Details

sample423.0ms

Algorithm

intervals

Results

63.0ms	419×	body	80	nan
45.0ms	298×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4135
3	665
2	154
1	49
0	21

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize54.0ms

Local error

Found 4 expressions with local error:

4.7b	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
5.8b	(* n (pow (/ l Om) 2.0))
8.9b	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
18.3b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

0.0ms	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
27.0ms	(* n (pow (/ l Om) 2.0))
57.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
73.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

series9.1s

Counts

4 → 12

Calls

4 calls:

1.7s	(fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))
205.0ms	(* n (pow (/ l Om) 2.0))
2.3s	(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0))))
4.9s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (- t (* (* (/ l Om) l) 2.0)))))

simplify2.2s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2103
1	444
0	187

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 20.0b

localize40.0ms

Local error

Found 4 expressions with local error:

4.7b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
8.9b	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
18.3b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1`
22×	`add-sqr-sqrt`
21×	`add-exp-log`
20×	`associate-r`
15×	`unpow-prod-down` `add-cbrt-cube`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow-prod-down`
10×	`times-frac` `prod-exp`
7×	`cbrt-unprod`
4×	`expm1-log1p-u` `sqrt-pow1` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
42.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
64.0ms	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
51.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

series8.5s

Counts

4 → 12

Calls

4 calls:

1.6s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
256.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
1.9s	(* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))
4.7s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

simplify2.3s

Counts

101 → 101

Iterations

Iter	Nodes
done	5002
2	2210
1	465
0	194

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 19.5b

localize51.0ms

Local error

Found 4 expressions with local error:

4.7b	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
5.0b	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
6.6b	(* n (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
24×	`add-exp-log`
21×	`add-sqr-sqrt`
18×	`add-cbrt-cube` `associate-r`
16×	`pow-prod-down`
15×	`unpow-prod-down`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`prod-exp`
10×	`times-frac`
9×	`cbrt-unprod`
5×	`sqrt-pow1` `fma-udef`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `associate-l` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-exp` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/2` `div-exp` `sqrt-prod` `div-inv`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
22.0ms	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
44.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
34.0ms	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

series8.8s

Counts

4 → 12

Calls

4 calls:

1.7s	(fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))
2.0s	(* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))
257.0ms	(* n (pow (/ l Om) (/ 2.0 2)))
5.0s	(sqrt (* (* 2.0 n) (* U (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0))))))

simplify1.8s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	1890
1	484
0	201

prune865.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.3b

localize68.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (pow (/ l Om) (/ 2.0 2)))
14.7b	(cbrt (pow (/ l Om) (/ 2.0 2)))
14.7b	(cbrt (pow (/ l Om) (/ 2.0 2)))
18.3b	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
39×	`unpow-prod-down`
28×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
14×	`pow1`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv` `sqr-pow`
1×	`pow1/2` `sqrt-prod`

Counts

4 → 96

Calls

4 calls:

4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
4.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
62.0ms	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

series5.3s

Counts

4 → 12

Calls

4 calls:

351.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
345.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
332.0ms	(cbrt (pow (/ l Om) (/ 2.0 2)))
4.3s	(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* n (* (cbrt (pow (/ l Om) (/ 2.0 2))) (cbrt (pow (/ l Om) (/ 2.0 2))))) (cbrt (pow (/ l Om) (/ 2.0 2)))) (pow (/ l Om) (/ 2.0 2))) (- t (* (* (/ l Om) l) 2.0)))))

simplify4.9s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
3	2148
2	644
1	303
0	153

prune783.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.3b

regimes951.0ms

Accuracy

23.3% (10.2b remaining)

Error of 27.5b against oracle of 17.3b and baseline of 30.6b

bsearch117.0ms

Steps

Iters	Range		Point
8	-5.352082936858468e-304	-1.6919138487008464e-307	-1.7120214689066866e-307

simplify12.0ms

Iterations

Iter	Nodes
done	54
1	54
0	40

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.1s	14935×	body	80	nan
1.1s	9147×	body	80	valid