Details

Time bar (total: 20.7s)

sample110.0ms

Algorithm
intervals
Results
60.0ms91×body1280valid
15.0ms124×body80valid
11.0ms19×body640valid
6.0ms15×body320valid
2.0ms7×body160valid

simplify88.0ms

Counts
1 → 1
Iterations
IterNodes
done90
590
471
355
239
121
09

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(+ 1/2 (/ 1/2 (hypot 1 x)))
0.0b
(/ 1/2 (hypot 1 x))
2.4b
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
13×add-cube-cbrt
9×times-frac
8×sqrt-prod add-log-exp
6×add-cbrt-cube add-exp-log
5×pow1
4×insert-posit16 difference-of-squares
3×associate-/r* distribute-lft-out associate-/l* distribute-lft-out--
2×flip3-+ sqrt-div flip-+
1×cbrt-undiv +-commutative rem-sqrt-square clear-num sum-log sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log div-exp div-inv flip--
Counts
4 → 78
Calls
4 calls:
14.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
12.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
7.0ms
(/ 1/2 (hypot 1 x))
46.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series157.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
28.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
6.0ms
(/ 1/2 (hypot 1 x))
55.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.8s

Counts
90 → 90
Iterations
IterNodes
done5000
32029
2747
1247
0118

prune448.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 15.8b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
0.0b
(/ 1/2 (hypot 1 x))
0.0b
(/ 1/2 (hypot 1 x))
1.9b
(- 1/2 (/ 1/2 (hypot 1 x)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt *-un-lft-identity
20×add-cube-cbrt
19×times-frac
8×add-cbrt-cube add-exp-log add-log-exp
6×associate-/r* associate-/l*
4×pow1 insert-posit16 distribute-lft-out
2×cbrt-undiv clear-num frac-2neg div-exp sqrt-prod div-inv difference-of-squares
1×+-commutative sum-log sub-neg flip3-+ flip3-- diff-log flip-+ flip-- distribute-lft-out--
Counts
4 → 87
Calls
4 calls:
28.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
13.0ms
(/ 1/2 (hypot 1 x))
8.0ms
(/ 1/2 (hypot 1 x))
12.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series151.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
10.0ms
(/ 1/2 (hypot 1 x))
10.0ms
(/ 1/2 (hypot 1 x))
55.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify2.0s

Counts
99 → 99
Iterations
IterNodes
done5007
32598
2714
1232
0106

prune477.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1)
0.0b
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
0.0b
(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
1.9b
(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

rewrite913.0ms

Algorithm
rewrite-expression-head
Rules
67×*-un-lft-identity
32×distribute-lft-out
23×add-sqr-sqrt
18×times-frac add-cube-cbrt
15×add-log-exp
10×pow1
8×flip3-+ add-cbrt-cube add-exp-log flip-+
7×associate-*l*
6×associate-/r* sum-log sqrt-div
5×sqrt-prod
4×frac-times associate-*r* insert-posit16
3×associate-/l*
2×distribute-rgt-in distribute-lft-in sqrt-pow1 pow-plus flip3-- pow1/2 associate-*l/ associate-*r/ associate-/r/ pow-prod-up flip-- associate--r+ unswap-sqr associate-/l/
1×cbrt-undiv +-commutative associate-+l+ clear-num sub-neg frac-2neg diff-log div-sub cube-unmult div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv
Counts
4 → 118
Calls
4 calls:
370.0ms
(+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1)
83.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
448.0ms
(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
9.0ms
(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1)
100.0ms
(* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))
221.0ms
(/ (- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
120.0ms
(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify2.3s

Counts
130 → 130
Iterations
IterNodes
done5002
22202
1526
0174

prune524.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.5b

localize92.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
0.0b
(/ (/ (- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ 1 (* (+ 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
0.5b
(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
1.9b
(- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))

rewrite628.0ms

Algorithm
rewrite-expression-head
Rules
220×*-un-lft-identity
153×times-frac
140×frac-times
122×flip3-+ flip-+
114×sqrt-div
113×pow1
98×distribute-lft-out
83×add-sqr-sqrt
72×add-cube-cbrt
55×pow-prod-up
46×associate-*l/ associate-*r/
36×pow-plus
34×sqrt-pow1 pow1/2
27×pow-prod-down
23×add-cbrt-cube add-exp-log
17×distribute-rgt-in distribute-lft-in
16×associate-/r/
15×associate-/l*
13×pow-sqr
9×prod-exp cbrt-unprod
8×associate-*l* div-inv associate--r+
7×cube-unmult
6×associate-/r* add-log-exp
5×associate-*r* sqrt-prod
4×insert-posit16
3×cbrt-undiv div-exp
2×div-sub *-commutative unswap-sqr
1×pow2 clear-num sub-neg frac-2neg flip3-- diff-log swap-sqr flip-- associate-/l/
Counts
4 → 345
Calls
4 calls:
42.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
449.0ms
(/ (/ (- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ 1 (* (+ 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
122.0ms
(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
6.0ms
(- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
102.0ms
(* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))
575.0ms
(/ (/ (- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ 1 (* (+ 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))))) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
416.0ms
(* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))
150.0ms
(- 1 (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))) (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x)))))))

simplify3.7s

Counts
357 → 357
Iterations
IterNodes
done5002
11639
0494

prune2.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 15.5b

regimes78.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.5b and baseline of 14.7b

bsearch0.0ms

simplify17.0ms

Iterations
IterNodes
done34
134
024

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.8s2839×body1280valid
860.0ms4058×body80valid
299.0ms623×body640valid
97.0ms326×body320valid
30.0ms154×body160valid