Details

Time bar (total: 8.9s)

sample31.0ms

Algorithm
intervals
Results
15.0ms95×body1280valid
4.0ms128×body80valid
2.0ms14×body640valid
1.0ms12×body160valid
1.0ms7×body320valid

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: 15.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.6b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt *-un-lft-identity
12×add-cube-cbrt
9×times-frac
7×pow1
6×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
4 → 61
Calls
4 calls:
0.0ms
(hypot 1.0 x)
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))))))

series349.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
256.0ms
(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))))))

simplify1.7s

Counts
73 → 73
Iterations

Useful iterations: 4 (703.0ms)

IterNodesCost
0106904
1202828
2455778
31201776
43819774
done5001774

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.1b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
7×pow1
6×associate-/r* associate-/l* add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 sqrt-div associate-*r/ div-exp clear-num div-inv associate--r+
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ pow1/2 diff-log pow-prod-down sqrt-prod flip-- flip-+
Counts
4 → 81
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
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 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series116.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
70.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
35.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.0s

Counts
93 → 93
Iterations

Useful iterations: 3 (312.0ms)

IterNodesCost
01121111
12411028
2687960
32432953
done5001953

prune253.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
0.0b
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.0b
(+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.1b
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
30×*-un-lft-identity times-frac difference-of-squares
26×sqr-pow
20×add-cube-cbrt
11×unpow-prod-down
10×associate-/l*
9×add-exp-log add-cbrt-cube
8×add-log-exp
7×pow1
5×distribute-lft-out--
3×pow-unpow flip3-+ associate-/r* flip-+
2×cube-div associate-+r+ flip3-- pow-pow associate-*r/ pow-exp associate-/r/ flip-- associate-/l/ rem-cube-cbrt
1×cbrt-undiv +-commutative distribute-rgt-in cube-mult pow-to-exp sub-neg frac-2neg distribute-lft-in diff-log unpow3 div-sub cube-prod div-exp pow-prod-down prod-exp clear-num sum-log cbrt-unprod div-inv
Counts
4 → 116
Calls
4 calls:
8.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
34.0ms
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
7.0ms
(+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
10.0ms
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

series579.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)
278.0ms
(/ (- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3)) (+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
79.0ms
(+ (pow 1.0 4) (* (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5) (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
142.0ms
(- (pow 1.0 6) (pow (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) 3))

simplify710.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (249.0ms)

IterNodesCost
02336120
16065873
220645505
done50015505

prune573.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 15.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.125 (pow (hypot 1.0 x) 3))
0.3b
(/ 0.25 (pow (hypot 1.0 x) 2))
0.4b
(/ 0.375 (pow (hypot 1.0 x) 2))
3.1b
(- (- 0.875 (+ (/ 0.375 (hypot 1.0 x)) (/ 0.375 (pow (hypot 1.0 x) 2)))) (/ 0.125 (pow (hypot 1.0 x) 3)))

rewrite739.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
76×add-sqr-sqrt
72×*-un-lft-identity
63×add-cube-cbrt
37×unpow-prod-down
28×associate-/r*
19×add-exp-log
13×cube-prod add-log-exp sqr-pow
10×add-cbrt-cube
9×div-exp associate-/l*
8×unpow2
5×diff-log distribute-lft-out-- difference-of-squares
4×pow1 cube-mult unpow3
3×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
2×sub-neg flip3-- associate--l+ frac-sub flip--
1×associate--l- sum-log distribute-lft-out
Counts
4 → 190
Calls
4 calls:
4.0ms
(/ 0.125 (pow (hypot 1.0 x) 3))
4.0ms
(/ 0.25 (pow (hypot 1.0 x) 2))
4.0ms
(/ 0.375 (pow (hypot 1.0 x) 2))
721.0ms
(- (- 0.875 (+ (/ 0.375 (hypot 1.0 x)) (/ 0.375 (pow (hypot 1.0 x) 2)))) (/ 0.125 (pow (hypot 1.0 x) 3)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 0.125 (pow (hypot 1.0 x) 3))
23.0ms
(/ 0.25 (pow (hypot 1.0 x) 2))
24.0ms
(/ 0.375 (pow (hypot 1.0 x) 2))
146.0ms
(- (- 0.875 (+ (/ 0.375 (hypot 1.0 x)) (/ 0.375 (pow (hypot 1.0 x) 2)))) (/ 0.125 (pow (hypot 1.0 x) 3)))

simplify714.0ms

Counts
202 → 202
Iterations

Useful iterations: 2 (269.0ms)

IterNodesCost
03033539
16003177
221582913
done50002913

prune691.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.7b

regimes101.0ms

Accuracy

0% (0.3b remaining)

Error of 14.5b against oracle of 14.3b and baseline of 14.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03154
13754
done3754

end0.0ms

sample810.0ms

Algorithm
intervals
Results
463.0ms2872×body1280valid
115.0ms4044×body80valid
84.0ms621×body640valid
28.0ms295×body320valid
9.0ms168×body160valid