Details

sample246.0ms

Algorithm

intervals

Results

110.0ms	462×	body	80	nan
87.0ms	296×	body	80	valid

simplify855.0ms

Counts: 1 → 1

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.2b

localize40.0ms

Local error

Found 4 expressions with local error:

17.6b	(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
8.7b	(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
8.2b	(/ Om (* l l))
7.8b	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

1844×	`times-frac`
803×	`add-sqr-sqrt`
774×	`*-un-lft-identity`
772×	`add-cube-cbrt`
580×	`associate-l`
98×	`div-inv`
47×	`add-cbrt-cube` `add-exp-log`
26×	`associate-*r/`
25×	`pow1`
17×	`cbrt-undiv` `div-exp`
14×	`distribute-rgt-in` `distribute-lft-in` `prod-exp` `associate-/r/` `cbrt-unprod`
13×	`pow-prod-down`
7×	`unswap-sqr`
6×	`associate-r`
4×	`sqrt-pow1` `flip3--` `sqrt-div` `frac-add` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/l*`
2×	`frac-times` `sub-neg` `flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `associate-/r` `frac-2neg` `pow1/2` `associate-l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 696

Calls

4 calls:

Slowest

183.0ms	(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
174.0ms	(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
42.0ms	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
6.0ms	(/ Om (* l l))

series2.6s

Counts

4 → 12

Calls

4 calls:

Slowest

2.0s	(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
453.0ms	(* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
144.0ms	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
29.0ms	(/ Om (* l l))

simplify2.1s

Counts: 735 → 708

prune14.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 20.7b

localize40.0ms

Local error

Found 4 expressions with local error:

17.6b	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
8.7b	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
7.8b	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
3.1b	(/ n (/ Om l))

rewrite578.0ms

Algorithm

rewrite-expression-head

Rules

1916×	`times-frac`
843×	`add-sqr-sqrt`
814×	`*-un-lft-identity`
812×	`add-cube-cbrt`
580×	`associate-l`
102×	`div-inv`
47×	`add-cbrt-cube` `add-exp-log`
26×	`associate-*r/`
25×	`pow1`
18×	`cbrt-undiv` `div-exp`
15×	`associate-/r/`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`unswap-sqr`
6×	`associate-r`
4×	`sqrt-pow1` `flip3--` `sqrt-div` `frac-add` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/l*`
2×	`frac-times` `sub-neg` `flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 745

Calls

4 calls:

Slowest

281.0ms	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
188.0ms	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
60.0ms	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
6.0ms	(/ n (/ Om l))

series2.8s

Counts

4 → 12

Calls

4 calls:

Slowest

2.2s	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
393.0ms	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
146.0ms	(* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))
41.0ms	(/ n (/ Om l))

simplify2.5s

Counts: 820 → 757

prune15.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 20.2b

localize139.0ms

Local error

Found 4 expressions with local error:

17.6b	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*)))))))))
8.7b	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))))))))
6.6b	(* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))
3.1b	(/ n (/ Om l))

rewrite789.0ms

Algorithm

rewrite-expression-head

Rules

6101×	`times-frac`
2625×	`add-sqr-sqrt`
2551×	`*-un-lft-identity`
2549×	`add-cube-cbrt`
1768×	`associate-l`
1596×	`cbrt-prod`
210×	`div-inv`
47×	`add-exp-log`
42×	`associate-/r/`
41×	`add-cbrt-cube`
26×	`associate-*r/`
25×	`pow1`
18×	`cbrt-undiv` `div-exp`
16×	`unswap-sqr`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`associate-/r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-r`
4×	`sqrt-pow1` `flip3--` `sqrt-div` `frac-add` `insert-posit16` `flip--` `add-log-exp`
3×	`associate-/l*`
2×	`frac-times` `sub-neg` `flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-*l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 1942

Calls

4 calls:

Slowest

323.0ms	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))))))))
220.0ms	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*)))))))))
91.0ms	(* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))
11.0ms	(/ n (/ Om l))

series3.5s

Counts

4 → 12

Calls

4 calls:

Slowest

2.7s	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*)))))))))
442.0ms	(* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (/ (* (cbrt Om) (cbrt Om)) (* (cbrt l) (cbrt l)))) (* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))))))))
338.0ms	(* (/ (/ n (/ Om l)) (/ (cbrt Om) (cbrt l))) (- U U*))
26.0ms	(/ n (/ Om l))

simplify6.4s

Counts: 2026 → 1954

prune53.3s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 20.2b

localize64.0ms

Local error

Found 4 expressions with local error:

17.6b	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (* (/ (/ n (/ Om l)) (cbrt (/ Om l))) (- U U*)))))))))
12.1b	(cbrt (/ Om l))
12.1b	(cbrt (/ Om l))
12.1b	(cbrt (/ Om l))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
12×	`associate-*r/`
6×	`pow-prod-down`
4×	`sqrt-pow1` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`frac-add`
1×	`flip3-+` `flip3--` `pow1/2` `sqrt-prod` `flip-+` `flip--`

Counts

4 → 87

Calls

4 calls:

Slowest

289.0ms	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (* (/ (/ n (/ Om l)) (cbrt (/ Om l))) (- U U*)))))))))
3.0ms	(cbrt (/ Om l))
2.0ms	(cbrt (/ Om l))
2.0ms	(cbrt (/ Om l))

series2.7s

Counts

4 → 12

Calls

4 calls:

Slowest

2.4s	(sqrt (* U (* 2 (* n (+ (/ -2 (/ (/ Om l) l)) (- t (* (/ 1 (* (cbrt (/ Om l)) (cbrt (/ Om l)))) (* (/ (/ n (/ Om l)) (cbrt (/ Om l))) (- U U*)))))))))
106.0ms	(cbrt (/ Om l))
84.0ms	(cbrt (/ Om l))
83.0ms	(cbrt (/ Om l))

simplify950.0ms

Counts: 142 → 99

prune1.9s

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 20.2b

regimes2.1s

Accuracy

35.5% (5.3b remaining)

Error of 26.5b against oracle of 21.2b and baseline of 29.4b

bsearch42.0ms

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.9s	14810×	body	80	nan
2.1s	9193×	body	80	valid