Details

sample283.0ms

Algorithm

intervals

Results

78.0ms	303×	body	80	valid
74.0ms	505×	body	80	nan

simplify1.3s

Counts: 1 → 1

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.3b

localize53.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
12.1b	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
7.0b	(* (* n (pow (/ l Om) 2)) (- U U*))
6.9b	(/ (* l l) Om)

rewrite322.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
30×	`prod-diff`
26×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`pow1`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube`
22×	`associate-*r/`
21×	`distribute-rgt-in` `distribute-lft-in`
16×	`prod-exp`
13×	`pow-prod-down`
11×	`flip3--` `flip--`
10×	`associate--l+` `cbrt-unprod`
8×	`associate-r` `frac-sub`
6×	`sub-neg` `sqrt-div`
4×	`expm1-log1p-u` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `div-exp`
2×	`cbrt-undiv` `associate-l` `pow-exp` `*-commutative`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow1/2` `sqrt-prod` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

Slowest

192.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
84.0ms	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
33.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
9.0ms	(/ (* l l) Om)

series2.3s

Counts

4 → 12

Calls

4 calls:

Slowest

1.5s	(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
589.0ms	(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
157.0ms	(* (* n (pow (/ l Om) 2)) (- U U*))
33.0ms	(/ (* l l) Om)

simplify2.0s

Counts: 157 → 157

prune3.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.6b

localize70.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
7.0b	(* (* n (* (/ l Om) (/ l Om))) (- U U*))
6.6b	(* n (* (/ l Om) (/ l Om)))
5.8b	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))

rewrite624.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-cbrt-cube` `add-exp-log`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
45×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`pow1`
42×	`add-cube-cbrt`
32×	`prod-exp` `cbrt-unprod`
26×	`associate-*r/`
25×	`pow-prod-down`
10×	`frac-times`
8×	`cbrt-undiv` `div-exp`
7×	`associate-r` `associate-*l/`
6×	`sub-neg` `flip3--` `flip--`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `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 → 186

Calls

4 calls:

Slowest

513.0ms	(* (* n (* (/ l Om) (/ l Om))) (- U U*))
42.0ms	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
36.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
28.0ms	(* n (* (/ l Om) (/ l Om)))

series1.8s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*)))))))
428.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
141.0ms	(* (* n (* (/ l Om) (/ l Om))) (- U U*))
54.0ms	(* n (* (/ l Om) (/ l Om)))

simplify1.4s

Counts: 198 → 198

prune3.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 18.9b

localize61.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))))
7.0b	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
5.8b	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
5.5b	(* n (/ l Om))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
51×	`*-un-lft-identity`
50×	`add-cbrt-cube` `add-exp-log`
49×	`add-cube-cbrt`
40×	`pow1`
27×	`prod-exp` `cbrt-unprod`
23×	`pow-prod-down`
20×	`associate-*r/`
19×	`associate-r`
10×	`times-frac`
9×	`frac-times`
6×	`cbrt-undiv` `sub-neg` `flip3--` `div-exp` `associate-*l/` `flip--`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 192

Calls

4 calls:

Slowest

87.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
41.0ms	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))))
32.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
14.0ms	(* n (/ l Om))

series1.8s

Counts

4 → 12

Calls

4 calls:

Slowest

1.2s	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))))
446.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
129.0ms	(* (* (* n (/ l Om)) (/ l Om)) (- U U*))
22.0ms	(* n (/ l Om))

simplify616.0ms

Counts: 204 → 204

prune3.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 18.4b

localize65.0ms

Local error

Found 4 expressions with local error:

19.0b	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))))
7.0b	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))
5.8b	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))))))
5.0b	(* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))

rewrite429.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
79×	`add-cbrt-cube`
72×	`prod-diff`
66×	`distribute-rgt-in` `distribute-lft-in`
64×	`prod-exp` `cbrt-unprod`
61×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
56×	`pow1`
55×	`add-cube-cbrt`
36×	`pow-prod-down`
27×	`associate-*r/`
11×	`cbrt-undiv` `div-exp` `associate-r`
9×	`frac-times`
8×	`sub-neg`
7×	`flip3--` `flip--`
6×	`associate-*l/`
5×	`sqrt-pow1` `associate-l`
4×	`expm1-log1p-u` `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 → 223

Calls

4 calls:

Slowest

347.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))
32.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))))))
31.0ms	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))))
14.0ms	(* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

Slowest

1.1s	(sqrt (* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))))
406.0ms	(* (* 2 n) (* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))))))
313.0ms	(* U (- t (fma 2 (/ l (/ Om l)) (* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*)))))
140.0ms	(* (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (/ l Om))) (/ l Om)) (- U U*))

simplify751.0ms

Counts: 235 → 235

prune3.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 18.4b

regimes857.0ms

Accuracy

24.1% (8.7b remaining)

Error of 26.8b against oracle of 18.1b and baseline of 29.6b

bsearch366.0ms

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.0s	14747×	body	80	nan
1.4s	9218×	body	80	valid