Details

Time bar (total: 18.5s)

sample51.0ms

Algorithm
intervals
Results
22.0ms82×body1280valid
7.0ms139×body80valid
4.0ms19×body640valid
2.0ms13×body320valid
0.0ms3×body160valid

simplify27.0ms

Counts
1 → 1
Iterations
IterNodes
done30
430
328
224
119
09

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.0b

localize17.0ms

Local error

Found 1 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 14
Calls
1 calls:
5.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series110.0ms

Counts
1 → 3
Calls
1 calls:
110.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.7s

Counts
17 → 17
Iterations
IterNodes
done5000
43476
3832
2252
188
043

prune83.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 15.4b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite550.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
22×associate-*r/
15×*-un-lft-identity
13×add-sqr-sqrt add-cube-cbrt
12×flip3-+ flip-+
11×add-cbrt-cube add-exp-log
9×times-frac pow-prod-down
8×distribute-rgt-in distribute-lft-in add-log-exp
6×sqrt-pow1 sqrt-div associate-/r/ pow-prod-up
4×frac-times associate-*l* frac-add associate--r+
3×associate-/r* pow-plus pow1/2 prod-exp cbrt-unprod associate-/l*
2×flip3-- associate-*l/ flip-- associate-/l/
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg diff-log div-sub div-exp associate-*r* *-commutative sqrt-prod div-inv distribute-lft-out
Counts
4 → 104
Calls
4 calls:
330.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
113.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
97.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series1.1s

Counts
4 → 12
Calls
4 calls:
492.0ms
(/ (- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))) (+ (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
223.0ms
(* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
119.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
228.0ms
(- (* 1.0 (* 1.0 1.0)) (* (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify2.6s

Counts
116 → 116
Iterations
IterNodes
done5004
23183
1666
0220

prune636.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize159.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.8b
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
1.3b
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
1.6b
(- (* (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)))))))

rewrite253.0ms

Algorithm
rewrite-expression-head
Rules
81×associate-*r/
48×sqrt-div
24×flip3-+ flip-+
19×frac-sub
12×add-log-exp
9×frac-times
8×associate-*l/
6×add-sqr-sqrt *-un-lft-identity sub-div
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip--
2×distribute-rgt-out--
1×distribute-lft-out-- difference-of-squares
Counts
4 → 77
Calls
4 calls:
103.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
16.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
16.0ms
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
112.0ms
(- (* (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)))))))

series830.0ms

Counts
4 → 12
Calls
4 calls:
251.0ms
(- (* (* 1.0 1.0) 1.0) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
111.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
95.0ms
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
372.0ms
(- (* (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)))))))

simplify2.0s

Counts
89 → 89
Iterations
IterNodes
done5002
22257
1605
0226

prune927.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize186.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (/ 1.0 (hypot 1.0 x)) 1.0)
0.8b
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
1.3b
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
1.6b
(- (* (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)))))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
81×associate-*r/
48×sqrt-div
24×flip3-+ flip-+
19×frac-sub
12×add-log-exp
11×add-sqr-sqrt
9×frac-times
8×*-un-lft-identity associate-*l/
6×sub-div
4×pow1 sub-neg flip3-- add-cbrt-cube diff-log add-exp-log add-cube-cbrt flip--
3×difference-of-squares
2×distribute-rgt-out-- distribute-lft-out--
1×times-frac
Counts
4 → 80
Calls
4 calls:
15.0ms
(- (/ 1.0 (hypot 1.0 x)) 1.0)
11.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
16.0ms
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
88.0ms
(- (* (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)))))))

series667.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (/ 1.0 (hypot 1.0 x)) 1.0)
107.0ms
(- (* (/ 1.0 (hypot 1.0 x)) (/ 1.0 (hypot 1.0 x))) (* 1.0 (/ 1.0 (hypot 1.0 x))))
137.0ms
(- (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 1.0)
379.0ms
(- (* (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)))))))

simplify1.9s

Counts
92 → 92
Iterations
IterNodes
done5002
21942
1548
0219

prune1.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

regimes212.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify19.0ms

Iterations
IterNodes
done64
164
041

end0.0ms

sample2.1s

Algorithm
intervals
Results
995.0ms2843×body1280valid
657.0ms4049×body80valid
183.0ms638×body640valid
98.0ms335×body320valid
14.0ms135×body160valid