Details

sample633.0ms

Algorithm

intervals

Results

357.0ms	498×	body	80	nan
100.0ms	292×	body	80	valid

simplify225.0ms

Calls

1 calls:

Slowest

224.0ms

(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.7b

localize48.0ms

Local error

Found 4 expressions with local error:

20.1b	(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
7.5b	(/ (* l l) Om)
6.3b	(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite22.6s

Algorithm

rewrite-expression-head

Rules

890×	`frac-times`
593×	`add-sqr-sqrt`
399×	`*-un-lft-identity`
385×	`add-cube-cbrt`
381×	`associate-/l*`
369×	`associate-*r/`
363×	`associate-/r*`
256×	`associate-*l/`
205×	`flip3--` `flip--`
191×	`associate-r`
149×	`times-frac`
147×	`associate-l`
127×	`clear-num`
121×	`frac-2neg`
100×	`unswap-sqr`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
52×	`add-cbrt-cube` `add-exp-log`
46×	`swap-sqr` `sqrt-prod`
28×	`pow1`
25×	`prod-exp` `cbrt-unprod`
16×	`*-commutative`
15×	`pow-prod-down`
13×	`difference-of-squares`
12×	`un-div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`div-inv`
6×	`sub-neg`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`sqrt-div`
1×	`pow1/2`

Calls

4 calls:

Slowest

22.2s	(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
205.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
67.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
12.0ms	(/ (* l l) Om)

series1.9s

Calls

4 calls:

Slowest

1.7s	(sqrt (* 2 (* U (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*))))))))
109.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
66.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
19.0ms	(/ (* l l) Om)

simplify2.3m

Calls

1233 calls:

Slowest

550.0ms	(* (* (sqrt l) (/ l (* (cbrt Om) (cbrt Om)))) (- (* U U) (* U* U*)))
515.0ms	(/ (* (* (* l l) (* l l)) (* l l)) (* (* Om Om) Om))
425.0ms	(* (* (* n n) n) (* (* (/ (* (* l l) l) (* (* Om Om) Om)) (/ (* (* l l) l) (* (* Om Om) Om))) (* (* (- U U) (- U U)) (- U U*))))
389.0ms	(* (* 1 l) (- (* U U) (* U* U*)))
389.0ms	(* (* (/ l (* (cbrt Om) (cbrt Om))) 1) (- (pow U 3) (pow U* 3)))

prune11.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 14.7b

localize46.0ms

Local error

Found 4 expressions with local error:

15.9b	(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
7.5b	(/ (* l l) Om)
6.3b	(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))

rewrite5.3s

Algorithm

rewrite-expression-head

Rules

890×	`frac-times`
589×	`add-sqr-sqrt`
398×	`*-un-lft-identity`
384×	`add-cube-cbrt`
381×	`associate-/l*`
367×	`associate-*r/`
363×	`associate-/r*`
256×	`associate-*l/`
205×	`flip3--` `flip--`
156×	`associate-r`
149×	`times-frac`
147×	`associate-l`
127×	`clear-num`
121×	`frac-2neg`
97×	`unswap-sqr`
55×	`distribute-rgt-in` `distribute-lft-in`
54×	`prod-diff`
52×	`add-cbrt-cube` `add-exp-log`
46×	`swap-sqr`
40×	`sqrt-prod`
25×	`prod-exp` `cbrt-unprod`
24×	`pow1`
15×	`*-commutative`
13×	`difference-of-squares`
12×	`pow-prod-down` `un-div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`div-inv`
7×	`cbrt-prod`
6×	`sub-neg`
5×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`sqrt-pow1`
2×	`sqrt-div`
1×	`pow1/2`

Calls

4 calls:

Slowest

5.0s	(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
194.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
65.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
12.0ms	(/ (* l l) Om)

series6.2s

Calls

4 calls:

Slowest

6.0s	(sqrt (* (cbrt U) (* n (- (fma (/ (* l l) Om) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
107.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
62.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))
22.0ms	(/ (* l l) Om)

simplify2.2m

Calls

1227 calls:

Slowest

511.0ms	(* (* (/ l Om) (* (cbrt l) (cbrt l))) (- (pow U 3) (pow U* 3)))
452.0ms	(* (* (* (cbrt l) (cbrt l)) (* (cbrt l) (cbrt l))) (- (* U U) (* U* U*)))
436.0ms	(* (* (- l) (- l)) (- (* U U) (* U* U*)))
425.0ms	(* (* (cbrt Om) (sqrt Om)) (+ (* U U) (+ (* U* U) ( U U*))))
422.0ms	(* (* (* n n) n) (* (* (/ (* (* l l) l) (* (* Om Om) Om)) (/ (* (* l l) l) (* (* Om Om) Om))) (* (* (- U U) (- U U)) (- U U*))))

prune14.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 13.2b

localize52.0ms

Local error

Found 4 expressions with local error:

15.9b	(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
6.3b	(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
3.6b	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))

rewrite6.2s

Algorithm

rewrite-expression-head

Rules

1454×	`add-sqr-sqrt`
890×	`frac-times`
748×	`*-un-lft-identity`
718×	`add-cube-cbrt`
670×	`associate-r`
564×	`prod-diff`
523×	`associate-l`
422×	`times-frac`
369×	`associate-*r/`
366×	`associate-/l*`
360×	`associate-/r*`
357×	`unswap-sqr`
313×	`distribute-rgt-in` `distribute-lft-in`
256×	`associate-*l/`
206×	`flip3--` `flip--`
138×	`swap-sqr`
126×	`clear-num`
120×	`frac-2neg`
49×	`add-cbrt-cube` `add-exp-log`
43×	`*-commutative`
40×	`sqrt-prod`
32×	`div-inv`
30×	`difference-of-squares`
26×	`pow1`
25×	`prod-exp` `cbrt-unprod`
13×	`pow-prod-down`
12×	`un-div-inv` `distribute-lft-out--`
8×	`cbrt-undiv` `sub-neg` `div-exp`
7×	`cbrt-prod`
5×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`sqrt-div` `associate--l+` `fma-udef`
1×	`pow1/2`

Calls

4 calls:

Slowest

5.0s	(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
921.0ms	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
194.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
65.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))

series6.4s

Calls

4 calls:

Slowest

5.9s	(sqrt (* (cbrt U) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
313.0ms	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
107.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
62.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))

simplify3.6m

Calls

1661 calls:

Slowest

565.0ms	(* (* (- l) (/ l Om)) (- (pow U 3) (pow U* 3)))
542.0ms	(* (* (/ l (sqrt Om)) (- l)) (- (* U U) (* U* U*)))
467.0ms	(* (fma (- (* (sqrt n) (* (* (sqrt (/ l Om)) (/ (sqrt l) (sqrt Om))) (sqrt (- U U))))) ( (sqrt n) (* (* (sqrt (/ l Om)) (/ (sqrt l) (sqrt Om))) (sqrt (- U U)))) ( (* (sqrt n) (* (* (sqrt (/ l Om)) (/ (sqrt l) (sqrt Om))) (sqrt (- U U)))) ( (sqrt n) (* (* (sqrt (/ l Om)) (/ (sqrt l) (sqrt Om))) (sqrt (- U U*)))))) n)
448.0ms	(* (* (- l) (- l)) (- (* U U) (* U* U*)))
442.0ms	(* (* (/ (cbrt l) (sqrt Om)) (/ (cbrt l) (sqrt Om))) (- U U*))

prune23.4s

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 12.5b

localize62.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (* (cbrt (cbrt U)) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
6.3b	(* (* (/ l Om) (/ l Om)) (- U U*))
6.1b	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
3.6b	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))

rewrite6.2s

Algorithm

rewrite-expression-head

Rules

1465×	`add-sqr-sqrt`
890×	`frac-times`
749×	`*-un-lft-identity`
719×	`add-cube-cbrt`
670×	`associate-r`
564×	`prod-diff`
526×	`associate-l`
422×	`times-frac`
369×	`associate-*r/`
366×	`associate-/l*`
363×	`unswap-sqr`
360×	`associate-/r*`
313×	`distribute-rgt-in` `distribute-lft-in`
256×	`associate-*l/`
206×	`flip3--` `flip--`
138×	`swap-sqr`
126×	`clear-num`
120×	`frac-2neg`
49×	`add-cbrt-cube` `add-exp-log`
45×	`sqrt-prod`
43×	`*-commutative`
32×	`div-inv`
30×	`difference-of-squares`
26×	`pow1`
25×	`prod-exp` `cbrt-unprod`
21×	`cbrt-prod`
13×	`pow-prod-down`
12×	`un-div-inv` `distribute-lft-out--`
8×	`cbrt-undiv` `sub-neg` `div-exp`
7×	`rem-sqrt-square`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1`
2×	`sqrt-div` `associate--l+` `fma-udef`
1×	`pow1/2`

Calls

4 calls:

Slowest

5.0s	(sqrt (* (cbrt (cbrt U)) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
915.0ms	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
194.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
64.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))

series6.7s

Calls

4 calls:

Slowest

6.2s	(sqrt (* (cbrt (cbrt U)) (* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))))
317.0ms	(* n (- (fma (* (/ (/ l (cbrt Om)) (cbrt Om)) (/ l (cbrt Om))) -2 t) (* n (* (* (/ l Om) (/ l Om)) (- U U*)))))
110.0ms	(* n (* (* (/ l Om) (/ l Om)) (- U U*)))
62.0ms	(* (* (/ l Om) (/ l Om)) (- U U*))