Details

sample424.0ms

Algorithm

intervals

Results

101.0ms	54×	body	1280	valid
100.0ms	171×	body	80	valid
82.0ms	43×	body	640	valid
15.0ms	20×	body	320	valid
11.0ms	53×	body	80	nan
3.0ms	6×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	152	26
4	362	26
5	1681	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
49×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
25×	`add-exp-log`
21×	`associate-r`
16×	`associate-l` `add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
5×	`div-exp` `div-inv`
4×	`pow-neg` `cbrt-unprod` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `neg-sub0` `pow-to-exp` `associate-r/` `pow-exp` `associate-/r` `associate-/l*` `pow-sub`
2×	`tan-quot` `frac-times` `associate-/r/` `*-commutative`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `un-div-inv`

Counts

4 → 155

Calls

4 calls:

6.0ms	(/ 1.0 (tan B))
20.0ms	(* x (/ 1.0 (tan B)))
334.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
108.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series880.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ 1.0 (tan B))
167.0ms	(* x (/ 1.0 (tan B)))
424.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
213.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.5s

Counts

167 → 167

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	306	2742
1	867	2581
2	3839	2427
done	5000	2423

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite558.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

258.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
29.0ms	(* x (/ 1.0 (tan B)))
181.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
74.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

510.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
159.0ms	(* x (/ 1.0 (tan B)))
449.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
248.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.2s

Counts

186 → 186

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	341	3949
1	955	3778
2	3905	3541
done	5000	3537

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

22.0ms	(/ (* x 1.0) (tan B))
246.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
186.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
105.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* x 1.0) (tan B))
513.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
455.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
204.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.1s

Counts

175 → 175

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	326	3851
1	905	3686
2	3895	3459
done	5000	3455

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (* x 1.0) (sin B)) (cos B))
0.2b	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
0.3b	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
16.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite552.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt` `times-frac`
54×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
29×	`add-exp-log`
28×	`associate-r`
25×	`unpow-prod-down`
20×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
10×	`associate-l`
9×	`pow1` `sqr-pow`
8×	`div-exp` `prod-exp`
7×	`associate-/l*`
6×	`cbrt-unprod`
5×	`div-inv` `unswap-sqr`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `associate-/r*`
2×	`neg-sub0` `pow-neg` `pow-prod-down` `*-commutative` `associate-/l/` `pow-sub`
1×	`neg-mul-1` `pow-pow` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 168

Calls

4 calls:

28.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
242.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
189.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
86.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (/ (* x 1.0) (sin B)) (cos B))
496.0ms	(* F (/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B)))
853.0ms	(/ (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))) (sin B))
197.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.3s

Counts

180 → 180

Iterations

Useful iterations: 2 (877.0ms)

Iter	Nodes	Cost
0	336	3994
1	949	3828
2	4212	3553
done	5001	3553

prune953.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes185.0ms

Accuracy

98% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.2b

bsearch422.0ms

Steps

Iters	Range		Point
7	1.7018957626216302	51.598513915430715	50.98469419077627
6	-31601356937510816.0	-7479483537821808.0	-7995080292970857.0

simplify26.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	83
1	63	83
2	71	83
done	71	83

end0.0ms

sample9.9s

Algorithm

intervals

Results

3.4s	1584×	body	1280	valid
2.2s	1364×	body	640	valid
2.0s	4941×	body	80	valid
638.0ms	693×	body	320	valid
541.0ms	348×	body	160	valid
497.0ms	1616×	body	80	nan