Details

sample250.0ms

Algorithm

intervals

Results

133.0ms	462×	body	80	nan
68.0ms	296×	body	80	valid

simplify1.2s

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.9b

localize73.0ms

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*)))

rewrite314.0ms

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

108.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
74.0ms	(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
64.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
63.0ms	(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))

series2.9s

Counts

4 → 12

Calls

4 calls:

Slowest

2.1s	(sqrt (* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
548.0ms	(* U (* (* 2 n) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
149.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
77.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))

simplify873.0ms

Counts: 364 → 248

prune4.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 19.5b

localize51.0ms

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*)))

rewrite308.0ms

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

112.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
70.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
64.0ms	(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
53.0ms	(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))

series3.0s

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*)))))))
505.0ms	(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))
189.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
104.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))

simplify706.0ms

Counts: 322 → 228

prune4.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.8b

localize64.0ms

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*))

rewrite323.0ms

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

166.0ms	(* n (* (/ l Om) (* (/ l Om) (- U U*))))
74.0ms	(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*)))))))
50.0ms	(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*))))))))
27.0ms	(* (/ l Om) (- U U*))

series2.8s

Counts

4 → 12

Calls

4 calls:

Slowest

2.1s	(sqrt (* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*))))))))
457.0ms	(* (* U (* 2 n)) (- t (fma (/ l Om) (* 2 l) (* n (* (/ l Om) (* (/ l Om) (- U U*)))))))
153.0ms	(* n (* (/ l Om) (* (/ l Om) (- U U*))))
86.0ms	(* (/ l Om) (- U U*))

simplify1.0s

Counts: 409 → 274

prune5.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.8b

localize90.0ms

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*)))

rewrite144.0ms

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

52.0ms	(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))))))))
49.0ms	(* (* 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)))))))
31.0ms	(* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)
10.0ms	(* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*)))

series22.6s

Counts

4 → 12

Calls

4 calls:

Slowest

16.4s	(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))))))))
5.7s	(* (* 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)))))))
336.0ms	(* (* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*))) n)
246.0ms	(* (/ l Om) (fma (* (cbrt U) (cbrt U)) (cbrt U) (- U*)))

simplify733.0ms

Counts: 166 → 141

prune3.5s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.6b

regimes1.4s

Accuracy

9.6% (10.4b remaining)

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

bsearch694.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.2s	14810×	body	80	nan
2.4s	9193×	body	80	valid