Details

sample469.0ms

Algorithm

intervals

Results

187.0ms	59×	body	1280	valid
80.0ms	47×	body	640	valid
62.0ms	149×	body	80	valid
28.0ms	23×	body	320	valid
17.0ms	46×	body	80	nan
5.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2153
5	683
4	275
3	137
2	81
1	45
0	20

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.2b	(/ (sin B) F)
6.3b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
18.4b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
143×	`*-un-lft-identity`
113×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`distribute-lft-out` `sqr-pow`
14×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-inv`
11×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 221

Calls

4 calls:

10.0ms	(/ x (tan B))
15.0ms	(/ (sin B) F)
87.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
70.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series839.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(/ x (tan B))
48.0ms	(/ (sin B) F)
240.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
352.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.4s

Counts

233 → 233

Iterations

Iter	Nodes
2	2537
1	920
0	396

prune3.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (sin B))
0.3b	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
0.4b	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
18.4b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

11.0ms	(/ 1 (sin B))
116.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
125.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
39.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

series582.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ 1 (sin B))
126.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
118.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
324.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

simplify3.0s

Counts

133 → 133

Iterations

Iter	Nodes
3	3956
2	1415
1	527
0	214

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 12.1b

localize58.0ms

Local error

Found 4 expressions with local error:

1.3b	(cbrt (* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)))
18.4b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
18.4b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
18.4b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`pow-unpow` `unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*l/`

Counts

4 → 65

Calls

4 calls:

78.0ms	(cbrt (* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)))
16.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
20.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
16.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

390.0ms	(cbrt (* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)))
318.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
291.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)
275.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

simplify3.2s

Counts

77 → 77

Iterations

Iter	Nodes
3	4884
2	1391
1	482
0	196

prune1.6s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.1b

localize69.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2))
3.4b	(/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2)))
18.4b	(sqrt (+ (+ (* 2 x) (* F F)) 2))
18.4b	(sqrt (+ (+ (* 2 x) (* F F)) 2))

rewrite440.0ms

Algorithm

rewrite-expression-head

Rules

4772×	`times-frac`
2620×	`*-un-lft-identity`
2226×	`unpow-prod-down`
1982×	`add-sqr-sqrt`
1980×	`add-cube-cbrt`
1280×	`sqrt-prod`
320×	`distribute-lft-out`
318×	`sqr-pow`
158×	`associate-/r*` `div-inv`
73×	`add-exp-log`
57×	`div-exp`
24×	`associate-/l*`
18×	`add-cbrt-cube`
15×	`pow-to-exp` `pow-exp`
9×	`cbrt-undiv`
6×	`pow1`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 2032

Calls

4 calls:

58.0ms	(/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2))
183.0ms	(/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2)))
30.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))
28.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))

series682.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2))
202.0ms	(/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (sin B) F) (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2)))
142.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))
171.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))

simplify21.3s

Counts

2044 → 2044

Iterations

Iter	Nodes
1	6131
0	2202

prune37.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 12.1b

regimes488.0ms

Accuracy

0% (0.6b remaining)

Error of 10.8b against oracle of 10.2b and baseline of 10.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	23
1	23
0	18

end0.0ms

sample13.1s

Algorithm

intervals

Results

5.7s	1689×	body	1280	valid
3.1s	1375×	body	640	valid
2.1s	4873×	body	80	valid
941.0ms	657×	body	320	valid
611.0ms	1652×	body	80	nan
262.0ms	308×	body	160	valid