Details

sample688.0ms

Algorithm

intervals

Results

103.0ms	139×	body	80	valid
101.0ms	52×	body	1280	valid
82.0ms	59×	body	640	valid
16.0ms	63×	body	80	nan
15.0ms	16×	body	320	valid
6.0ms	10×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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))))
14.4b	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

rewrite241.0ms

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:

9.0ms	(/ (* x 1.0) (tan B))
90.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
67.0ms	(/ (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:

190.0ms	(/ (* x 1.0) (tan B))
409.0ms	(/ F (/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))))
355.0ms	(/ (sin B) (pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0))))
239.0ms	(pow (+ (+ (* F F) 2.0) (* x 2.0)) (- (/ 1.0 2.0)))

simplify592.0ms

Counts

255 → 255

Iterations

Iter	Nodes
done	5000
1	1326
0	474

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
0.2b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
14.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

85×	`add-sqr-sqrt`
80×	`times-frac`
59×	`add-exp-log`
55×	`*-un-lft-identity`
51×	`add-cube-cbrt`
27×	`unpow-prod-down`
25×	`div-exp` `associate-r`
23×	`add-cbrt-cube`
17×	`prod-exp`
13×	`pow-unpow` `associate-l`
12×	`unswap-sqr`
11×	`sqr-pow`
10×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`cbrt-unprod` `div-inv`
4×	`rec-exp` `1-exp` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `associate-/r/` `*-commutative`

Counts

4 → 176

Calls

4 calls:

16.0ms	(/ (* x 1.0) (tan B))
102.0ms	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
198.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
71.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

179.0ms	(/ (* x 1.0) (tan B))
325.0ms	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
532.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
524.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

simplify591.0ms

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
1	1051
0	357

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 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))))
14.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

rewrite426.0ms

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))
174.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
174.0ms	(* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
61.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

series1.6s

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (* x 1.0) (tan B))
591.0ms	(* (/ 1 (sin B)) (* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))))
320.0ms	(* F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0))))
548.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (- (/ 1.0 2.0)))

simplify2.6s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	4441
1	969
0	334

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
0.2b	(* (/ (* 1.0 x) (sin B)) (cos B))
0.2b	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
14.4b	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`times-frac`
63×	`add-exp-log`
56×	`*-un-lft-identity`
52×	`add-cube-cbrt`
28×	`associate-r`
27×	`unpow-prod-down` `add-cbrt-cube`
25×	`div-exp`
20×	`associate-l` `prod-exp`
13×	`pow-unpow` `unswap-sqr`
11×	`sqr-pow`
9×	`pow1`
8×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-/r*`
6×	`pow-to-exp` `pow-exp`
5×	`div-inv`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`associate-/l*`
2×	`pow-prod-down` `associate-l/` `-commutative`
1×	`frac-times` `clear-num` `pow-pow` `frac-2neg` `associate-*r/`

Counts

4 → 181

Calls

4 calls:

106.0ms	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
24.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
187.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
55.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

328.0ms	(/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0)))
193.0ms	(* (/ (* 1.0 x) (sin B)) (cos B))
609.0ms	(* (/ 1 (sin B)) (/ F (pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))))
519.0ms	(pow (+ (+ (* x 2.0) 2.0) (* F F)) (/ 1.0 2.0))

simplify646.0ms

Counts

193 → 193

Iterations

Iter	Nodes
done	5001
1	1087
0	367

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes363.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.5b

bsearch529.0ms

Steps

Iters	Range		Point
8	383123.6636286385	488997712.5877659	60622479.674600124
9	-2.8555728020291845e+22	-29272228678884.97	-9.321248393599965e+17

simplify7.0ms

Iterations

Iter	Nodes
done	50
1	50
0	39

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.0s	1698×	body	1280	valid
2.4s	1407×	body	640	valid
1.4s	4690×	body	80	valid
587.0ms	711×	body	320	valid
402.0ms	1650×	body	80	nan
276.0ms	351×	body	160	valid