Details

sample637.0ms

Algorithm

intervals

Results

336.0ms	51×	body	1280	valid
68.0ms	48×	body	640	valid
52.0ms	152×	body	80	valid
17.0ms	15×	body	320	valid
9.0ms	37×	body	80	nan
8.0ms	10×	body	160	valid

simplify2.4s

Counts: 1 → 1

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.9b

localize93.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.2b	(* x (/ 1.0 (tan B)))
6.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite432.0ms

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:

9.0ms	(/ 1.0 (tan B))
21.0ms	(* x (/ 1.0 (tan B)))
299.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
95.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series827.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ 1.0 (tan B))
150.0ms	(* x (/ 1.0 (tan B)))
404.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
211.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.3s

Counts: 167 → 167

prune960.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin B))
0.6b	(cbrt (sin B))
3.1b	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite385.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
42×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
22×	`associate-l`
18×	`add-exp-log` `cbrt-prod`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`unpow-prod-down` `unswap-sqr`
8×	`add-cbrt-cube`
7×	`associate-r`
6×	`prod-exp`
5×	`pow1` `sqr-pow`
4×	`pow-neg` `add-log-exp`
3×	`neg-sub0` `pow-to-exp` `div-exp` `pow-exp` `div-inv` `pow-sub`
2×	`frac-times` `pow1/3` `associate-*r/` `cbrt-unprod`
1×	`cbrt-undiv` `neg-mul-1` `pow-pow` `associate-l/` `un-div-inv` `-commutative`

Counts

4 → 128

Calls

4 calls:

2.0ms	(cbrt (sin B))
3.0ms	(cbrt (sin B))
299.0ms	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
75.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series974.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (sin B))
146.0ms	(cbrt (sin B))
479.0ms	(* (/ F (cbrt (sin B))) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
195.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify980.0ms

Counts: 140 → 140

prune965.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
6.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite404.0ms

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:

16.0ms	(/ (* x 1.0) (tan B))
6.0ms	(/ F (sin B))
262.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
110.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series909.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ (* x 1.0) (tan B))
72.0ms	(/ F (sin B))
411.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
253.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.2s

Counts: 155 → 155

prune937.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ F (sin B))
6.6b	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.7b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite277.0ms

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:

22.0ms	(/ (* x 1.0) (tan B))
11.0ms	(/ F (sin B))
163.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
62.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

635.0ms	(/ (* x 1.0) (tan B))
92.0ms	(/ F (sin B))
468.0ms	(/ (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
222.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.5s

Counts: 218 → 218

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes310.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 11.8b

bsearch653.0ms

Steps

Iters	Range		Point
11	9.573845907245406	1.6755873679111776e+21	2173295.4413889716
9	-9.082619704937706e+32	-5.206915496164732e+24	-5.875481726059853e+25

simplify1.4s

end0.0ms

sample10.2s

Algorithm

intervals

Results

4.4s	1686×	body	1280	valid
1.9s	1413×	body	640	valid
1.5s	4733×	body	80	valid
906.0ms	1589×	body	80	nan
576.0ms	653×	body	320	valid
267.0ms	341×	body	160	valid