Details

sample583.0ms

Algorithm

intervals

Results

259.0ms	49×	body	1280	valid
78.0ms	162×	body	80	valid
61.0ms	45×	body	640	valid
20.0ms	22×	body	320	valid
15.0ms	58×	body	80	nan
9.0ms	16×	body	160	valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	151	26
4	345	26
5	876	26
6	3195	26
done	5000	26

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
6.3b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
14.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite422.0ms

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))
34.0ms	(* x (/ 1.0 (tan B)))
298.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
76.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series896.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (tan B))
161.0ms	(* x (/ 1.0 (tan B)))
447.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
219.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.7s

Counts

167 → 167

Iterations

Useful iterations: 2 (620.0ms)

Iter	Nodes	Cost
0	306	2742
1	747	2573
2	2039	2415
done	5000	2415

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
14.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

290.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
77.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
34.0ms	(* x (/ 1.0 (tan B)))
86.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

468.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
511.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
165.0ms	(* x (/ 1.0 (tan B)))
165.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.7s

Counts

120 → 120

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	265	2158
1	644	2039
2	1970	1853
done	5001	1841

prune674.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 1.0 x) (tan B))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
14.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

23.0ms	(/ (* 1.0 x) (tan B))
251.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
104.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
77.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (* 1.0 x) (tan B))
333.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
492.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
221.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.1s

Counts

109 → 109

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	250	2060
1	601	1951
2	1943	1765
done	5000	1753

prune521.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
0.2b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(/ 1.0 (/ (tan B) x))
14.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite462.0ms

Algorithm

rewrite-expression-head

Rules

87×	`times-frac`
64×	`add-sqr-sqrt`
59×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-/r*`
13×	`pow-unpow`
7×	`unpow-prod-down` `div-exp` `associate-r` `div-inv`
6×	`prod-exp` `associate-/l*`
5×	`pow1` `cbrt-undiv`
4×	`add-log-exp`
3×	`pow-to-exp` `associate-l` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`pow-pow` `associate-/r/` `*-commutative`

Counts

4 → 145

Calls

4 calls:

239.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
85.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
19.0ms	(/ 1.0 (/ (tan B) x))
112.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

420.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
498.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
145.0ms	(/ 1.0 (/ (tan B) x))
219.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify2.0s

Counts

157 → 157

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	343	2830
1	788	2657
2	2463	2465
done	5000	2451

prune917.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes275.0ms

Accuracy

95.1% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 10.9b

bsearch584.0ms

Steps

Iters	Range		Point
9	1.333194511359792e-15	1.61241819481061e-09	1.594018864811414e-09
9	-3.852270064556066e+38	-3.1641101034949086e+31	-1.9160350797409808e+33

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	73
1	41	73
done	41	73

end0.0ms

sample9.7s

Algorithm

intervals

Results

4.4s	1594×	body	1280	valid
2.0s	1429×	body	640	valid
1.3s	4814×	body	80	valid
681.0ms	700×	body	320	valid
496.0ms	1618×	body	80	nan
233.0ms	334×	body	160	valid