Details

Time bar (total: 35.1s)

sample352.0ms

Algorithm
intervals
Results
130.0ms459×body80nan
63.0ms299×body80valid

simplify1.3s

Counts
1 → 1

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.2b

localize71.0ms

Local error

Found 4 expressions with local error:

18.5b
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
7.6b
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
7.0b
(* (* (/ l Om) (/ l Om)) (- U U*))
5.3b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite289.0ms

Algorithm
rewrite-expression-head
Rules
99×distribute-rgt-in distribute-lft-in
90×prod-diff
70×add-sqr-sqrt
69×*-un-lft-identity
67×add-cube-cbrt
56×add-cbrt-cube add-exp-log
37×pow1
30×prod-exp cbrt-unprod
29×associate-*r/
21×pow-prod-down
18×frac-times
12×associate-*l/
10×sub-neg flip3-- flip--
8×cbrt-undiv div-exp
7×associate-*r* associate-*l*
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×sqrt-div
1×pow1/2 sqrt-prod distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 236
Calls
4 calls:
Slowest
99.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
75.0ms
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
55.0ms
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
49.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

series2.9s

Counts
4 → 12
Calls
4 calls:
Slowest
2.2s
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
515.0ms
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
156.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
115.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

simplify829.0ms

Counts
248 → 248

prune4.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.4b

localize36.0ms

Local error

Found 4 expressions with local error:

18.5b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
9.8b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
7.0b
(* (* (/ l Om) (/ l Om)) (- U U*))
5.3b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
72×prod-diff
66×distribute-rgt-in distribute-lft-in
60×add-sqr-sqrt
59×*-un-lft-identity
56×add-cbrt-cube add-exp-log
55×add-cube-cbrt
37×pow1
30×prod-exp cbrt-unprod
25×associate-*r/
21×pow-prod-down
18×frac-times
12×associate-*l/
11×associate-*r*
10×flip3-- flip--
8×cbrt-undiv sub-neg div-exp
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×sqrt-div distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod unswap-sqr
Counts
4 → 216
Calls
4 calls:
Slowest
91.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
57.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
48.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
39.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

series2.5s

Counts
4 → 12
Calls
4 calls:
Slowest
1.8s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
419.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
132.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
80.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

simplify614.0ms

Counts
228 → 228

prune3.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 16.5b

localize33.0ms

Local error

Found 4 expressions with local error:

18.5b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
9.8b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
5.6b
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
4.5b
(* n (* (/ l Om) (/ l Om)))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
56×add-cbrt-cube add-exp-log
37×pow1
36×add-sqr-sqrt prod-diff
35×*-un-lft-identity
31×add-cube-cbrt
30×prod-exp cbrt-unprod
22×distribute-rgt-in distribute-lft-in associate-*r/
21×pow-prod-down
11×associate-*r*
10×frac-times
8×cbrt-undiv div-exp
7×associate-*l/
6×flip3-- flip--
5×associate-*l*
4×expm1-log1p-u sub-neg sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×sqrt-div distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod unswap-sqr
Counts
4 → 164
Calls
4 calls:
Slowest
78.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
47.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
44.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
22.0ms
(* n (* (/ l Om) (/ l Om)))

series2.1s

Counts
4 → 12
Calls
4 calls:
Slowest
1.6s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
345.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))
108.0ms
(* (* n (* (/ l Om) (/ l Om))) (- U U*))
52.0ms
(* n (* (/ l Om) (/ l Om)))

simplify1.1s

Counts
176 → 176

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 16.2b

localize32.0ms

Local error

Found 4 expressions with local error:

18.5b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
9.8b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
6.1b
(* n (/ l Om))
5.6b
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt add-cbrt-cube add-exp-log
42×*-un-lft-identity
38×add-cube-cbrt
36×prod-diff
34×pow1
25×prod-exp cbrt-unprod
23×associate-*r*
22×distribute-rgt-in distribute-lft-in
19×pow-prod-down
16×associate-*r/
10×times-frac
9×frac-times
6×cbrt-undiv flip3-- div-exp associate-*l/ flip--
5×associate-*l*
4×expm1-log1p-u sub-neg sqrt-pow1 insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×sqrt-div distribute-lft-out-- difference-of-squares unswap-sqr
1×pow1/2 sqrt-prod div-inv
Counts
4 → 170
Calls
4 calls:
Slowest
74.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
41.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
38.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
9.0ms
(* n (/ l Om))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
349.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))
109.0ms
(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
21.0ms
(* n (/ l Om))

simplify1.1s

Counts
182 → 182

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.5b

regimes841.0ms

Accuracy

14.7% (10.2b remaining)

Error of 28.3b against oracle of 18.1b and baseline of 30.1b

bsearch370.0ms

end0.0ms

sample5.8s

Algorithm
intervals
Results
3.0s14946×body80nan
1.6s9183×body80valid