Details

Time bar (total: 25.4s)

sample118.0ms

Algorithm
intervals
Results
61.0ms90×body1280valid
20.0ms16×body640valid
16.0ms134×body80valid
3.0ms9×body320valid
2.0ms7×body160valid

simplify49.0ms

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize37.0ms

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)))))

rewrite38.0ms

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:
7.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
6.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
4.0ms
(/ 1/2 (hypot 1 x))
20.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

series160.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (+ 1/2 (/ 1/2 (hypot 1 x))))
44.0ms
(+ 1/2 (/ 1/2 (hypot 1 x)))
11.0ms
(/ 1/2 (hypot 1 x))
63.0ms
(- 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))

simplify1.1s

Counts
90 → 90
Iterations
IterNodes
done2001
32001
2747
1247
0118

prune776.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.7b

localize25.0ms

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)))

rewrite33.0ms

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:
18.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
3.0ms
(/ 1/2 (hypot 1 x))
4.0ms
(/ 1/2 (hypot 1 x))
5.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

series155.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ 1 (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))
11.0ms
(/ 1/2 (hypot 1 x))
10.0ms
(/ 1/2 (hypot 1 x))
58.0ms
(- 1/2 (/ 1/2 (hypot 1 x)))

simplify1.0s

Counts
99 → 99
Iterations
IterNodes
done2006
32006
2714
1232
0106

prune943.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

localize386.0ms

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

rewrite857.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
34×distribute-lft-out
20×add-log-exp
19×add-sqr-sqrt
18×times-frac
15×add-cube-cbrt
9×sum-log
7×flip3-+ flip-+
6×associate-/r* add-cbrt-cube add-exp-log
4×pow1 sqrt-div frac-add insert-posit16
3×distribute-rgt-out associate-/l*
2×+-commutative associate-+l+ flip3-- associate-/r/ sqrt-prod flip-- associate--r+ associate-/l/
1×distribute-rgt-in cbrt-undiv clear-num sub-neg frac-2neg distribute-lft-in distribute-lft1-in diff-log div-sub div-exp div-inv
Counts
4 → 102
Calls
4 calls:
98.0ms
(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
367.0ms
(+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1)
385.0ms
(/ (- 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))
4.0ms
(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

series560.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)))
97.0ms
(+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1)
226.0ms
(/ (- 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))
137.0ms
(- 1 (* (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2)) (+ (/ 1/2 (hypot 1 x)) 1/2)))

simplify1.8s

Counts
114 → 114
Iterations
IterNodes
done2001
32001
21930
1458
0167

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

localize143.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.1s

Algorithm
rewrite-expression-head
Rules
292×*-un-lft-identity
272×frac-times
224×flip3-+ flip-+
216×sqrt-div
192×times-frac
135×distribute-lft-out
130×pow1
91×add-sqr-sqrt
88×associate-*l/ associate-*r/
79×add-cube-cbrt
50×pow-prod-up
40×pow-prod-down
33×add-cbrt-cube add-exp-log
18×associate-/l*
16×sqrt-pow1 pow1/2 prod-exp associate-/r/ cbrt-unprod
14×pow-sqr
12×pow3
8×div-inv
6×associate-/r* add-log-exp
4×pow-plus insert-posit16
3×cbrt-undiv div-exp
2×pow2 div-sub swap-sqr associate-*r* associate-*l* *-commutative
1×clear-num sub-neg frac-2neg flip3-- diff-log flip-- associate-/l/
Counts
4 → 416
Calls
4 calls:
1.8s
(/ (/ (- 1 (* (* (* (+ 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))) (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))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) 1)) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
128.0ms
(* (* (+ 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))))))
114.0ms
(* (* (+ 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))))))
10.0ms
(- 1 (* (* (* (+ 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))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))

series966.0ms

Counts
4 → 12
Calls
4 calls:
627.0ms
(/ (/ (- 1 (* (* (* (+ 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))) (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))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))) 1)) (+ (+ (+ (/ 1/2 (hypot 1 x)) 1/2) (sqrt (+ (/ 1/2 (hypot 1 x)) 1/2))) 1))
63.0ms
(* (* (+ 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))))))
81.0ms
(* (* (+ 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))))))
195.0ms
(- 1 (* (* (* (+ 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))) (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))))))

simplify1.9s

Counts
428 → 428
Iterations
IterNodes
done2028
22028
11496
0453

prune7.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 12.4b

regimes56.0ms

Accuracy

0% (0.8b remaining)

Error of 15.6b against oracle of 14.8b and baseline of 15.6b

bsearch0.0ms

simplify23.0ms

Iterations
IterNodes
done40
140
027

end0.0ms

sample3.2s

Algorithm
intervals
Results
2.1s2799×body1280valid
448.0ms4097×body80valid
317.0ms624×body640valid
132.0ms321×body320valid
29.0ms159×body160valid