Details

sample455.0ms

Algorithm

intervals

Results

51.0ms	52×	body	1280	valid
49.0ms	42×	body	640	valid
23.0ms	156×	body	80	valid
9.0ms	20×	body	320	valid
5.0ms	50×	body	80	nan
4.0ms	14×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 2 (18.0ms)

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))
7.2b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite255.0ms

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))
17.0ms	(* x (/ 1.0 (tan B)))
171.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
55.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (tan B))
114.0ms	(* x (/ 1.0 (tan B)))
289.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
155.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.0s

Counts

167 → 167

Iterations

Useful iterations: 2 (375.0ms)

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

prune633.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite270.0ms

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:

17.0ms	(* x (/ 1.0 (tan B)))
47.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
155.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
47.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series809.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* x (/ 1.0 (tan B)))
310.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
255.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
132.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify993.0ms

Counts

120 → 120

Iterations

Useful iterations: done (990.0ms)

Iter	Nodes	Cost
0	265	2158
1	644	2039
2	1974	1853
done	5001	1841

prune434.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.3b	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite261.0ms

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:

10.0ms	(/ (* x 1.0) (tan B))
47.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
154.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
47.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series813.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(/ (* x 1.0) (tan B))
308.0ms	(/ F (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
250.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
136.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify996.0ms

Counts

109 → 109

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	250	2060
1	601	1951
2	1936	1765
done	5000	1753

prune380.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
0.3b	(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
0.3b	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
18.6b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

245.0ms	(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
90.0ms	(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
154.0ms	(* (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))

series1.5s

Counts

4 → 12

Calls

4 calls:

312.0ms	(* F (/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))))
764.0ms	(/ 1 (* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))))
250.0ms	(* (sin B) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0)))
137.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	250	2973
1	616	2706
2	1794	2416
done	5000	2394

prune359.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

98.3% (0.2b remaining)

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

bsearch281.0ms

Steps

Iters	Range		Point
10	1.7678340640407463e-12	1126179.5725289274	678669.4676816912
8	-2.508529027316973e+152	-5.0947934852509e+147	-5.192214669414231e+147

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	75
1	44	75
done	44	75

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.8s	1673×	body	1280	valid
864.0ms	1364×	body	640	valid
635.0ms	4733×	body	80	valid
298.0ms	709×	body	320	valid
165.0ms	1641×	body	80	nan
97.0ms	350×	body	160	valid