Details

sample915.0ms

Algorithm

intervals

Results

272.0ms	148×	body	80	valid
265.0ms	67×	body	1280	valid
136.0ms	38×	body	640	valid
31.0ms	18×	body	320	valid
20.0ms	43×	body	80	nan
8.0ms	9×	body	160	valid

simplify9.9s

Counts

1 → 1

Iterations

Iter	Nodes
7	8510
6	1843
5	606
4	239
3	124
2	80
1	46
0	20

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.4b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
19.2b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-exp-log`
19×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
9×	`unpow-prod-down`
8×	`associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 99

Calls

4 calls:

5.0ms	(/ x (tan B))
98.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
61.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
32.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series833.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(/ x (tan B))
128.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
217.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
318.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.0s

Counts

111 → 111

Iterations

Iter	Nodes
3	4660
2	1225
1	453
0	213

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.7b

localize84.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin B))
0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.3b	(* (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (/ 1 (sin B)))
19.2b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`times-frac`
16×	`associate-r`
10×	`div-exp`
9×	`unpow-prod-down` `associate-l`
8×	`pow1`
7×	`cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
5×	`rec-exp` `1-exp`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow`

Counts

4 → 124

Calls

4 calls:

8.0ms	(/ 1 (sin B))
76.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
160.0ms	(* (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (/ 1 (sin B)))
38.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series616.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (sin B))
124.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
241.0ms	(* (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (/ 1 (sin B)))
236.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.1s

Counts

136 → 136

Iterations

Iter	Nodes
3	4019
2	1410
1	526
0	214

prune2.0s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.2b	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
0.4b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
19.2b	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
23×	`*-un-lft-identity`
21×	`associate-l`
19×	`add-cube-cbrt`
16×	`add-cbrt-cube`
13×	`times-frac`
9×	`unpow-prod-down`
8×	`prod-exp`
7×	`pow1`
6×	`associate-r`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-/r*` `pow-exp` `sqr-pow`
2×	`*-commutative` `div-inv` `distribute-lft-out`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `associate-/l`

Counts

4 → 103

Calls

4 calls:

15.0ms	(* (/ x (sin B)) (cos B))
73.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
32.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
37.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

series751.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ x (sin B)) (cos B))
121.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F)
231.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) -1/2) F) (sin B))
289.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) -1/2)

simplify2.3s

Counts

115 → 115

Iterations

Iter	Nodes
3	5717
2	1536
1	512
0	220

prune2.0s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.7b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)
0.4b	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)) (sin B))
19.7b	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
19.7b	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
31×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`pow-unpow`
25×	`add-cube-cbrt`
24×	`prod-exp`
21×	`times-frac`
15×	`add-cbrt-cube`
13×	`unpow-prod-down` `div-exp`
10×	`pow-to-exp` `pow-exp`
8×	`associate-l`
6×	`pow1`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `associate-/r` `associate-r*` `div-inv` `distribute-lft-out` `unswap-sqr`
2×	`pow-pow`
1×	`clear-num` `frac-2neg` `-commutative` `associate-/l`

Counts

4 → 119

Calls

4 calls:

88.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)
96.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)) (sin B))
21.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
32.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

460.0ms	(* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)
251.0ms	(/ (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) (* (pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2)) F)) (sin B))
286.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))
298.0ms	(pow (+ 2 (+ (* 2 x) (* F F))) (/ -1/2 2))

simplify4.8s

Counts

131 → 131

Iterations

Iter	Nodes
3	8010
2	1972
1	639
0	234

prune2.1s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.7b

regimes678.0ms

Accuracy

0% (0.6b remaining)

Error of 10.4b against oracle of 9.8b and baseline of 10.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
2	25
1	25
0	18

end0.0ms

sample13.3s

Algorithm

intervals

Results

5.0s	1752×	body	1280	valid
2.8s	1362×	body	640	valid
2.4s	4720×	body	80	valid
1.8s	706×	body	320	valid
645.0ms	1689×	body	80	nan
356.0ms	360×	body	160	valid