Details

sample615.0ms

Algorithm

intervals

Results

234.0ms	50×	body	1280	valid
114.0ms	54×	body	640	valid
67.0ms	147×	body	80	valid
30.0ms	74×	body	80	nan
27.0ms	17×	body	320	valid
14.0ms	14×	body	160	valid

simplify979.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin B) F)
0.1b	(/ x (tan B))
6.7b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
19.0b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite239.0ms

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:

16.0ms	(/ (sin B) F)
10.0ms	(/ x (tan B))
159.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
40.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series759.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (sin B) F)
171.0ms	(/ x (tan B))
224.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
311.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.5s

Counts

233 → 233

Iterations

Iter	Nodes
2	2521
1	920
0	396

prune3.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
19.0b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite288.0ms

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))
92.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
135.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
34.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series837.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ x (tan B))
227.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
188.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
273.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.1s

Counts

548 → 548

Iterations

Iter	Nodes
1	2372
0	828

prune9.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
0.3b	(/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
0.3b	(/ (/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))) (/ 1 F))
19.0b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

4355×	`times-frac`
2064×	`*-un-lft-identity`
1778×	`add-sqr-sqrt` `add-cube-cbrt`
572×	`unpow-prod-down`
189×	`add-exp-log`
166×	`div-exp`
153×	`div-inv`
143×	`distribute-lft-out` `sqr-pow`
95×	`associate-/l*`
49×	`associate-/r*`
33×	`rec-exp` `1-exp`
32×	`add-cbrt-cube`
19×	`cbrt-undiv`
17×	`pow-to-exp` `pow-exp`
16×	`associate-/r/`
6×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
1×	`pow-pow` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 1542

Calls

4 calls:

75.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
73.0ms	(/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
120.0ms	(/ (/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))) (/ 1 F))
68.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series845.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2)))
287.0ms	(/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))
168.0ms	(/ (/ 1 (/ (sin B) (pow (+ (+ (* 2 x) (* F F)) 2) -1/2))) (/ 1 F))
298.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.3m

Counts

1554 → 1554

Iterations

Iter	Nodes
1	7001
0	2132

prune28.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.7b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x (sin B)) (cos B))
0.3b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
0.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
19.0b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

995×	`times-frac`
538×	`*-un-lft-identity`
449×	`add-sqr-sqrt`
444×	`add-cube-cbrt`
188×	`unpow-prod-down`
59×	`add-exp-log`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-inv`
40×	`div-exp`
36×	`associate-/l*`
23×	`add-cbrt-cube`
16×	`associate-/r*`
13×	`associate-l`
10×	`cbrt-undiv`
7×	`pow1`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-r`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`pow-pow` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/`

Counts

4 → 540

Calls

4 calls:

29.0ms	(* (/ x (sin B)) (cos B))
151.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
155.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
40.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series813.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (/ x (sin B)) (cos B))
215.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
206.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
266.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.1s

Counts

552 → 552

Iterations

Iter	Nodes
1	2431
0	836

prune10.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 10.6b

regimes543.0ms

Accuracy

0% (0.6b remaining)

Error of 10.7b against oracle of 10.1b and baseline of 10.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
2	22
1	22
0	19

end0.0ms

sample13.8s

Algorithm

intervals

Results

5.1s	1636×	body	1280	valid
3.3s	1395×	body	640	valid
2.5s	4772×	body	80	valid
960.0ms	695×	body	320	valid
820.0ms	1707×	body	80	nan
743.0ms	367×	body	160	valid