Details

sample475.0ms

Algorithm

intervals

Results

161.0ms	49×	body	1280	valid
64.0ms	45×	body	640	valid
48.0ms	162×	body	80	valid
20.0ms	22×	body	320	valid
15.0ms	58×	body	80	nan
9.0ms	16×	body	160	valid

simplify175.0ms

Counts: 1 → 1

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.7b

localize79.0ms

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)))

rewrite478.0ms

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:

13.0ms	(/ 1.0 (tan B))
40.0ms	(* x (/ 1.0 (tan B)))
338.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
79.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series958.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/ 1.0 (tan B))
163.0ms	(* x (/ 1.0 (tan B)))
508.0ms	(* (/ 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)))

simplify79.0ms

Counts: 167 → 167

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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))

rewrite434.0ms

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:

236.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
82.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
29.0ms	(* x (/ 1.0 (tan B)))
83.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

403.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
493.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
193.0ms	(* x (/ 1.0 (tan B)))
219.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify91.0ms

Counts: 120 → 120

prune699.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (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))

rewrite393.0ms

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:

15.0ms	(/ (* x 1.0) (tan B))
232.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
64.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
79.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ (* x 1.0) (tan B))
371.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
474.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
196.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify84.0ms

Counts: 109 → 109

prune577.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

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

rewrite454.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
41×	`add-exp-log`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-cbrt-cube`
16×	`div-exp`
13×	`pow-unpow`
9×	`prod-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `unpow-prod-down` `associate-r` `div-inv`
6×	`pow1` `associate-/l*`
4×	`add-log-exp`
3×	`pow-to-exp` `rec-exp` `1-exp` `associate-l` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-/r/` `*-commutative` `inv-pow`

Counts

4 → 131

Calls

4 calls:

291.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
65.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
28.0ms	(/ 1 (/ (tan B) (* x 1.0)))
62.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

399.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
466.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
176.0ms	(/ 1 (/ (tan B) (* x 1.0)))
238.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify100.0ms

Counts: 143 → 143

prune753.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes253.0ms

Accuracy

95.1% (0.5b remaining)

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

bsearch1.0s

Steps

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

simplify51.0ms

end0.0ms

sample9.4s

Algorithm

intervals

Results

3.5s	1594×	body	1280	valid
2.0s	1429×	body	640	valid
1.4s	4814×	body	80	valid
1.1s	1618×	body	80	nan
572.0ms	700×	body	320	valid
216.0ms	334×	body	160	valid