Details

sample558.0ms

Algorithm

intervals

Results

313.0ms	47×	body	1280	valid
75.0ms	55×	body	640	valid
39.0ms	138×	body	80	valid
22.0ms	25×	body	320	valid
13.0ms	46×	body	80	nan
6.0ms	9×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	20	27
1	42	27
2	83	26
3	152	26
4	362	26
5	1681	26
done	5000	26

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.3b	(* x (/ 1.0 (tan B)))
5.3b	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite463.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`times-frac`
37×	`add-cube-cbrt` `*-un-lft-identity`
30×	`pow-unpow`
23×	`add-exp-log`
21×	`associate-r`
16×	`associate-l`
14×	`add-cbrt-cube`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
9×	`add-log-exp`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
7×	`pow1`
4×	`pow-neg` `div-exp` `cbrt-unprod` `div-inv` `sqr-pow`
3×	`neg-sub0` `pow-to-exp` `associate-*r/` `pow-exp` `sum-log` `pow-sub`
2×	`cbrt-undiv` `frac-times` `*-commutative`
1×	`tan-quot` `+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `flip3-+` `pow-prod-down` `associate-*l/` `associate-/r/` `un-div-inv` `flip-+`

Counts

4 → 140

Calls

4 calls:

71.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
40.0ms	(* x (/ 1.0 (tan B)))
259.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
80.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series949.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
176.0ms	(* x (/ 1.0 (tan B)))
470.0ms	(* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
267.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify2.7s

Counts

152 → 152

Iterations

Useful iterations: 2 (929.0ms)

Iter	Nodes	Cost
0	304	2706
1	909	2548
2	4311	2389
done	5000	2389

prune917.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x (/ 1.0 (tan B)))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite512.0ms

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:

19.0ms	(* x (/ 1.0 (tan B)))
241.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
129.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
119.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

145.0ms	(* x (/ 1.0 (tan B)))
300.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
525.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
195.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.8s

Counts

145 → 145

Iterations

Useful iterations: 2 (732.0ms)

Iter	Nodes	Cost
0	285	2554
1	810	2396
2	3319	2201
done	5000	2201

prune896.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.3b	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
0.3b	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
15.4b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

rewrite584.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt` `pow-unpow`
25×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
20×	`add-exp-log`
13×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
11×	`add-cbrt-cube`
9×	`add-log-exp`
7×	`unpow-prod-down` `associate-r`
6×	`prod-exp`
5×	`pow1` `pow-neg`
4×	`associate-*r/` `div-exp`
3×	`neg-sub0` `pow-to-exp` `associate-l` `pow-exp` `associate-/r*` `sum-log` `div-inv` `associate-/l/` `pow-sub` `unswap-sqr` `sqr-pow`
2×	`cbrt-undiv` `un-div-inv` `cbrt-unprod`
1×	`+-commutative` `neg-mul-1` `associate-+l+` `pow-pow` `frac-2neg` `flip3-+` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 113

Calls

4 calls:

74.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
276.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
140.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
86.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

series1.1s

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
287.0ms	(* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0))))
565.0ms	(/ (* F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))) (sin B))
213.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (- (/ 1.0 2.0)))

simplify1.8s

Counts

125 → 125

Iterations

Useful iterations: 2 (701.0ms)

Iter	Nodes	Cost
0	237	2444
1	711	2293
2	3222	2115
done	5002	2115

prune709.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* x 1.0) (tan B))
0.2b	(+ (+ (* F F) 2.0) (* 2.0 x))
0.3b	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
15.3b	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

171×	`times-frac`
96×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
39×	`unpow-prod-down`
26×	`associate-/l*`
20×	`add-exp-log`
14×	`add-cbrt-cube`
13×	`pow-unpow` `sqr-pow`
9×	`div-exp` `add-log-exp`
7×	`div-inv`
6×	`associate-/r*`
5×	`pow1` `cbrt-undiv`
3×	`sum-log`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`tan-quot` `+-commutative` `associate-+l+` `pow-pow` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `associate-/l/`

Counts

4 → 182

Calls

4 calls:

11.0ms	(/ (* x 1.0) (tan B))
37.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
173.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
88.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

series984.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(/ (* x 1.0) (tan B))
45.0ms	(+ (+ (* F F) 2.0) (* 2.0 x))
515.0ms	(/ (/ F (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))) (sin B))
237.0ms	(pow (+ (+ (* F F) 2.0) (* 2.0 x)) (/ 1.0 2.0))

simplify1.1s

Counts

194 → 194

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	423	5234
1	1134	5048
done	5000	4881

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes247.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.1b

bsearch550.0ms

Steps

Iters	Range		Point
7	3569.546420151095	319047.6340860353	312418.1274754623
10	-4.330524065673414e+42	-2.8022496391700208e+32	-4.284481847442339e+42

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	71
1	44	71
done	44	71

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.9s	1697×	body	1280	valid
2.0s	1376×	body	640	valid
1.5s	4760×	body	80	valid
1.4s	676×	body	320	valid
508.0ms	1604×	body	80	nan
201.0ms	371×	body	160	valid