Details

sample452.0ms

Algorithm

intervals

Results

113.0ms	159×	body	80	valid
109.0ms	48×	body	1280	valid
59.0ms	41×	body	640	valid
22.0ms	21×	body	320	valid
15.0ms	47×	body	80	nan
7.0ms	13×	body	160	valid

simplify5.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2685
5	812
4	310
3	144
2	82
1	42
0	20

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize120.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.2b	(* (/ 1.0 (tan B)) x)
5.9b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
14.5b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite355.0ms

Algorithm

rewrite-expression-head

Rules

212×	`times-frac`
130×	`add-sqr-sqrt`
125×	`*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
34×	`pow-unpow`
25×	`add-exp-log`
16×	`associate-/r*` `add-cbrt-cube`
15×	`sqr-pow`
14×	`associate-l`
12×	`div-inv`
11×	`div-exp`
10×	`associate-/l*`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`pow1`
5×	`cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `neg-mul-1` `associate-r` `pow-exp` `associate-/r/`
2×	`neg-sub0` `pow-neg` `clear-num` `frac-2neg` `div-sub` `prod-exp` `tan-quot` `distribute-frac-neg` `cbrt-unprod` `pow-sub` `unswap-sqr` `associate-/l/`
1×	`pow-pow` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 247

Calls

4 calls:

16.0ms	(/ 1.0 (tan B))
30.0ms	(* (/ 1.0 (tan B)) x)
195.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
76.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

129.0ms	(/ 1.0 (tan B))
261.0ms	(* (/ 1.0 (tan B)) x)
909.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (/ (sin B) F))
287.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify6.6s

Counts

259 → 259

Iterations

Iter	Nodes
done	5004
2	3850
1	1286
0	479

prune4.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (tan B)) x)
0.4b	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
14.5b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite604.0ms

Algorithm

rewrite-expression-head

Rules

914×	`times-frac`
432×	`add-sqr-sqrt`
427×	`*-un-lft-identity` `add-cube-cbrt`
141×	`unpow-prod-down`
59×	`add-exp-log`
47×	`sqr-pow`
44×	`div-inv`
40×	`div-exp`
34×	`pow-unpow`
32×	`associate-/l*`
23×	`add-cbrt-cube`
16×	`associate-/r*`
14×	`associate-l`
10×	`cbrt-undiv`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
7×	`pow1`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`neg-mul-1` `associate-r` `associate-/l/`
2×	`neg-sub0` `pow-neg` `clear-num` `frac-2neg` `div-sub` `prod-exp` `distribute-frac-neg` `associate-/r/` `cbrt-unprod` `pow-sub` `unswap-sqr`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `-commutative`

Counts

4 → 529

Calls

4 calls:

31.0ms	(* (/ 1.0 (tan B)) x)
217.0ms	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
146.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
78.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (/ 1.0 (tan B)) x)
851.0ms	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
880.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
267.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify5.2s

Counts

541 → 541

Iterations

Iter	Nodes
done	5003
1	2787
0	919

prune8.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize116.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.4b	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
14.5b	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

913×	`times-frac`
427×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
141×	`unpow-prod-down`
56×	`add-exp-log`
47×	`sqr-pow`
44×	`div-inv`
40×	`div-exp`
35×	`associate-/l*`
34×	`pow-unpow`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
9×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`clear-num` `neg-mul-1` `frac-2neg` `associate-/l/`
2×	`neg-sub0` `pow-neg` `div-sub` `distribute-frac-neg` `associate-/r/` `pow-sub`
1×	`pow-pow` `tan-quot`

Counts

4 → 524

Calls

4 calls:

18.0ms	(/ x (tan B))
188.0ms	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
153.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
52.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

series2.2s

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ x (tan B))
831.0ms	(/ (/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B)) (/ 1 F))
916.0ms	(/ (pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0)) (sin B))
264.0ms	(pow (+ (+ 2.0 (* F F)) (* 2.0 x)) (/ (- 1.0) 2.0))

simplify5.4s

Counts

536 → 536

Iterations

Iter	Nodes
done	5000
1	2714
0	902

prune7.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (+ 2.0 (+ (* F F) (* 2.0 x))))
0.4b	(/ (/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B)) (/ 1 F))
0.4b	(/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B))
14.2b	(pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0))

rewrite924.0ms

Algorithm

rewrite-expression-head

Rules

3124×	`times-frac`
1574×	`*-un-lft-identity`
1284×	`add-sqr-sqrt` `add-cube-cbrt`
846×	`unpow-prod-down`
145×	`distribute-lft-out`
136×	`div-inv`
112×	`add-exp-log`
97×	`associate-/r/`
95×	`associate-/l*`
86×	`div-exp`
48×	`flip3-+` `flip-+`
47×	`sqr-pow`
24×	`pow-exp`
20×	`associate-/r*` `add-cbrt-cube`
14×	`rec-exp` `1-exp`
13×	`pow-unpow`
10×	`cbrt-undiv`
7×	`pow1`
6×	`pow-to-exp`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `pow-pow` `frac-2neg`
2×	`pow-flip` `inv-pow`
1×	`associate-/l/`

Counts

4 → 1233

Calls

4 calls:

75.0ms	(/ 1 (+ 2.0 (+ (* F F) (* 2.0 x))))
208.0ms	(/ (/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B)) (/ 1 F))
183.0ms	(/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B))
84.0ms	(pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ 1 (+ 2.0 (+ (* F F) (* 2.0 x))))
857.0ms	(/ (/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B)) (/ 1 F))
841.0ms	(/ (pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0)) (sin B))
271.0ms	(pow (/ 1 (+ 2.0 (+ (* F F) (* 2.0 x)))) (/ 1.0 2.0))

simplify4.6s

Counts

1245 → 1245

Iterations

Iter	Nodes
done	5000
0	1709

prune15.8s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes904.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.0b

bsearch635.0ms

Steps

Iters	Range		Point
9	2.87861304207683e+32	5.299444720085814e+37	2.906298232033359e+32
10	-135490375.57476136	-3.8822111449762154e-05	-32050963.10631644

simplify22.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample10.7s

Algorithm

intervals

Results

4.2s	1683×	body	1280	valid
2.4s	1409×	body	640	valid
1.6s	4706×	body	80	valid
893.0ms	1644×	body	80	nan
763.0ms	719×	body	320	valid
193.0ms	349×	body	160	valid