Details

sample341.0ms

Algorithm

intervals

Results

96.0ms	161×	body	80	valid
73.0ms	49×	body	1280	valid
51.0ms	45×	body	640	valid
25.0ms	27×	body	320	valid
11.0ms	62×	body	80	nan
3.0ms	6×	body	160	valid

simplify2.4s

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
5.7b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite339.0ms

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))
28.0ms	(* x (/ 1.0 (tan B)))
217.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
82.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ 1.0 (tan B))
180.0ms	(* x (/ 1.0 (tan B)))
483.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
204.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.4s

Counts: 167 → 167

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

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	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(* x (/ 1.0 (tan B)))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite552.0ms

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:

139.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
268.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
21.0ms	(* x (/ 1.0 (tan B)))
114.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

579.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
341.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
160.0ms	(* x (/ 1.0 (tan B)))
246.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.3s

Counts: 145 → 145

prune805.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

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))
0.2b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
17.1b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite469.0ms

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:

15.0ms	(/ (* x 1.0) (tan B))
113.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
251.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
85.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (* x 1.0) (tan B))
570.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
343.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
238.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.2s

Counts: 134 → 134

prune731.0ms

Pruning

13 alts after pruning (13 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)) 0)) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.2b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
17.0b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite524.0ms

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))
158.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0)) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
282.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
68.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (* x 1.0) (tan B))
577.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) 0)) (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
784.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
204.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.2s

Counts: 119 → 119

prune498.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes330.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 11.0b

bsearch353.0ms

Steps

Iters	Range		Point
6	1.08747095259914e+85	7.092422111271889e+85	1.3703993603622044e+85
7	-15819646.165075496	-484708.3437711309	-2496357.5085318577

simplify470.0ms

end0.0ms

sample10.1s

Algorithm

intervals

Results

3.9s	1644×	body	1280	valid
2.4s	1388×	body	640	valid
1.9s	4817×	body	80	valid
693.0ms	725×	body	320	valid
383.0ms	1721×	body	80	nan
191.0ms	361×	body	160	valid