Details

Time bar (total: 34.5s)

sample208.0ms

Algorithm
intervals
Results
93.0ms470×body80nan
74.0ms291×body80valid

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
done2001
42001
3642
2155
150
021

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.5b

localize36.0ms

Local error

Found 4 expressions with local error:

6.5b
(* n (/ l Om))
7.6b
(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l)))))
7.8b
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
18.9b
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
50×add-cbrt-cube add-exp-log
40×pow1
27×prod-exp cbrt-unprod
23×pow-prod-down
20×add-sqr-sqrt associate-*r/
19×associate-*r*
15×*-un-lft-identity
13×add-cube-cbrt
10×distribute-rgt-in distribute-lft-in times-frac
9×frac-times
6×cbrt-undiv sub-neg flip3-- div-exp associate-*l/ flip--
5×sqrt-pow1 associate-*l*
4×insert-posit16 add-log-exp
3×*-commutative
2×sqrt-div unswap-sqr
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 130
Calls
4 calls:
8.0ms
(* n (/ l Om))
620.0ms
(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l)))))
116.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
674.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
30.0ms
(* n (/ l Om))
453.0ms
(* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l)))))
142.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
1.9s
(sqrt (* (* U 2) (* n (- t (+ (* (* (* n (/ l Om)) (/ l Om)) (- U U*)) (* (* (/ l Om) 2) l))))))

simplify903.0ms

Counts
142 → 142
Iterations
IterNodes
done2001
22001
1905
0292

prune784.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.4b

localize54.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (/ l Om) (- U U*))
6.5b
(* n (/ l Om))
7.6b
(* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l)))))
18.9b
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l))))))

rewrite597.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1
32×add-sqr-sqrt
26×add-cbrt-cube add-exp-log
22×*-un-lft-identity
20×times-frac add-cube-cbrt
19×associate-*r*
18×pow-prod-down
17×associate-*l*
12×prod-exp cbrt-unprod
11×associate-*r/
10×distribute-rgt-in distribute-lft-in
6×sub-neg
5×sqrt-pow1
4×flip3-- insert-posit16 flip-- add-log-exp unswap-sqr
3×*-commutative
2×frac-times cbrt-undiv sqrt-div div-exp div-inv
1×pow1/2 associate-*l/ sqrt-prod distribute-lft-out-- difference-of-squares
Counts
4 → 126
Calls
4 calls:
18.0ms
(* (/ l Om) (- U U*))
8.0ms
(* n (/ l Om))
274.0ms
(* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l)))))
295.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l))))))

series2.3s

Counts
4 → 12
Calls
4 calls:
57.0ms
(* (/ l Om) (- U U*))
26.0ms
(* n (/ l Om))
446.0ms
(* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l)))))
1.7s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (/ l Om) (- U U*))) (* (* (/ l Om) 2) l))))))

simplify971.0ms

Counts
138 → 138
Iterations
IterNodes
done2006
22006
1797
0274

prune899.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 18.8b

localize68.0ms

Local error

Found 4 expressions with local error:

12.0b
(cbrt (* (/ l Om) (- U U*)))
12.0b
(cbrt (* (/ l Om) (- U U*)))
12.0b
(cbrt (* (/ l Om) (- U U*)))
18.9b
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

rewrite430.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
15×cbrt-div
10×associate-*r/
8×pow-prod-down
7×flip3-- flip--
6×frac-times
5×sqrt-pow1
4×add-sqr-sqrt *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod pow1/3 associate-*l/
2×sqrt-div
1×pow1/2 sqrt-prod
Counts
4 → 62
Calls
4 calls:
6.0ms
(cbrt (* (/ l Om) (- U U*)))
6.0ms
(cbrt (* (/ l Om) (- U U*)))
7.0ms
(cbrt (* (/ l Om) (- U U*)))
409.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (* (/ l Om) (- U U*)))
157.0ms
(cbrt (* (/ l Om) (- U U*)))
134.0ms
(cbrt (* (/ l Om) (- U U*)))
1.9s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

simplify1.0s

Counts
74 → 74
Iterations
IterNodes
done2005
32005
21171
1347
0142

prune984.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 18.8b

localize101.0ms

Local error

Found 4 expressions with local error:

12.0b
(cbrt (* (/ l Om) (- U U*)))
12.0b
(cbrt (* (/ l Om) (- U U*)))
18.9b
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
18.9b
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

rewrite682.0ms

Algorithm
rewrite-expression-head
Rules
30×pow1
16×pow-prod-down
12×associate-*r/
10×cbrt-div sqrt-pow1
6×flip3-- flip--
4×add-sqr-sqrt frac-times *-un-lft-identity add-cbrt-cube sqrt-div add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×cbrt-prod pow1/2 pow1/3 associate-*l/ sqrt-prod
Counts
4 → 64
Calls
4 calls:
7.0ms
(cbrt (* (/ l Om) (- U U*)))
8.0ms
(cbrt (* (/ l Om) (- U U*)))
336.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
330.0ms
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

series4.6s

Counts
4 → 12
Calls
4 calls:
171.0ms
(cbrt (* (/ l Om) (- U U*)))
198.0ms
(cbrt (* (/ l Om) (- U U*)))
2.2s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))
2.0s
(sqrt (* (* U 2) (* n (- t (+ (* (* n (/ l Om)) (* (* (cbrt (* (/ l Om) (- U U*))) (cbrt (* (/ l Om) (- U U*)))) (cbrt (* (/ l Om) (- U U*))))) (* (* (/ l Om) 2) l))))))

simplify1.2s

Counts
76 → 76
Iterations
IterNodes
done2005
32005
21171
1347
0142

prune893.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 18.8b

regimes1.5s

Accuracy

38.7% (5.5b remaining)

Error of 26.3b against oracle of 20.8b and baseline of 29.8b

bsearch250.0ms

Steps
ItersRangePoint
8
9.676127460712857e-291
3.0105414651711707e-287
1.0337592973629363e-288

simplify8.0ms

Iterations
IterNodes
done36
136
026

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.9s14938×body80nan
2.5s9232×body80valid