Details

Time bar (total: 48.0s)

sample386.0ms

Algorithm
intervals
Results
157.0ms462×body80nan
68.0ms296×body80valid

simplify1.2s

Counts
1 → 1

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize53.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
8.7b
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
6.3b
(* (* (/ l Om) (/ l Om)) (- U U*))
5.4b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite353.0ms

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
103.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
100.0ms
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
95.0ms
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
48.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

series2.7s

Counts
4 → 12
Calls
4 calls:
Slowest
2.0s
(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
449.0ms
(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
124.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
101.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

simplify973.0ms

Counts
364 → 248

prune4.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.5b

localize48.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
9.6b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
6.3b
(* (* (/ l Om) (/ l Om)) (- U U*))
5.4b
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite279.0ms

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
107.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
81.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
49.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
38.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

series2.4s

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*)))))))
415.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
140.0ms
(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
75.0ms
(* (* (/ l Om) (/ l Om)) (- U U*))

simplify606.0ms

Counts
322 → 228

prune3.4s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.8b

localize31.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*))))))))
9.6b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*)))))))
5.4b
(* n (* (/ l Om) (* (/ l Om) (- U U*))))
5.2b
(* (/ l Om) (- U U*))

rewrite186.0ms

Algorithm
rewrite-expression-head
Rules
154×distribute-rgt-in distribute-lft-in
108×prod-diff
95×add-sqr-sqrt
90×*-un-lft-identity
86×add-cube-cbrt
47×add-cbrt-cube add-exp-log
34×pow1
26×associate-*r/
25×prod-exp cbrt-unprod
19×pow-prod-down
17×associate-*l*
12×sub-neg
11×frac-times associate-*r*
10×times-frac
8×flip3-- flip--
6×cbrt-undiv div-exp
4×expm1-log1p-u sqrt-pow1 associate-*l/ 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 → 262
Calls
4 calls:
Slowest
83.0ms
(* n (* (/ l Om) (* (/ l Om) (- U U*))))
40.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*)))))))
39.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*))))))))
18.0ms
(* (/ l Om) (- U U*))

series1.9s

Counts
4 → 12
Calls
4 calls:
Slowest
1.4s
(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*)))))))
107.0ms
(* n (* (/ l Om) (* (/ l Om) (- U U*))))
53.0ms
(* (/ l Om) (- U U*))

simplify691.0ms

Counts
409 → 274

prune3.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.8b

localize58.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*))))))))
9.6b
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*)))))))
6.6b
(* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)
5.2b
(* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
30×pow1
28×*-un-lft-identity
27×add-cbrt-cube add-exp-log
26×add-cube-cbrt
18×prod-diff
16×pow-prod-down
15×associate-*l*
13×prod-exp cbrt-unprod
12×distribute-rgt-in distribute-lft-in
11×associate-*r*
10×times-frac
4×expm1-log1p-u sqrt-pow1 associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l/ *-commutative
2×cbrt-undiv sub-neg flip3-- sqrt-div div-exp fma-udef flip-- unswap-sqr
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 129
Calls
4 calls:
Slowest
41.0ms
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*)))))))
38.0ms
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*))))))))
21.0ms
(* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)
9.0ms
(* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*)))

series15.0s

Counts
4 → 12
Calls
4 calls:
Slowest
11.0s
(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*))))))))
3.7s
(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (+ (* (/ l Om) (* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)) (* (* n (/ l Om)) (* (/ l Om) (fma (- U*) 1 U*)))))))
201.0ms
(* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)
166.0ms
(* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*)))

simplify514.0ms

Counts
166 → 141

prune2.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.6b

regimes887.0ms

Accuracy

9.6% (10.4b remaining)

Error of 28.6b against oracle of 18.2b and baseline of 29.7b

bsearch466.0ms

end0.0ms

sample5.5s

Algorithm
intervals
Results
2.9s14810×body80nan
1.7s9193×body80valid