Details

Time bar (total: 7.8s)

sample31.0ms

Algorithm
intervals
Results
16.0ms98×body1280valid
4.0ms123×body80valid
3.0ms21×body640valid
1.0ms10×body320valid
0.0ms4×body160valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22212
32612
42812
53312
63512
done3512

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt *-un-lft-identity
11×add-cube-cbrt
9×times-frac
6×pow1
5×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×sqrt-pow1 sqrt-div associate-*r/
1×cbrt-undiv sub-neg flip3-- frac-2neg flip3-+ pow1/2 diff-log div-exp pow-prod-down clear-num sqrt-prod flip-- flip-+ div-inv distribute-lft-out-- difference-of-squares
Counts
3 → 54
Calls
3 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series169.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
76.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
87.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify1.0s

Counts
63 → 63
Iterations

Useful iterations: 3 (202.0ms)

IterNodesCost
0105855
1201779
2488735
31603733
done5000733

prune133.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.4b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity
21×add-sqr-sqrt add-cube-cbrt times-frac
8×add-exp-log add-cbrt-cube add-log-exp
7×associate-/r*
6×associate-/l*
5×distribute-lft-out
4×pow1
2×cbrt-undiv flip3-- frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-- flip-+ div-inv associate-/l/ associate--r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in diff-log div-sub sum-log
Counts
4 → 89
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
11.0ms
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series271.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
78.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
156.0ms
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
32.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify485.0ms

Counts
101 → 101
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
01492415
13552319
211662115
done50002113

prune261.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
0.9b
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
31×*-un-lft-identity
30×times-frac difference-of-squares
26×sqr-pow
21×add-cube-cbrt
14×add-exp-log add-cbrt-cube
12×pow1
11×unpow-prod-down
10×associate-*r/ associate-/l*
8×flip3-+ flip-+
6×add-log-exp
5×distribute-lft-out--
4×frac-times pow-prod-down prod-exp cbrt-unprod
3×pow-unpow associate-*r* associate-/r*
2×cube-div flip3-- pow-pow associate-*l/ pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×cbrt-undiv distribute-rgt-in cube-mult pow-to-exp sub-neg frac-2neg distribute-lft-in diff-log unpow3 div-sub cube-prod div-exp associate-*l* clear-num *-commutative div-inv
Counts
4 → 131
Calls
4 calls:
31.0ms
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
34.0ms
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
9.0ms
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series573.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
89.0ms
(* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
79.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
145.0ms
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify1.5s

Counts
143 → 143
Iterations

Useful iterations: 2 (463.0ms)

IterNodesCost
02726671
17906322
237305906
done50005906

prune605.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
0.0b
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
0.5b
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
0.9b
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
40×cbrt-prod
37×add-sqr-sqrt
34×unpow-prod-down
27×cube-prod
23×sqr-pow
21×difference-of-squares
13×*-un-lft-identity
11×add-exp-log add-cube-cbrt
10×cube-div
8×pow-exp add-cbrt-cube
7×pow1 cube-mult unpow3
6×pow-unpow associate-*l/ add-log-exp
3×pow-to-exp pow-pow flip3-+ flip-+ rem-cube-cbrt
2×cbrt-div prod-exp
1×sub-neg flip3-- pow1/3 diff-log pow-prod-down flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out--
Counts
4 → 129
Calls
4 calls:
8.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
3.0ms
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
3.0ms
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
20.0ms
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

series442.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3)
120.0ms
(pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)
100.0ms
(cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3))
145.0ms
(- (pow 1.0 6) (cbrt (pow (pow (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) 3) 3)))

simplify590.0ms

Counts
141 → 141
Iterations

Useful iterations: 2 (173.0ms)

IterNodesCost
01823535
14512728
216272631
done50002631

prune443.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 14.4b

regimes208.0ms

Accuracy

0% (0.0b remaining)

Error of 14.7b against oracle of 14.6b and baseline of 14.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02559
13059
done3059

end0.0ms

sample804.0ms

Algorithm
intervals
Results
465.0ms2909×body1280valid
116.0ms4022×body80valid
81.0ms621×body640valid
25.0ms293×body320valid
9.0ms155×body160valid