Details

sample449.0ms

Algorithm

intervals

Results

155.0ms	50×	body	1280	valid
73.0ms	54×	body	640	valid
50.0ms	146×	body	80	valid
38.0ms	44×	body	80	nan
33.0ms	28×	body	320	valid
7.0ms	8×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin B) F)
0.2b	(/ x (tan B))
5.9b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
19.2b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite209.0ms

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:

15.0ms	(/ (sin B) F)
10.0ms	(/ x (tan B))
119.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
55.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series684.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin B) F)
155.0ms	(/ x (tan B))
195.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
296.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.5s

Counts

233 → 233

Iterations

Iter	Nodes
2	2521
1	920
0	396

prune1.6s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
0.8b	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
19.2b	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

56×	`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`
9×	`div-exp`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `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/` `tan-quot` `associate-/r/`

Counts

4 → 118

Calls

4 calls:

9.0ms	(/ x (tan B))
86.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
121.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
35.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

series726.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ x (tan B))
129.0ms	(* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F)
151.0ms	(* (/ 1 (sin B)) (* (pow (+ (* 2 x) (+ 2 (* F F))) -1/2) F))
311.0ms	(pow (+ (* 2 x) (+ 2 (* F F))) -1/2)

simplify3.5s

Counts

130 → 130

Iterations

Iter	Nodes
3	3981
2	1429
1	572
0	246

prune911.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite336.0ms

Algorithm

rewrite-expression-head

Rules

994×	`times-frac`
538×	`*-un-lft-identity`
444×	`add-sqr-sqrt` `add-cube-cbrt`
188×	`unpow-prod-down`
56×	`add-exp-log`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-inv`
40×	`div-exp`
39×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot` `associate-/l/`

Counts

4 → 536

Calls

4 calls:

5.0ms	(/ x (tan B))
130.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
121.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
66.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series783.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ x (tan B))
206.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
164.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
279.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.6s

Counts

548 → 548

Iterations

Iter	Nodes
1	2372
0	828

prune3.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.2b

localize69.0ms

Local error

Found 4 expressions with local error:

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

rewrite515.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-sqr-sqrt`
135×	`times-frac`
103×	`*-un-lft-identity`
85×	`add-exp-log`
67×	`add-cube-cbrt`
63×	`unpow-prod-down`
48×	`div-exp`
28×	`associate-r` `associate-l` `prod-exp` `unswap-sqr`
27×	`sqr-pow`
26×	`pow-unpow`
18×	`pow-to-exp` `add-cbrt-cube` `pow-exp`
12×	`1-exp` `distribute-lft-out`
8×	`pow1` `associate-/l*`
5×	`cbrt-undiv` `div-inv`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`associate-/r*`
2×	`pow-pow`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 237

Calls

4 calls:

119.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) (sin B))
307.0ms	(* (/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) 1) (/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) (sin B)))
35.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2))
49.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

557.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) (sin B))
198.0ms	(* (/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) 1) (/ (pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2)) (sin B)))
268.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2))
275.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) (/ -1/2 2))

simplify2.1s

Counts

249 → 249

Iterations

Iter	Nodes
2	2731
1	1088
0	351

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.2b

regimes545.0ms

Accuracy

0% (0.7b remaining)

Error of 11.0b against oracle of 10.3b and baseline of 11.0b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	30
1	30
0	24

end1.0ms

sample13.9s

Algorithm

intervals

Results

5.6s	1575×	body	1280	valid
2.9s	1430×	body	640	valid
2.4s	4800×	body	80	valid
1.2s	1614×	body	80	nan
1.0s	722×	body	320	valid
387.0ms	374×	body	160	valid