Details

sample477.0ms

Algorithm

intervals

Results

74.0ms	53×	body	1280	valid
29.0ms	44×	body	640	valid
24.0ms	156×	body	80	valid
14.0ms	30×	body	320	valid
5.0ms	46×	body	80	nan
4.0ms	11×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	42	15
1	83	14
2	151	14
3	356	14
4	1063	14
5	5002	14
done	5002	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ F (sin B))
0.2b	(* x (/ 1.0 (tan B)))
5.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite254.0ms

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×	`frac-times` `*-commutative`
1×	`tan-quot` `neg-mul-1` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `clear-num` `associate-/r/` `un-div-inv`

Counts

4 → 154

Calls

4 calls:

5.0ms	(/ F (sin B))
17.0ms	(* x (/ 1.0 (tan B)))
165.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
56.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ F (sin B))
116.0ms	(* x (/ 1.0 (tan B)))
294.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
156.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify86.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	765	1418
1	3213	1329
2	5001	1328
done	5001	1328

prune643.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
1.0b	(* (/ (* (cbrt F) (cbrt F)) (* (cbrt (sin B)) (cbrt (sin B)))) (* (/ (cbrt F) (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-exp-log`
93×	`prod-exp`
43×	`div-exp`
39×	`add-cbrt-cube`
37×	`cbrt-unprod`
30×	`pow-unpow`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
17×	`cbrt-undiv`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`pow-to-exp` `pow-exp`
10×	`frac-times` `associate-*r/`
7×	`pow1` `pow-neg`
6×	`cbrt-prod`
5×	`neg-sub0` `associate-l` `pow-sub`
4×	`add-log-exp`
3×	`unpow-prod-down` `associate-*l/` `div-inv`
2×	`pow1/3` `un-div-inv`
1×	`neg-mul-1` `pow-pow` `associate-r` `pow-prod-down` `*-commutative` `sqr-pow`

Counts

4 → 146

Calls

4 calls:

1.0ms	(cbrt (sin B))
1.0ms	(cbrt (sin B))
219.0ms	(* (/ (* (cbrt F) (cbrt F)) (* (cbrt (sin B)) (cbrt (sin B)))) (* (/ (cbrt F) (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
50.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series654.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (sin B))
97.0ms	(cbrt (sin B))
317.0ms	(* (/ (* (cbrt F) (cbrt F)) (* (cbrt (sin B)) (cbrt (sin B)))) (* (/ (cbrt F) (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))))
144.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify114.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	882	2700
1	4144	2053
2	5001	1780
done	5001	1780

prune529.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
5.1b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 143

Calls

4 calls:

10.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ F (sin B))
162.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
48.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (* x 1.0) (tan B))
49.0ms	(/ F (sin B))
285.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
138.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify71.0ms

Counts

155 → 155

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	718	1363
1	2971	1274
2	5001	1273
done	5001	1273

prune558.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.2b	(/ F (sin B))
5.0b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
15.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

184×	`times-frac`
106×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
45×	`unpow-prod-down`
25×	`add-exp-log`
17×	`associate-/l*`
16×	`add-cbrt-cube`
15×	`sqr-pow`
13×	`pow-unpow` `associate-/r*`
12×	`div-exp` `div-inv`
6×	`cbrt-undiv`
5×	`pow1`
4×	`add-log-exp`
3×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `pow-pow` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/`

Counts

4 → 206

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ F (sin B))
79.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
46.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series599.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
55.0ms	(/ F (sin B))
301.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
131.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify97.0ms

Counts

218 → 218

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	939	3042
1	4072	2953
2	5001	2952
done	5001	2952

prune779.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes198.0ms

Accuracy

91.8% (0.9b remaining)

Error of 1.0b against oracle of 0.0b and baseline of 11.0b

bsearch247.0ms

Steps

Iters	Range		Point
8	5.276955647516397	78679.13042368767	46343.85507146435
8	-3.1509700019023008e+146	-3.353618392490091e+143	-3.39118563700077e+143

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	40
1	55	40
2	55	40
done	55	40

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1650×	body	1280	valid
911.0ms	1409×	body	640	valid
665.0ms	4747×	body	80	valid
321.0ms	728×	body	320	valid
174.0ms	1644×	body	80	nan
101.0ms	331×	body	160	valid