Details

sample205.0ms

Algorithm

intervals

Results

78.0ms	544×	body	80	nan
65.0ms	289×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3618
3	693
2	157
1	50
0	21

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.2b

localize45.0ms

Local error

Found 4 expressions with local error:

7.1b	(* (/ (/ (* l l) Om) Om) (- U* U))
7.2b	(/ (* l l) Om)
7.2b	(/ (* l l) Om)
19.0b	(sqrt (* (* U (fma (* (/ (/ (* l l) Om) Om) (- U* U)) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
39×	`times-frac`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
25×	`associate-l`
19×	`pow1`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`cbrt-undiv` `div-exp` `pow-prod-down`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r*` `div-inv`
5×	`sqrt-pow1` `associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `clear-num` `sub-neg` `frac-2neg` `flip3--` `associate-r/` `flip--` `associate-/l`
1×	`pow1/2` `associate-l/` `-commutative` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 145

Calls

4 calls:

40.0ms	(* (/ (/ (* l l) Om) Om) (- U* U))
10.0ms	(/ (* l l) Om)
10.0ms	(/ (* l l) Om)
20.0ms	(sqrt (* (* U (fma (* (/ (/ (* l l) Om) Om) (- U* U)) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

series2.7s

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ (/ (* l l) Om) Om) (- U* U))
24.0ms	(/ (* l l) Om)
25.0ms	(/ (* l l) Om)
2.6s	(sqrt (* (* U (fma (* (/ (/ (* l l) Om) Om) (- U* U)) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

simplify1.6s

Counts

157 → 157

Iterations

Iter	Nodes
done	5095
2	2797
1	764
0	262

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 26.5b

localize84.0ms

Local error

Found 4 expressions with local error:

6.7b	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))
7.2b	(/ (* l l) Om)
8.1b	(* (/ (/ l (cbrt Om)) Om) (- U* U))
19.0b	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
96×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
70×	`associate-l`
28×	`cbrt-prod`
19×	`pow1`
18×	`prod-diff` `add-exp-log`
17×	`add-cbrt-cube`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow-prod-down`
5×	`cbrt-undiv` `sqrt-pow1` `div-exp` `associate-r` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/r*`
2×	`frac-times` `sub-neg` `flip3--` `associate-*r/` `flip--`
1×	`clear-num` `frac-2neg` `pow1/2` `associate-l/` `-commutative` `sqrt-prod` `fma-udef` `associate-/l*` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 176

Calls

4 calls:

0.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))
10.0ms	(/ (* l l) Om)
38.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
22.0ms	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

series3.1s

Counts

4 → 12

Calls

4 calls:

276.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))
30.0ms	(/ (* l l) Om)
253.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
2.5s	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (/ (* l l) Om) -2 t))) (* 2 n)))

simplify1.7s

Counts

188 → 188

Iterations

Iter	Nodes
done	5010
2	3454
1	994
0	364

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 22.6b

localize63.0ms

Local error

Found 4 expressions with local error:

5.5b	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t)))
6.7b	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))
8.1b	(* (/ (/ l (cbrt Om)) Om) (- U* U))
19.0b	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))) (* 2 n)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

125×	`times-frac`
98×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
73×	`associate-l`
28×	`cbrt-prod`
21×	`pow1`
18×	`prod-diff`
15×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-prod-down`
8×	`associate-r`
5×	`sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `fma-udef`
2×	`frac-times` `sub-neg` `flip3--` `associate-r/` `-commutative` `flip--`
1×	`pow1/2` `associate-*l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 175

Calls

4 calls:

12.0ms	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t)))
0.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))
39.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
26.0ms	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))) (* 2 n)))

series4.1s

Counts

4 → 12

Calls

4 calls:

443.0ms	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t)))
340.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))
303.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
3.0s	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l Om) l) -2 t))) (* 2 n)))

simplify2.3s

Counts

187 → 187

Iterations

Iter	Nodes
done	5000
2	2996
1	975
0	366

prune2.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 22.0b

localize91.0ms

Local error

Found 4 expressions with local error:

5.5b	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t)))
6.7b	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))
8.1b	(* (/ (/ l (cbrt Om)) Om) (- U* U))
19.0b	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))) (* 2 n)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

125×	`times-frac`
98×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
81×	`add-cube-cbrt`
73×	`associate-l`
28×	`cbrt-prod`
21×	`pow1`
18×	`prod-diff`
15×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-prod-down`
8×	`associate-r`
5×	`sqrt-pow1` `unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `fma-udef`
2×	`frac-times` `sub-neg` `flip3--` `associate-r/` `-commutative` `flip--`
1×	`pow1/2` `associate-*l/` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 175

Calls

4 calls:

9.0ms	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t)))
0.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))
34.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
34.0ms	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))) (* 2 n)))

series4.2s

Counts

4 → 12

Calls

4 calls:

506.0ms	(* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t)))
406.0ms	(fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))
290.0ms	(* (/ (/ l (cbrt Om)) Om) (- U* U))
3.0s	(sqrt (* (* U (fma (* (/ (/ l (* (cbrt Om) (cbrt Om))) 1) (* (/ (/ l (cbrt Om)) Om) (- U* U))) n (fma (* (/ l (* (cbrt Om) (cbrt Om))) (/ l (cbrt Om))) -2 t))) (* 2 n)))

simplify2.6s

Counts

187 → 187

Iterations

Iter	Nodes
done	5003
2	3184
1	973
0	365

prune1.8s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 21.0b

regimes2.8s

Accuracy

20.9% (8.4b remaining)

Error of 28.6b against oracle of 20.2b and baseline of 30.8b

bsearch5.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	68
1	68
0	53

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.7s	14841×	body	80	nan
2.4s	9189×	body	80	valid