Details

sample302.0ms

Algorithm

intervals

Results

89.0ms	48×	body	640	valid
85.0ms	57×	body	1280	valid
31.0ms	144×	body	80	valid
12.0ms	19×	body	320	valid
9.0ms	52×	body	80	nan
5.0ms	12×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1702
4	362
3	152
2	83
1	42
0	20

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
0.3b	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
17.6b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

207×	`times-frac`
122×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
37×	`associate-/r*`
30×	`pow-unpow`
25×	`add-exp-log`
17×	`sqr-pow`
16×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
12×	`div-exp` `associate-/r/`
9×	`div-inv`
7×	`associate-/l*`
6×	`neg-sub0` `cbrt-undiv` `pow-neg` `pow-sub`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp`
1×	`neg-mul-1` `pow-pow` `prod-exp` `tan-quot` `cbrt-unprod`

Counts

4 → 243

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
105.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
103.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
62.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (* x 1.0) (tan B))
407.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
327.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
253.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify783.0ms

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
1	1326
0	474

prune2.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))))
0.3b	(/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
0.4b	(/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
17.5b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

rewrite370.0ms

Algorithm

rewrite-expression-head

Rules

981×	`times-frac`
463×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
159×	`unpow-prod-down`
112×	`associate-/r*`
66×	`add-exp-log`
53×	`sqr-pow`
49×	`div-exp`
24×	`div-inv`
20×	`add-cbrt-cube`
13×	`pow-unpow`
10×	`pow-to-exp` `cbrt-undiv` `pow-exp`
9×	`rec-exp` `1-exp` `associate-/l*`
6×	`associate-/r/`
5×	`pow1`
4×	`add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`pow-pow` `pow-flip` `inv-pow`

Counts

4 → 554

Calls

4 calls:

96.0ms	(/ F (/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))))
91.0ms	(/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
82.0ms	(/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
46.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

series3.2s

Counts

4 → 12

Calls

4 calls:

492.0ms	(/ F (/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))))
1.0s	(/ (sin B) (/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
1.3s	(/ 1 (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
450.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

simplify1.9s

Counts

566 → 566

Iterations

Iter	Nodes
done	5001
1	2873
0	952

prune3.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F)
0.2b	(* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0)))
0.4b	(/ 1 (/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F))
17.5b	(pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))

rewrite665.0ms

Algorithm

rewrite-expression-head

Rules

153×	`add-exp-log`
92×	`div-exp`
60×	`times-frac`
57×	`add-sqr-sqrt`
45×	`prod-exp`
42×	`*-un-lft-identity`
39×	`add-cube-cbrt`
32×	`add-cbrt-cube`
26×	`1-exp`
16×	`pow-to-exp` `pow-exp`
13×	`cbrt-undiv` `pow-unpow` `associate-l`
11×	`rec-exp`
10×	`associate-/r*`
9×	`unpow-prod-down` `unswap-sqr`
8×	`div-inv`
7×	`associate-r`
6×	`pow1` `cbrt-unprod`
5×	`sqr-pow`
4×	`associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 188

Calls

4 calls:

41.0ms	(/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F)
110.0ms	(* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0)))
459.0ms	(/ 1 (/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F))
40.0ms	(pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))

series6.1s

Counts

4 → 12

Calls

4 calls:

2.7s	(/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F)
1.0s	(* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0)))
1.9s	(/ 1 (/ (* (/ (sin B) 1) (pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))) F))
477.0ms	(pow (+ (* x 2.0) (+ 2.0 (* F F))) (/ 1.0 2.0))

simplify501.0ms

Counts

200 → 200

Iterations

Iter	Nodes
done	5001
1	1115
0	382

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* (/ 1 (sin B)) (* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
0.3b	(* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
17.6b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
37×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
30×	`pow-unpow` `times-frac`
23×	`add-cbrt-cube`
16×	`associate-l`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`div-exp`
9×	`associate-*r/`
8×	`associate-r` `cbrt-unprod`
7×	`pow1` `pow-neg` `unpow-prod-down`
6×	`pow-to-exp` `pow-exp`
4×	`neg-sub0` `cbrt-undiv` `rec-exp` `1-exp` `div-inv` `pow-sub` `add-log-exp`
3×	`frac-times` `associate-/r*` `un-div-inv` `unswap-sqr` `sqr-pow`
2×	`*-commutative`
1×	`clear-num` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `associate-/l`

Counts

4 → 146

Calls

4 calls:

8.0ms	(/ (* x 1.0) (tan B))
195.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
220.0ms	(* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
60.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (* x 1.0) (tan B))
560.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
336.0ms	(* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
461.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

simplify2.4s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4441
1	969
0	334

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes408.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.6b

bsearch372.0ms

Steps

Iters	Range		Point
6	6968.3439428623215	61777.909360781356	15322.3293260381
5	-13147460999.383293	-3658128597.9917617	-5105757622.280994

simplify7.0ms

Iterations

Iter	Nodes
done	43
2	43
1	42
0	34

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.0s	1674×	body	1280	valid
1.8s	4747×	body	80	valid
1.8s	1403×	body	640	valid
709.0ms	684×	body	320	valid
394.0ms	1704×	body	80	nan
267.0ms	347×	body	160	valid