Details

sample229.0ms

Algorithm

intervals

Results

130.0ms	460×	body	80	nan
59.0ms	300×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
4	3017
3	618
2	155
1	50
0	21

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 26.3b

localize37.0ms

Local error

Found 4 expressions with local error:

4.6b	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
5.0b	(/ n (/ Om l))
6.3b	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
19.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
46×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
29×	`pow1`
21×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down`
13×	`associate-/r*`
8×	`prod-exp` `cbrt-unprod`
5×	`sqrt-pow1` `fma-udef` `div-inv`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-r` `associate-l` `associate-/r/` `*-commutative` `sqrt-prod`

Counts

4 → 130

Calls

4 calls:

0.0ms	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
9.0ms	(/ n (/ Om l))
26.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
39.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

317.0ms	(fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
38.0ms	(/ n (/ Om l))
415.0ms	(* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.3s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify874.0ms

Counts

142 → 142

Iterations

Iter	Nodes
2	2590
1	740
0	284

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.3b

localize57.0ms

Local error

Found 4 expressions with local error:

4.5b	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
4.6b	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
6.3b	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
19.3b	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`fma-udef`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in` `sqrt-pow1`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`pow1/2` `sqrt-prod` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

8.0ms	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
0.0ms	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
36.0ms	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
24.0ms	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.3s

Counts

4 → 12

Calls

4 calls:

329.0ms	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
347.0ms	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
385.0ms	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.3s	(sqrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify4.0s

Counts

92 → 92

Iterations

Iter	Nodes
3	7883
2	1351
1	360
0	144

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.0b

localize157.0ms

Local error

Found 4 expressions with local error:

19.3b	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
20.5b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.5b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
20.5b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`pow-prod-up`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 63

Calls

4 calls:

117.0ms	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
29.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
28.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
30.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series3.9s

Counts

4 → 12

Calls

4 calls:

2.2s	(sqrt (* (* (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))) (cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))))
585.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
544.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
572.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify826.0ms

Counts

75 → 75

Iterations

Iter	Nodes
3	2713
2	782
1	293
0	134

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.0b

localize76.0ms

Local error

Found 4 expressions with local error:

4.5b	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
4.6b	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
6.3b	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
20.5b	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`fma-udef`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`cbrt-prod` `pow1/3` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

11.0ms	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
0.0ms	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
36.0ms	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
17.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

397.0ms	(* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
343.0ms	(fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))
374.0ms	(* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
632.0ms	(cbrt (* (* U 2) (* n (fma (- U* U) (/ (* (* (/ (* (cbrt n) (cbrt l)) (cbrt Om)) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ (* (cbrt n) (cbrt l)) (cbrt Om))) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))

simplify5.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	7125
2	1337
1	409
0	169

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 16.9b

regimes1.2s

Accuracy

-6.1% (7.4b remaining)

Error of 23.9b against oracle of 16.6b and baseline of 23.5b

bsearch688.0ms

Steps

Iters	Range		Point
10	1.1540831383133497e-75	5.077645077777853e-58	2.6158530040231545e-73
9	2.3578502464846e-162	1.0576568489982568e-154	1.0022495870274159e-154

simplify24.0ms

Iterations

Iter	Nodes
2	50
1	50
0	40

end0.0ms

sample8.6s

Algorithm

intervals

Results

4.3s	14817×	body	80	nan
3.1s	9245×	body	80	valid