Details

Time bar (total: 8.8s)

sample30.0ms

Algorithm
intervals
Results
15.0ms90×body1280valid
4.0ms133×body80valid
2.0ms17×body640valid
1.0ms8×body320valid
0.0ms8×body160valid

simplify24.0ms

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: 15.8b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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)
7.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
76.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms
(/ 1.0 (hypot 1.0 x))
88.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.3s

Counts
73 → 73
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0106904
1202828
2455778
31196776
43747774
done5001774

prune157.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.7b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
18×times-frac
8×add-exp-log add-cbrt-cube add-log-exp
6×associate-/r* associate-/l*
4×pow1
2×cbrt-undiv frac-2neg div-exp clear-num div-inv associate--r+
1×+-commutative distribute-rgt-in sub-neg flip3-- distribute-lft-in flip3-+ diff-log sum-log flip-- flip-+ distribute-lft-out
Counts
4 → 80
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series129.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
37.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.3s

Counts
92 → 92
Iterations

Useful iterations: 3 (384.0ms)

IterNodesCost
01091174
12471108
26841008
32438999
done5000999

prune252.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.1b
(exp (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×exp-prod
3×log-prod exp-sum
2×cbrt-undiv log-div flip3-- frac-2neg exp-diff div-exp clear-num flip-- div-inv associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in diff-log log-pow rem-exp-log
Counts
4 → 85
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(exp (log (- (* 1.0 1.0) (* 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)))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(exp (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
37.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts
97 → 97
Iterations

Useful iterations: 3 (252.0ms)

IterNodesCost
01121324
12171239
25421090
316441082
done50001082

prune295.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.1b
(pow E (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.7b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
9×add-exp-log
8×add-cbrt-cube
6×pow1 associate-/r* associate-/l* add-log-exp
4×pow-unpow
3×unpow-prod-up unpow-prod-down log-prod
2×cbrt-undiv log-div flip3-- frac-2neg div-exp pow-exp clear-num flip-- div-inv associate--r+ pow-sub
1×distribute-rgt-in pow-to-exp sub-neg e-exp-1 pow-pow distribute-lft-in diff-log log-pow sqr-pow
Counts
4 → 92
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
4.0ms
(pow E (log (- (* 1.0 1.0) (* 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)))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
250.0ms
(pow E (log (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
37.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.2s

Counts
104 → 104
Iterations

Useful iterations: 3 (378.0ms)

IterNodesCost
01261553
12761462
27021340
320871332
done50001332

prune316.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 15.2b

regimes150.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02762
13562
23762
done3762

end0.0ms

sample1000.0ms

Algorithm
intervals
Results
661.0ms2809×body1280valid
118.0ms4111×body80valid
79.0ms621×body640valid
26.0ms287×body320valid
10.0ms172×body160valid