Details

Time bar (total: 6.9s)

sample30.0ms

Algorithm
intervals
Results
15.0ms92×body1280valid
4.0ms137×body80valid
3.0ms17×body640valid
1.0ms7×body320valid
0.0ms3×body160valid

simplify19.0ms

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: 13.1b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.3b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series90.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.0s

Counts
47 → 47
Iterations

Useful iterations: 4 (715.0ms)

IterNodesCost
085626
1158590
2372542
31145540
43447538
done5001538

prune99.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.8b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
6×add-log-exp
4×pow1 distribute-lft-out
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
2×flip3-- associate-/r/ flip-- associate-/l/ associate--r+
1×distribute-rgt-in sub-neg distribute-lft-in flip3-+ diff-log div-sub flip-+
Counts
4 → 104
Calls
4 calls:
11.0ms
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
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)))))

series195.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
34.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify478.0ms

Counts
116 → 116
Iterations

Useful iterations: 2 (112.0ms)

IterNodesCost
01422407
13392325
211362133
done50002133

prune289.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.6b

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))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
0.8b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
18×log-prod exp-sum
8×add-exp-log add-cbrt-cube
6×associate-/r* associate-/l* add-log-exp
5×pow1
4×exp-prod
3×div-inv distribute-lft-out
2×cbrt-undiv frac-2neg div-exp clear-num associate-/r/ associate--r+
1×distribute-rgt-in sub-neg log-div flip3-- distribute-lft-in flip3-+ exp-diff diff-log log-pow flip-- flip-+ rem-exp-log
Counts
4 → 99
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(exp (log (/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
3.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series202.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
156.0ms
(exp (log (/ (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (+ 1.0 (sqrt (* (+ 1.0 (/ 1.0 (hypot 1.0 x))) 0.5))))))
35.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify720.0ms

Counts
111 → 111
Iterations

Useful iterations: done (717.0ms)

IterNodesCost
01942388
13832213
210602001
done50011705

prune321.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 12.6b

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))
0.8b
(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.8b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite16.0ms

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 log-prod
4×log-pow
3×exp-prod
2×cbrt-undiv sub-neg frac-2neg div-exp exp-sum clear-num div-inv associate--r+
1×distribute-rgt-in log-div flip3-- distribute-lft-in exp-diff diff-log rem-log-exp flip--
Counts
4 → 86
Calls
4 calls:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
7.0ms
(log (exp (- (* 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)))))

series77.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
32.0ms
(log (exp (- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
34.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify1.1s

Counts
98 → 98
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
01071281
12111205
25761081
322251081
done50001081

prune281.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 12.6b

regimes65.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01528
11728
done1728

end0.0ms

sample816.0ms

Algorithm
intervals
Results
455.0ms2825×body1280valid
122.0ms4065×body80valid
88.0ms637×body640valid
29.0ms331×body320valid
8.0ms142×body160valid