Details

sample465.0ms

Algorithm

intervals

Results

81.0ms	58×	body	1280	valid
28.0ms	44×	body	640	valid
23.0ms	153×	body	80	valid
9.0ms	21×	body	320	valid
5.0ms	53×	body	80	nan
4.0ms	14×	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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.9b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite264.0ms

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))
18.0ms	(* x (/ 1.0 (tan B)))
174.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
60.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (tan B))
115.0ms	(* x (/ 1.0 (tan B)))
296.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
160.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify80.0ms

Counts

167 → 167

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	767	1428
1	3183	1338
2	5001	1337
done	5001	1337

prune648.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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))
0.2b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

69.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
19.0ms	(* x (/ 1.0 (tan B)))
160.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
51.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series810.0ms

Counts

4 → 12

Calls

4 calls:

350.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
112.0ms	(* x (/ 1.0 (tan B)))
207.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
142.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify84.0ms

Counts

145 → 145

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	721	1300
1	3143	1182
2	5002	1182
done	5002	1182

prune525.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
19.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
67.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
159.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
49.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series811.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (* x 1.0) (tan B))
352.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
202.0ms	(* F (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)))

simplify70.0ms

Counts

134 → 134

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	674	1245
1	2898	1127
2	5001	1127
done	5001	1127

prune490.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.3b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0)) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
19.2b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite333.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
28×	`prod-exp`
23×	`add-cbrt-cube`
22×	`add-sqr-sqrt`
18×	`div-exp`
17×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow-unpow` `times-frac`
10×	`pow-to-exp` `pow-exp`
7×	`unpow-prod-down` `associate-r`
6×	`cbrt-undiv` `cbrt-unprod`
5×	`pow1`
4×	`associate-/r*` `add-log-exp`
3×	`associate-l` `div-inv` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `associate-/l*`
1×	`tan-quot` `pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 107

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
160.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
112.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0)) (* (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))

series890.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (* x 1.0) (tan B))
257.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
377.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0)) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
139.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify80.0ms

Counts

119 → 119

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	693	1292
1	3286	1075
2	5001	1065
done	5001	1065

prune408.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes166.0ms

Accuracy

98.1% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.3b

bsearch298.0ms

Steps

Iters	Range		Point
9	1103.318926425695	30646363810.07727	60420.701327165734
8	-3.0722031062910235e+124	-7.0065691084106e+119	-1.8001637340014387e+124

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	54
1	89	54
2	94	54
3	94	54
done	94	54

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.7s	1720×	body	1280	valid
864.0ms	1353×	body	640	valid
656.0ms	4791×	body	80	valid
307.0ms	708×	body	320	valid
176.0ms	1727×	body	80	nan
94.0ms	329×	body	160	valid