associate-*r/ frac-sub div-inv flip--
1×+-commutative sum-log flip3-+ diff-log prod-exp cbrt-unprod flip-+ distribute-lft-out
Counts
4 → 78
Calls
4 calls:
4.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
7.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
4.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x)))

series141.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
8.0ms
(/ (* 0.5 1.0) (hypot 1.0 x))
7.0ms
(/ 1.0 (hypot 1.0 x))
40.0ms
(- (* 1.0 (- 1.0 0.5)) (/ (* 0.5 1.0) (hypot 1.0 x)))

simplify804.0ms

Counts
90 → 90
Iterations
IterNodes
done5002
22043
1411
0157

prune452.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
1.8b
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
32×associate-*l/
18×add-sqr-sqrt
16×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
12×times-frac
8×frac-sub
6×pow1 flip3-+ flip3-- flip-+ flip-- associate-/l* add-log-exp associate-/l/
4×associate-/r* associate-*r/
3×cbrt-undiv div-exp associate-*r* associate-*l*
2×clear-num frac-2neg prod-exp associate-/r/ cbrt-unprod div-inv
1×distribute-rgt-in sub-neg distribute-lft-in diff-log div-sub pow-prod-down *-commutative unswap-sqr
Counts
4 → 95
Calls
4 calls:
17.0ms
(* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))
4.0ms
(/ 1.0 (hypot 1.0 x))
262.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
139.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

series206.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))
14.0ms
(/ 1.0 (hypot 1.0 x))
107.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))
48.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

simplify1.6s

Counts
107 → 107
Iterations
IterNodes
done5001
24285
1656
0198

prune819.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.3b

localize93.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))))
0.1b
(/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))))
1.8b
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

rewrite978.0ms

Algorithm
rewrite-expression-head
Rules
51×times-frac
34×associate-*l/
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×add-cbrt-cube add-exp-log
15×associate-/r*
11×associate-/r/
10×flip3-+ flip-+
8×cbrt-undiv div-exp frac-sub associate-/l/
7×div-inv associate-/l*
6×flip3-- flip-- add-log-exp
4×pow1
3×clear-num frac-2neg
2×prod-exp cbrt-unprod
1×sub-neg diff-log div-sub
Counts
4 → 131
Calls
4 calls:
7.0ms
(/ 1.0 (hypot 1.0 x))
531.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))))
305.0ms
(/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))))
126.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

series265.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(/ 1.0 (hypot 1.0 x))
122.0ms
(/ (- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5)) (/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0)))))))
62.0ms
(/ (* (+ (pow (* (+ 0.5 1.0) 0.5) 3) (pow 1.0 6)) (hypot 1.0 x)) (+ (* (* 1.0 1.0) (* 1.0 1.0)) (- (* (* 0.5 (+ 0.5 1.0)) (* 0.5 (+ 0.5 1.0))) (* (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))))))
73.0ms
(- (* (* (- (pow 1.0 3) (pow 0.5 3)) 1.0) (hypot 1.0 x)) (* (* (+ (* 1.0 1.0) (* 0.5 (+ 0.5 1.0))) 1.0) 0.5))

simplify438.0ms

Counts
143 → 143
Iterations
IterNodes
done5001
1955
0289

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 15.3b

regimes220.0ms

Accuracy

0% (0.4b remaining)

Error of 14.8b against oracle of 14.3b and baseline of 14.8b

bsearch0.0ms

simplify24.0ms

Iterations
IterNodes
done56
356
254
150
036

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.5s2865×body1280valid
456.0ms4052×body80valid
153.0ms599×body640valid
55.0ms327×body320valid
19.0ms157×body160valid