Details

Time bar (total: 19.2s)

sample40.0ms

Algorithm
intervals
Results
19.0ms88×body1280valid
6.0ms135×body80valid
3.0ms16×body640valid
2.0ms15×body320valid
0.0ms2×body160valid

simplify42.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0912
11912
22412
32812
43012
53512
63612
done3612

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg pow1/2 diff-log div-exp pow-prod-down clear-num sum-log sqrt-prod flip-- div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 66
Calls
4 calls:
10.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
14.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
9.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series208.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
77.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms
(/ 1.0 (hypot 1.0 x))
90.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify523.0ms

Counts
78 → 78
Iterations

Useful iterations: done (520.0ms)

IterNodesCost
01121034
1238951
2840887
done5001885

prune251.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.8b

localize15.0ms

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 (* 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))
0.9b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite76.0ms

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:
43.0ms
(/ (- (* 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)))))))
9.0ms
(/ 1.0 (hypot 1.0 x))
12.0ms
(/ 1.0 (hypot 1.0 x))
9.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
167.0ms
(/ (- (* 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)))))))
7.0ms
(/ 1.0 (hypot 1.0 x))
11.0ms
(/ 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
116 → 116
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01412407
13752331
219152143
done50002112

prune347.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.9b
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.7b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite356.0ms

Algorithm
rewrite-expression-head
Rules
90×associate-*r/
62×sqrt-div
57×pow1
31×flip3-+ flip-+
30×sqrt-pow1
21×pow-prod-down
16×frac-sub
13×add-sqr-sqrt
12×frac-times
11×add-cube-cbrt *-un-lft-identity pow1/2
10×pow-prod-up
8×associate-*l/ add-log-exp
7×add-exp-log add-cbrt-cube
6×sqrt-prod pow-sqr
4×unpow-prod-down pow-pow cube-prod swap-sqr associate-*r* associate-*l* sub-div
3×pow-unpow
2×cube-div sub-neg flip3-- diff-log flip-- associate--r+
1×pow2 distribute-rgt-in cube-mult pow-to-exp distribute-rgt-out-- distribute-lft-in pow-plus sqrt-unprod unpow3 pow-exp prod-exp rem-square-sqrt *-commutative sqrt-pow2 cbrt-unprod rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 135
Calls
4 calls:
139.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
27.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
15.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
167.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series697.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
155.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
37.0ms
(- (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
402.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify5.6s

Counts
147 → 147
Iterations

Useful iterations: 2 (989.0ms)

IterNodesCost
02325302
17293813
246423397
done50003397

prune598.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 13.8b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.9b
(- 0.5 (/ 0.5 (hypot 1.0 x)))
1.7b
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

rewrite339.0ms

Algorithm
rewrite-expression-head
Rules
90×associate-*r/
62×sqrt-div
57×pow1
31×flip3-+ flip-+
30×sqrt-pow1
21×pow-prod-down
18×add-sqr-sqrt
16×frac-sub
13×*-un-lft-identity
12×frac-times
11×add-cube-cbrt pow1/2
10×pow-prod-up
8×associate-*l/ add-log-exp
7×add-exp-log add-cbrt-cube
6×sqrt-prod pow-sqr
4×unpow-prod-down pow-pow cube-prod swap-sqr associate-*r* associate-*l* sub-div
3×pow-unpow
2×cube-div sub-neg flip3-- diff-log flip-- difference-of-squares
1×pow2 cube-mult pow-to-exp distribute-rgt-out-- times-frac pow-plus sqrt-unprod unpow3 pow-exp prod-exp rem-square-sqrt *-commutative sqrt-pow2 cbrt-unprod distribute-lft-out-- rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 136
Calls
4 calls:
131.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
30.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
12.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))
153.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
216.0ms
(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
47.0ms
(- 0.5 (/ 0.5 (hypot 1.0 x)))
390.0ms
(- (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))

simplify4.6s

Counts
148 → 148
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02375217
17253740
244203351
done50003351

prune704.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 13.8b

regimes132.0ms

Accuracy

0% (0.0b remaining)

Error of 15.0b against oracle of 15.0b and baseline of 15.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02069
12669
done2669

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2874×body1280valid
508.0ms627×body640valid
236.0ms4004×body80valid
61.0ms336×body320valid
19.0ms159×body160valid