Details

Time bar (total: 4.4m)

sample59.0ms

Algorithm
intervals
Results
31.0ms92×body1280valid
8.0ms134×body80valid
4.0ms16×body640valid
2.0ms10×body320valid
0.0ms4×body160valid

simplify27.0ms

Counts
1 → 1
Iterations
IterNodes
done37
637
535
430
328
224
119
09

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize26.0ms

Local error

Found 3 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)))))
1.9b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity add-log-exp
6×pow1
5×add-sqr-sqrt
3×add-cbrt-cube add-exp-log add-cube-cbrt
2×sqrt-pow1 flip3-+ sqrt-div associate-*r/ flip-+
1×+-commutative sum-log sub-neg flip3-- pow1/2 diff-log pow-prod-down sqrt-prod flip-- distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
3 → 39
Calls
3 calls:
9.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
10.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
26.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series251.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
105.0ms
(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
117.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify384.0ms

Counts
48 → 48
Iterations
IterNodes
done5000
2625
1161
072

prune220.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×*-un-lft-identity
7×pow1
4×add-sqr-sqrt add-cbrt-cube associate--l+ associate-*r/ add-exp-log add-cube-cbrt
3×sub-neg flip3-+ flip-+
2×distribute-rgt-in +-commutative sum-log distribute-lft-in sqrt-pow1 flip3-- sqrt-div frac-sub flip-- distribute-lft-out
1×pow1/2 diff-log pow-prod-down sqrt-prod
Counts
4 → 55
Calls
4 calls:
9.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
24.0ms
(+ (/ 1.0 (hypot 1.0 x)) 1.0)
28.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
25.0ms
(- (* 1.0 (- 1.0 0.5)) (/ (* 1.0 0.5) (hypot 1.0 x)))

series336.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
48.0ms
(+ (/ 1.0 (hypot 1.0 x)) 1.0)
107.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
43.0ms
(- (* 1.0 (- 1.0 0.5)) (/ (* 1.0 0.5) (hypot 1.0 x)))

simplify758.0ms

Counts
67 → 67
Iterations
IterNodes
done5001
21334
1307
0118

prune396.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.6b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
54×associate-*l/
51×times-frac
46×*-un-lft-identity
34×associate-*r/
24×add-sqr-sqrt flip3-+ add-cube-cbrt flip-+
16×frac-sub
13×add-cbrt-cube add-exp-log
12×associate-/r/
11×distribute-lft-out
9×associate-/l*
8×frac-times add-log-exp
7×pow1 flip3-- flip--
6×div-inv
5×cbrt-undiv div-exp
4×associate-/r*
2×sqrt-pow1 sqrt-div div-sub sub-div
1×+-commutative clear-num sum-log sub-neg frac-2neg pow1/2 diff-log pow-prod-down prod-exp sqrt-prod cbrt-unprod associate-/l/
Counts
4 → 124
Calls
4 calls:
233.0ms
(/ (/ (- (* (hypot 1.0 x) (* (+ 1.0 0.5) (* (- 1.0 0.5) 1.0))) (* (* (+ 1.0 0.5) 1.0) 0.5)) (* (hypot 1.0 x) (+ 1.0 0.5))) (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
8.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
17.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
117.0ms
(- (* (hypot 1.0 x) (* (+ 1.0 0.5) (* (- 1.0 0.5) 1.0))) (* (* (+ 1.0 0.5) 1.0) 0.5))

series651.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ (/ (- (* (hypot 1.0 x) (* (+ 1.0 0.5) (* (- 1.0 0.5) 1.0))) (* (* (+ 1.0 0.5) 1.0) 0.5)) (* (hypot 1.0 x) (+ 1.0 0.5))) (+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))))
136.0ms
(+ 1.0 (sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0))))
105.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
57.0ms
(- (* (hypot 1.0 x) (* (+ 1.0 0.5) (* (- 1.0 0.5) 1.0))) (* (* (+ 1.0 0.5) 1.0) 0.5))

simplify535.0ms

Counts
136 → 136
Iterations
IterNodes
done5000
11055
0317

prune1.0s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.6b

localize124.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
0.1b
(* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0)))))
0.1b
(/ (- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (* (+ 0.5 1.0) (- 1.0 0.5))))
1.3b
(- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3)))))

rewrite11.2s

Algorithm
rewrite-expression-head
Rules
43732×frac-times
39800×associate-*r/
21642×flip3-+ flip-+
18140×associate-*l/
12985×flip3-- flip--
12584×frac-sub
6314×associate-/l/
78×add-cbrt-cube add-exp-log
72×pow1
54×prod-exp cbrt-unprod
52×pow-prod-down
40×sub-div
26×associate-/r/
12×distribute-rgt-in distribute-lft-in
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
4×associate--l+ associate--r+
3×cbrt-undiv times-frac div-exp associate-/l*
2×sqrt-pow1 sqrt-div
1×clear-num associate-/r* sub-neg frac-2neg pow1/2 diff-log div-sub associate-*r* associate-*l* *-commutative sqrt-prod div-inv
Counts
4 → 13007
Calls
4 calls:
21.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
734.0ms
(* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0)))))
3.0s
(/ (- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (* (+ 0.5 1.0) (- 1.0 0.5))))
1.1s
(- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3)))))

series378.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(sqrt (* 0.5 (+ (/ 1.0 (hypot 1.0 x)) 1.0)))
46.0ms
(* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0)))))
129.0ms
(/ (- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3))))) (* (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))) (* (+ 0.5 1.0) (- 1.0 0.5))))
86.0ms
(- (* (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* 1.0 (* (+ 0.5 1.0) (- 1.0 0.5)))) (* (hypot 1.0 x) (+ (* 1.0 1.0) (* 0.5 (- 0.5 1.0))))) (* (* (+ 0.5 1.0) (- 1.0 0.5)) (* (* 0.5 1.0) (+ (pow 0.5 3) (pow 1.0 3)))))

simplify15.0s

Counts
13019 → 13019
Iterations
IterNodes
done29492
029492

prune3.9m

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.3b

regimes112.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done35
235
134
023

end0.0ms

sample1.3s

Algorithm
intervals
Results
741.0ms2829×body1280valid
243.0ms4058×body80valid
98.0ms627×body640valid
39.0ms334×body320valid
11.0ms152×body160valid