Details

sample240.0ms

Algorithm

intervals

Results

110.0ms	550×	body	80	nan
42.0ms	299×	body	80	valid

simplify6.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
4	2913
3	614
2	150
1	49
0	21

prune65.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 27.8b

localize218.0ms

Local error

Found 4 expressions with local error:

5.5b	(* n (pow (/ l Om) 2.0))
6.7b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
6.9b	(* (* n (pow (/ l Om) 2.0)) (- U U*))
18.6b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite855.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
35×	`add-exp-log`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
23×	`associate-r`
20×	`add-cbrt-cube`
19×	`prod-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`times-frac` `associate-*r/` `cbrt-unprod`
7×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `div-exp` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 133

Calls

4 calls:

104.0ms	(* n (pow (/ l Om) 2.0))
305.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
166.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
257.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series26.7s

Counts

4 → 12

Calls

4 calls:

402.0ms	(* n (pow (/ l Om) 2.0))
2.8s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
979.0ms	(* (* n (pow (/ l Om) 2.0)) (- U U*))
22.5s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify5.6s

Counts

145 → 145

Iterations

Iter	Nodes
done	5005
2	3310
1	978
0	357

prune2.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 21.8b

localize246.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
18.6b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

99×	`add-exp-log`
67×	`prod-exp`
37×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`pow1`
24×	`add-cbrt-cube`
23×	`associate-r`
20×	`pow-exp`
18×	`prod-diff`
15×	`unpow-prod-down`
13×	`pow-prod-down` `cbrt-unprod`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow-to-exp` `times-frac` `div-exp` `associate-*r/`
7×	`associate-l`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`flip3--` `*-commutative` `flip--`
2×	`sub-neg` `sqrt-div` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 150

Calls

4 calls:

85.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
278.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
419.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
680.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series28.4s

Counts

4 → 12

Calls

4 calls:

670.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
3.3s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
1.1s	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
23.3s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify7.6s

Counts

162 → 162

Iterations

Iter	Nodes
done	5008
2	3687
1	1068
0	393

prune2.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.6b

localize214.0ms

Local error

Found 4 expressions with local error:

5.7b	(* n (pow (/ l Om) (/ 2.0 2)))
6.7b	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
7.9b	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
18.6b	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

rewrite731.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
35×	`add-cube-cbrt`
30×	`unpow-prod-down`
29×	`add-exp-log`
23×	`pow1` `associate-r` `associate-l`
20×	`times-frac`
18×	`prod-diff`
17×	`add-cbrt-cube`
14×	`prod-exp`
12×	`pow-prod-down`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`associate-*r/`
8×	`cbrt-unprod` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-*l/` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`flip3--` `*-commutative` `flip--`
2×	`pow-to-exp` `sub-neg` `sqrt-div` `div-exp` `div-inv`
1×	`pow1/2` `sqrt-prod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 150

Calls

4 calls:

78.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
253.0ms	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
141.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
241.0ms	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

series27.6s

Counts

4 → 12

Calls

4 calls:

500.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
3.0s	(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
956.0ms	(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
23.1s	(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

simplify6.7s

Counts

162 → 162

Iterations

Iter	Nodes
done	5005
2	3350
1	1007
0	402

prune3.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.4b

localize344.0ms

Local error

Found 4 expressions with local error:

4.7b	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.7b	(* n (pow (/ l Om) (/ 2.0 2)))
6.9b	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
18.6b	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

92×	`add-exp-log`
62×	`prod-exp`
54×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
41×	`pow1`
40×	`add-cube-cbrt`
36×	`prod-diff`
27×	`associate-r`
26×	`pow-prod-down`
22×	`distribute-rgt-in` `distribute-lft-in`
20×	`pow-exp`
17×	`add-cbrt-cube`
15×	`unpow-prod-down`
10×	`pow-to-exp` `times-frac` `div-exp` `associate-*r/`
9×	`sqrt-pow1`
8×	`cbrt-unprod`
7×	`associate-l`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `sub-neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`sqrt-div` `associate-*l/` `distribute-lft-out--` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-prod` `div-inv`

Counts

4 → 176

Calls

4 calls:

71.0ms	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
96.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
425.0ms	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
889.0ms	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))

series31.2s

Counts

4 → 12

Calls

4 calls:

2.6s	(* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
601.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.1s	(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
26.8s	(sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))))

simplify7.3s

Counts

188 → 188

Iterations

Iter	Nodes
done	5002
2	3413
1	1086
0	433

prune3.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 17.4b

regimes5.8s

Accuracy

45.7% (4.4b remaining)

Error of 22.5b against oracle of 18.2b and baseline of 26.2b

bsearch9.0ms

simplify34.0ms

Iterations

Iter	Nodes
done	60
1	60
0	43

end0.0ms

sample7.1s

Algorithm

intervals

Results

3.3s	14949×	body	80	nan
1.9s	9174×	body	80	valid